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CLAUDII PTOLEMAE(BOPERA aUAE EXSTANT OMNIA
VOLUMEN I.
SYNTAXIS MATHEMATICA
EDIDIT
J. L. HEIBERG,PBOFESSOR HAUNIENSIS.
PARS I
LIBROS I VI CONTINENS.
LIPSIAEIN AEDIBUS B. G. TEUBNERL
MDCCCLXXXXVIII.
PA/4-H-OH"
ft*
LIPSIAE : TYPIS B. G. TEUBNEEI
PRAEFATIO.
Ad Ptolemaeum edendum adcessi aBibliopola hone-stissimo rogatus, nee inuitus obsecutus sum, cum id
maxime opus esse uiderem, quod praestare me posse puta-
bam, ut codicibus denuo collatis aestimatisque fundamen-
tum quoddam recensionis iaceretur. nam editio princepsSyntaxis (Basileae 1538), ut mos erat illorum temporum,uno nee eo bono codice nititur, et Halma, abbas Pari-
sinus, qui delude solus Graecam editionem curauit (Parisiis
1813sqq.) hodie rarissimam, ut optimum codicem Parisi-
num adhibuit, ita neque negotii critici neque sermonis
Graeci satis peritus fuit. mihi igitur incipiendum erat a
codicibus conquirendis, inspiciendis, conferendis, ubi opusesse uisum erat. quern laborem ut per annos 1893 et
1894 profligare possem, effectum est ope et liberalitate
summi Ministerii, quod cultui scholisque Daniae
praeest, maximeque Instituti Carlsbergici, bonarumavtium in rebus angustis adminiculi locupletissimi ,
cuius
praesidibus hoc loco ex animi sententia maximas ago gratias.
Inspectis examinatisque codicibus, qui quidem innotuis-
sent, omnibus, de quibus in Prolegomenis partis\ poste-
rioris agam, hos elegi ut recensioni et utiles et sufficientes:
A codex Parisinus Graecus 2389, membranaceus in
folio, litteris uncialibus binis columnis scriptus s. IX
(u. Omont, Inventaire II p. 251), charactere, ut Henrico
Omont uidetur, Aegyptio. constat foliis 376, quorumprimum ad extremum libruni XIII pertinet et paenedetritum est, foil. 207210, 255 270, 374 375
IV PRAEFATIO.
suppleta sunt s. XV (a); post fol. 68 quattuor folia
desunt (u. p. 200, 7 et p. 209, 21), ut ex quaternionumratione colligitur. scriptus est codex omnium praestan-tissimus duabus manibus eiusdem temporis, quarum una
(A sine A2
) atramento rauo, altera (A1
) badio utiturj
A1, quae a fol. 175 (p. 487, 17) incipit, sed iam in
priore parte nonnulla correxit, litteras inclinatiores habet,i adscriptum interdum ab A2
semper fere omittit, ad-
centus uero spiritusque plures adponit quam A2, spe-
cimen exstat apud Omont Facsimiles des plus anciens
Manuscrits Grecs en onciale et en minuscule de la Biblio-
theque Nationale tab. IX. correctiones paucae manibus
recentiori (A3
)et recentissimae (A
4,
s. XVI) debentur.
contuli ipse Parisiis 1893. spiritus adcentusque hie ut
semper in adparatu neglexi.B - - codex Uaticanus Graecus 1594, membranaceus in
folio s. IX, quo nullum pulchriorem elegantioremque
unquam uidi. constat foliis 284, sed olim plura habuit^nam fol. 284V legitur: j\ fitfikog amy rrjg peydKrig 6vv-
rd^ecog k'%i cpvkXcc TIE nctl dvo slg tr^v (XQ%r}v rov fiifiXlov
aTtokvTK. post fol. 65 unum folium excidit, cui manusrecens s XV duo substituit (u. p. 224, 14 et p. 228, 20).eontin codex: fol. 1 8 Prolegomena anonyma adPtole-
maeum. fol. 9 263 Ptolemaei Syntaxin cum scholiis,
fol. 264 272 r Ptolemaeum de apparentiis, fol. 272V
276 Pt^lemaeum Ttegl x^tr^^tov, fol. 277r tabulam cate-
goriarum (fol. 277V uacat), fol. 278 283r Ptolemaei
hypotheses, fol. 283V 284 notasuarias. inde a folio 271V
extreme duabus columnis uti desinit. - -inuestigaui
ipse et, quoad potui, contuli Romae 1894. P. 232, 4
p. 546, 20 mea causa contulit loannes Tschiedel.C - codex Marcianus Graecus 313, membranaceus in folio
s. X, ab imperito librario pulcherrime scriptus non sine
compendiis maxime uersus finem. correctus est duabus
manibus recentioribus (C2
s. XIV XV) et una recen-
tissima (C3
,fortasse ipsius Halmae; nam fuit Parisiis
initio huius saeculi). continet: fol. 1 30r
Prolegomena
PRAEFATIO. V
ad Ptolemaeum ab initio mutila, fol. 30V 370 Ptole-
maei Syntaxin cum scholiis. ex archetype codicis Bdescriptus est. - - contuli ipse Uenetiis 1893.
D codex Uaticamis Graecus 180, membranaceus in
quarto s. XII, compluribus manibus eiusdem temporis
scriptus, saltim alio alibi calamo atramentoque, et dua-
bus minimum manibus antiquis (D2 D 3
),una recentiore
(D4)correctus. continet: fol. 1 2 notas quasdam astro-
nomicas a manu recenti, fol. 3 280r Ptolemaei Syn-taxin cum scholiis, fol. 280V notas uarias manuurn
recentium, in imo mg. opov gjiUAor a 8do(Jii]KOvrcc ema
(debuit computari 278). deriuatus est ab exemplari
optimo et uetustissimo, quod saepe cum codice A con-
sentiebat contra BC, saepe etiam solum ueram scriptu-
ram seruabat, sed ab hornine rerum perito audacter
interpolatum erat siue ipsum siue aliquod eius apo-
graphum; nam imperitis librariis codicis D interpola-
tiones illae adtribui minime possunt. quorum errores
incredibiles,
ex itacismo et ex compendiis male intel-
lectis plerumque ortos, saepe omisi, sed numquam nisi
monito lectore (u.ad p. 4, 3; 12, 20; 27, 2; 29, 23;
cfr. p. 40, 20). compendiorum usum significaui, quiaad aetatem genusque archetypi definienda uiflia sunt.
contuli ipse Romae 1893 94.
E - - codex Marcianus Graecus 310, chartdceus s. XV.continet: fol. 1 13 r
Prolegomena ad Ptolemaeum,fol. 13V 151 Ptolemaei Syntaxin cum scholiis (fol. 152
uacat), fol. 153 261 Theonis commentaria in Syntaxin
(fol. 262 264 uacant), fol. 265286 alia manu Ca-
basilae commentaria aliaque eius opera, fol. 287 288Barlaami quaedam. adcedit ad BC. inspexi paucislocis Uenetiis 1893.
F codex Parisinus Graecus 2390, bombycinus s. XIII,de quo u. Omont Inventaire II p. 251. arte cohaeret
cum BC. hie illic inspexi Parisiis 1893.
Horum codicum ope uerba Ptolemaei talia restitui
posse 'confido, qualia a uiris doctis Alexandriae anno cir-
VI PRAEFATIO.
citer 500 legerentur. interpretationibus commentariisqueArabum uti non potui, Latinis nolui. interpretationemmeam siue Latinam siue linguae recentioris in tanta rerum
difficultate addere ausus non sum; de ea re uideant astro-
nomi, si interpretationem desiderauerint.
In adparatu ad p. 227, 10 et p. 481, 15 pro Halma
reponendum ed. Basil, ad p. 522, 49 delendum <?'] // A1?;
nam etiam in A est $', ut ab Henrico Omont posteacertior factus sum. ad p. 539, 7 haec adnotatio addatur:
7. inrog] scripsi, Ivrog A1 BCD.In plagulis corrigendis opem peritam diligentemque
beneuolenter mihi praestitit Henricus Menge amicus.
Scr. Hauniae mense Maio MDCCCLXXXXVIII.
J. L. Heiberg.
KAATAIOT IITOAEMAIOT
MA<H)HMATIKHS
Ptolemaeus, ed. Heiberg.
A'.
Tads V6riv v TGJ jrpcjTtp r^g IIroA,[iciiov
a.
$' . 3t$i rrls rcc&as rcbv
y'. on <J<jpcctpOfcd\ 6 OVQCCVOQ
d'. cm xlij yij 6<pcuQOidris 6nv n$bs afafrqew cog
. on p6r] rov
$'. on 6r][iiov Adyov %ei icgos ra OVQKVLCC ij yij. 10
f. ort ovdc xivyGiv twee nBraftatLKriv noisltut,r\ yij.
if . on dvo dicupOQal T&V XQ&TCOV xivtfte&v i6iv iv
TfiJ OVQCIV&.
&'. 7t$l r&v Kara ptgos KccraA.r)t}>G)v.
i . 7tQl r?\<s Ttrjfa^Trjros tcbv v Ttp KVK&G) sv&ei&v. 15
W. XCCVOVIOV XG)V SV
ngo-A, v-^avSiov nrol8(jLaiov ^ctd-rj^KTiKfjs Gvvtd&cos fiiptiov
TIQ&XOV B, om. CD. 2 p. 4, 5. om. A. 2. rads] corr. exrdd' D 8
. TT^COTOT 3. avvrd&mg] a D. 4. a'] om. D, et
sic deinceps. fr/*cf$00f] D, 0WTa|fcog BC. 6. orqoatpoet^ws 6
ov^iavog] ccpttiQOSLSrjs 6 ovquvbg nod GcpaiQOSidobs fpsgsrui D.
7. jtat 8. /*^>7]] GcpuLQOi8'r]g v.a.1 i] yfj D. 10. |JUA} postras. 2 litt. B, 8^fi 17 yf) D. ra yrf} rbv OVQKVOV D. 11.
noisiTui iLtxafiKTwriv D, noisltKi corr. ex noifixui m. 1. 12.
ffotv] om. D. 15. xfjs srrj/ltxdrTjTog] om. D. rc5] om. B.16. ta'] al B, et similiter deinceps. xavdvtov ebfrsuov]
xal Eot-d'fCts xarortx^ D. KCCVOVIOV p. 4, 1. TCBQI] in ras.
m. 1 B.
4 KAATAIOT HTOAEMAIOT
ift'. 7tQi rrjs iiTct%v tibv
id'. 7tql rcbv fisra^v TOV
if
. xccvoviov Aojco<?0).
5 is'. TtSQi T&V in dQ&ijs rife 6<pcciQccs
a .
Ildvv xaA&s Oi yvrjGicas (pi%o6o(piJ6avTS) d) 2/up,tf /not x%a)()iXvai TO &coQrjTixbv Tils cptAotfogptag
aitb TOV TtgaxTiXOv. xccl ydg i &v^^x xal TW
10 TCQaXTlXG) 1tQOTQOV CiVTOV TOVTOV &O)Qr)Tt,X(p TVy%KVl,V,
ovdev fjTTov av Tis VQOt, iifydhrjv ov0ccv iv
OV [IOVOV did TO T&V [lV YJ^iXK)V
WvaG&ai rtoMots xccl %&QiS
Tijs $ Tfbv oAcw fa&Qias ddvvaTOV dvau rv^lv avzv
15 didaGxccMccS) AA xal TK> Trjv jtfaidTrjv cocpefaictv Xt
[lV X T^S V CCVTOiS TOiS 3lQdy[ia6i 6VV%OVS VQ-8' X TilS W TOiS
1. TteQKpSQBiag] corr. ex Treptqpf^tag D 3. 2. fo/^etg] corr.
ex Sethis D 3. 3. TOV] post ras. 3 litt. D. x-yx/Lov] corr. ex
Y.OV D 8. itEQicpfQti&v] corr. ex 7iQi(pfQLfbv D 3
;similes eiTores,
quibus scatet D, posthac non notabo. 4. uavoviovom. D. 5. KvatpoQ&v] TOV dice psccov ncci TOV
D (a supra scr. D 3). Seq. old' on &vr}Tog scpvv
KCtl S(pd[l8QOS' &M,' OTUV CC6TQCOV \ 1%VV(O Y.UTO. VOVV CC}lCpt.dQ6(lOVg'
sitnpava) yafyg TIOGLV,&Ma TCKQ' O.VT&I
\ r]vi
itlaiicu d/n^oatrjg CD (idem in mg. inf. B, sed6. a'~\ om. A, mg. B, -nJLavdtov 7tTote[iaLov iia&ir]-
, 7tTOlE[LClloV GVVTCcl$ D. 7tQOOi^,LOv] Om. A.8. x%co^r]>tfVat D, sed corr. 9. na (alt.)] del. D. 10.
TrpaxrtHw] corr. ex TIQCCKTMOV C 3. CCVTOV TOVTOV] mut. in
CIVTO TOVTO C 2. 14. cc8vvccTov\ corr. ex SVVCITOV A 3
. 16.
D. 18. nciQccyCvsGQ'cii, yi- in ras., D 3.
MA0HMATIKHS 2TNTABE&S A'. 5
tag [iV nga^eig iv rats ai)ro3V rcbv tpavratfiav iiti-
oit&s pyd' iv rots rv%ov6iv BTCI-
a rrjs ngbs rrjv xaAqv xal evraxrov xard-
') rtf de 6%oAfi %aQLt>e6%'cci rb jttettirov
noM&v xai KK^COV ovr&v 5
ds slg r^v rcbv tdicsg
[icc&rj[iccrMG)v. xal yap av xccl rb
6 'AQiGrordKris Jtdvv fftftfAcog Big ryCa, ra itQ&ra ysvrj
dicuQst r6 re <pv6i,xbv xccl rb iia&r}[iarixbv xccl rb ftso-
hoyixov. Ttdvrov yap rcov '6vrov rr\v vitccQ%iv fyovrcw 10
sx re vlris xccl effiovs xccl xwt]6eG)s %coQlg per exddrov
rovr&v xccra rb {jxoxeipevov fteaQetd&cu pr} dwccpevov,
voelGftcti de povov., xccl ccvev r&v Aotjrrav, rb [lev rr^g
r&v oAcdv TtQcbryg xwtJGe&s rtg&rov ccl'riov, el' rig xccra
rb ccitAovv ^xAaiiftdvoi,) &ebv d6^arov xal axiwiyrov av 15
fjyiJGairo xal rb rovrov fyjvrjTixbv eldog fteokoyiKov
area nov negl ra pere&Qorara rov x66{iov rj]g roiavrrj$
vorj&efarjs av povov xal xa&dita% xe^oQi&^e-
r&v afa&rjrav ovGicbv rb de rijg tifoxris xal atel
itoioryrog dieQevvrjnxbv eldo$ itegi re rb 20
Aevxbv xal rb ftegiibv xal rb ykvKv xccl rb ccTtahbv
xal ra roiavra xarayi/
yv6^tevov (pvtiixbv av xcckdtieie
rr\g roiccvrrig ovtiiag ev rots tp&agrots cos snl tb itohv
xal V7toxdro3 rijg G^yviaxiis 6<pcciQK$ dva6rQ(poiievrjs'
rb $ rr^g xccra ra d'drj xal ras perafiarixas xivriGeig 25
2. indctv&ccvcopEQ'u] snda\ fruvaiieofa* A, v add. A 2
. 3.
Tijc] corr. ex xr\ D 3. 4. An rr)g ^8 a^o^g? cfr. Boll, Studien
viber Cl. Ptolemaus p. 68 not. 3. 8. 'AQLCXOTE^S] Metaph. E 1;
cfr. Boll p. 71. 9. re] om. D. jtta^Ttxdv D, corr. D 2.
15. Klcc[ipdvi D, corr. D 2. KV.LVT]XOV xal CCOQCCTOV D. 17.
ufTfto^toTaTa C, sed corr. 19. afoi'] &fi CD. 20. TB\ om. D.22. tiKTccyivo^fvov C et corr. ex naTayivofitvaiv D. 23. Ante
tTfc del. s" D. 24. xai] om. D.
6 KAATAIOT HTOAEMAIOT
jtoiorytog [i(pavi,6nxbv sidog 6%ijiiKt6g rs xccl
rrjros xal 7trjA,ix6rr]ros en TE roitov xal %$6vov xocl
rcbv b^iOLCDV fyrynxov vndg^ov dtg iia&rjiianxbv civ
K<pOQi6Ei rils roLccvrys ovGfas HETCC^V &6itSQ EKEIVGW
5 rcbv dvo TtinrovGrjS ov povov r& xccl di afad"iJ6Ci)g
ftri<5G) dvvaG&ui voft^at, aM.K xal r&
rols ovtii tivppefit]xevtb KK\ ftvyrots xal
rots V&v afel pBtufittM<ov6i Kara TO sldog
rb Ki&QiGrov 6viJi[iei;a(laM,oiievriv, rots ds uidioi$ xal
10 i% cct&Q(bdovs (pvcte&s GwtrjQOvGccv axivyTov rb rov
si'dovg c^isrK^rjrov. % d>v diavori&Bvres, on r& psv
dvo ysvy rov ftscoQrjnxov paMov KV n<s
Ttt^rrj^oviKrjv sfaoi, rb {LEV
dia rb 3tavrsA.K>s oupavss avrov xal avsTtttrjTtrov ,rb
15 ds <pv6ixbv dia rb rrjs vAqs atirarov xal
dia rovro iiqdEitore av iKitfaui TtEQi avr&v
rovs cpihoGocpovvTaS) povov d rb iia&rjiiccnxoV) el' ng
%era6nxG)s avrtp 7tQo6EQ%oiTO, ^Kiav xal a
rotg iieitt%siQi,oiivois tyv fi'drjGi
20 rrls ajtodffef&s 8i>' ccva^i^^r^rov od&v
xara vvcc[ii,v r]s roiavrrjs
7t()l XGi &ttt Xtt.1 OVQKVICC
rccvrrjs 7tgl rfjv r&v aiel
25 xa
3. HK&rjiiamov B. 5. 81,'] 810. BC. 8. rots] suprascr. D 3
. octet] A, &et BCD. [u-zapdUovcl A. TO elSos]
mg. add. D 3. 9. Se] S' D. 13. efaoi] corr. ex efasv D.
14. Ttavxtk&g] -06- in ras. B. nut] ncti 8C C. ccvsni^riTttov]a- in ras. 2 litt. C, post -rj- ras. 2 litt. D. 16. ^dsnor' D.
18. ccfifrccTiLarov] mut. in apsraneiGTov D 3. 19. Mg. y$.
Gvvidi6Lv D 2. 20. yivofievn? CD. 22. iidJLiara] supra
scr. D 3. 24. alst] A, &et BCD. aiel V.KI ma-] in ras. D 3
.
MA0HMATIKH2 STNTABE&S A'.
rovr6 re dvvarrjg ovGrjs xal avrijg itgl psv rr\v
oixeCav xardArjifrw ovts adyhov ovrs draxrov ovdav
atei xal cadavrcog fysw, ojto 6rlv I'diov fjutfrifp??,
itgbg $ rag aMag ov% tfrrov avr&v dxuv&v Gwegyetv.ro re yaQ fteokoyiKov eldog avxr] ^dh6r' av jtQoodo- 5
axivijrov xal %a)QL6rils VQyiccs djcb r
rcav it()l rag afa&rjtccs pv xal xivovtiag t xal xivov-
aidiovg df xal aTtaftfig ovGiag 6v^^x6r(Dvi t rag tpogag xal rag rd&ig r&v xt,vrj6G)v' itgog 10
r rb (pvGixov ov rb ivyjbv av GviifidMoiro' 6%$bv
yag rb xaO-oAou rijg vfaxijg ovGiag i'diov anb rijg xard
rv\v iifrafiarixrjv XLV^LV tdiorgoytiag xarayatvfrai,
<og rb pv tp&agrbv avrb xal rb acp&agrov aitb ryg
v&i'ag xal rr^g fyxvxMov, rb $ flagy xal rb xovtpov 15
^ rb itu&rirLxbv xal rb noirjrixbv dnb rrjg iitl rb [i6ov
xal ri\g ditb rov p&ov. TtQog y /LM)V rqv xara rag
xal rb rj&og xakoxaya&iav Ttdvrcov av avrrj
dioganxovg xara6xvd<jiv aitb ri\g itQ\ ra
G)QOVfivr]g oftotdr^rog xal fvra&ag xal 6vp- 20
xal arvyiag fyatirag plv noiovtia rovg
xoAov&ovvrag rov &LOV rovrov xdMovg,81 xal &6itQ tpvGiovGa Jtgbg rtfv bpoiav rr\g
xara6ra6iv.
rovrov dy xal avrol rbv Ho&ra rrjg rcbv aid xal 25
fotiavrcog tyovr&v &G)aiag xard rb 0vv%sg av&iv
1. Tt] corr. ex 8 D. rifv] mut. in TOLV C. 3. ccki] AB,afi CD. Post Y.KL del. cb(j{ D. 7. ^oo^tar^g] corr. ex %COQIS
TI~]$ C 2. 8. Tf] supra ras. 3 litt. D 3
. 11. ro qpvfftxov] corr.
ex T&V (pv6i*.a)v C. 14. avrd] -6 e corr. D 3. 15.
in f-v&efas D. 16. ano] corrigere uoluit C 2. 18.
in ras. D 3. 19. ite^i ra] bis C. 25. ccsi D. 26.
pr. v ins. A 2.
8 KAATAIOT HTOAEMAIOT
TtsiQcjps&a iiav&dvovrfg [ilv ret ijdq xart,^rj^va r&v
rotovrcov [iad"T][idrG)v vjtb r&v yvr}6(X)$ xal fyrrjnx&s
avrotg 3tQo6sA.&6vTG)v , 7tQoat,QOV[ivoi ds xal avrol
roGavrfjV TCQOti&riXriV 6VVl6V'yXtV 5 00r]V 6%$bv 6
5 JtQoGys'yovcos an sxsivcw %QOVOS p%Qi tov xa&' rtficcs
dvvaw' av TtegiitoiYiGai. xal o6a ye dr} vo^o^isv in\
rov jtagovTOs sis <p&S Wtv cA^Av^fVat, TCeiQciGoiifd'a
8ia PQCC%G)V &s BVI iidAiGra, xal &s av 01 r^dri xal
ejtl Jtotibv 7tQOXXO(p6rS dvvccwto TtaQaxoAovd'flv, VTCO-
10 iivrjiiarfaae&at, rov [iv rsfoiov ri}g 7tQay[iari
aTcavra ra ^^L^a itgbs rrjv r&v ovgavicwKara, r^v oiKefav ra^iv xn,&iivot,, dia $ rb p
7toiiv rbv Aoyov ra plv vnb r&v nahaicbv
a di(>%6nvoi ii6vov, ra $r) nqd* oAog xara-
15 Arjy&wra ij ^ &s vrjv v%Qifi6rG)$, ravra df xara
IIspl rrjs rd$(os rCov &&()r][idra)v.
ij ttQOxeipwrjs ^Iv Gvvrd&cos TtQorjytirai (iVrb XY\V xaO-oAov 6%B6iv Idelv o^rjs rqs yifc agog
20 rbv ovgavov, r&v de xara IIZ'QOS qdr] xal *(p%ijs
rov [iv avsi'rj
rb dtf&hfalv rbv K6yov rbv itSQi rijg
&<5G)S rov Ao|ot> xvxAov xal r&v rdit&v rfjs xa&
otxovpfvrjs n re rijs itQbs aMtjAovs avr&v
xa6rov oQi&vra naga rag
1. xtrmfoj/u, | privet C. 2. pccftrifLdTcov] -[id- supra scr. D 3.
3. itQOsl&ovtaiv C. 5. nQOCysyovrng] BD, nqoysyovms AC.8. ^ga%ifov\ corr. ex XCL%(QV D 3
. 9. Mg. itQOGxsyivcpOTfs C 8.
11. ra] ins. D 3. 14. ij] supra_scr.
D 3. olog C. 15. $e]
del. C 2. 17.
fi']om. CD, x<p. ^ D 2
. 18. Srf\ Si C. 19.
TO] seq. ras. 1 litt. D. 23. hi re] eha D. 24.
-x/li- in ras. D.
MA0HMATIKHS 2TNTAEE&S A'.
sv rats rd%6iv diatpogag'
rovr&v fi-scoQicc r^v r&v koiit&v InfaKstyw evodars-
$av itciQfyei' dfvrsQOv ds nsgl ryg ^Amjcife xiviJ6G)g
xal iris GeArjviax'fjs xal rav ravraig itt,6v{i(lcuv6vtG)v
dlt&H&ftV %&Qlg yap ryg rovrcw 3tQoxataA.tjil>G)s 5
ovds ra Ttegl rovg aGrsgas ol6v rs av yevoiro dts^o-
dixGJs ^scoQrlGca. rsAevraiov d' ovros &S ^905 ccvryv
r^v b'yodov TOV nsgl r&v KGregov AoyovKV sMr&s xal SVTCCV&CC ra rtsgl t^g r&v
(StpKiQag, sitoito ds ra Ttsgl T&V Jtevrs 10
f'xccGra ds rovt&v
[ISV XCll
fig rrjv avsvQ0iv %Q(&[ivoi, rolg
xal rccZg adiGTKXTOig t&v rs jtcdcu&v xal r&v
rag d' q>sijg r&v Karahtffa&v <pagii6- 15
a rcov iv ratg
rb [iv ovv xaftoAov roiovrov av
ori, r 6cpai,QOt,drig i^nv 6 ovgavbg nal yegsrai
)xai on ^ yv\ rca pv 6%rjiian xccl avrrj 6(pai,-
6rw agog afaftyGiv &g xa&' oAa pfQr} happa- 20
rr] ds &s6st, [i6rj rov Ttavrbg OVQKVOVre* $ yLsysfi'Si xal r&
%st, ngbg rr\v rcov
a<frQG)v Gcpatgav avrrj
1. ra&Gi BD. 2. svoScaT^av'] svo- e corr. D. 3.
rb TtfQt A. xivrjfffcos xat rfjg Of/lrjviaxryg] v-ul fff^rjvtax^g6(og D. 6. re] x
3
D. 7. $'] Ss D. 8. nQordcoiTO D.12. nfLQttGoiLS&cc] corr. ex TcsiQKGwine&a A 2
. 13. ivuqysGiv D,y e corr. Deinde add. xca comp. D 3
. 14. Ante re del.
nev C 2. 15. rj]QLGB(ov C, corr. C 2
. *'] Si D. 19. rco\corr. ex ro C 2
. 20. sen B. Icc^avofisvriL C. 24. ccvrij]
ccvrr) EC.
10 KAATAIOT HTOAEMAIOT
noiovpf'vexev
rovrov <T exaGrov
y'.f
'Ori GcpaiQOSLd&s 6 ovgccvbg
Tag [iev ovv TtQ&rccg evvoiccg vtegi rovrcov coco
5 roiavrrjg rwbg TtaQarqQrjtfecos rolg JtaAcuoZs evAoyov
TtccQccyeyovevai,' S&QWV yag rov re %\kiQv xal r^v
nal toi>s d'AAovg aGtegas cpegopsvovs aito
iiti dv6^ag aisl xara
xal C(.Q%OILVOV$ plv10 onto rov raneivov xal &671EQ
J
| avrijs
QI&IISVOVS $ Kara IMXQOV els v^og, STtsiTa
xara rb uvaAoyov HQiQXO(ir
vovs re xal ev raiteivcc)-
ccv reAeov &67teQ fyrtfGovres el$
sir
15 peivccvras ev r& KcpuviGyiG) &67teQ cat
KvarfAAovrccs re xal dvvovrccs, rovg de XQOVOVS rov-
rovs xal k'xi rovs r&v avaroAcbv ncti dv0cov rojfovg
re KOI ofioiog tbg tniitav avrccnodido-
20 fiaAttfra de ccvrovg yyev efe rrjv 6tpttiQi,xr}v evvotav
fj rfov alel yaveQcbv a6rQ&v neQiGrgoyxccl jtegl xevrgov ev xal rb ccvrb
aroAog yag avayxuios exelvo rb
1. ^'] ^' D. 2. TtQodielisvGotie&cc D. 3. y'] B, om.
ACD, Xfqp. y D 2. GCpttiQOSlS&S 6 OVQKVOg] 6CpCClQOLdi]$ 6
OVQCCVOS Hal 6CpaLQOlS(Q$ D. 7. CpSQOflEVOVs] (fKCVO^SVOVg BC,corr. C a
. 8. &ei D. 13. yivopsvovg D. smg] o>s BC,corr. C 2
. coffee] ^GTCSQ ndliv D. 14. ndhv] n- e corr. A,om. D. 15. [LSLvavteg D, corr. D 3
. SIGTISQ] itaJkiv WCTCSQ D.16. 8] d- in ras. A. 17. Svascov] dvGfi&v D, supra (i ras.
18. cog] om. D, xca to? supra scr. D 3. 20. Ss] 8* D. 21.
ItSi CD. CCGTQfOV D.
MA0HMATIKH2 STNTABE&S A'. 11
eyivsro rqg OVQKVIOV GtpaiQccg r&v [iv pccMov ccvr&
itgbg rqv rrjg
xvxAovg v rfi TtSQiyQatpri itoiovvr&v, fcog av
rj <x7to6Tcc6i,g xal ft^()t r&v cupavi^oyievGiv tpfrdGr}) xal 5
rovrcov ds ra per syyvg t&v ctlel qjavsgav
G)Q&v iit bUyov %QOVOV v x& cupaviGpKt
ra d' ano&ev avcdoycog jtdhv jtl nfaiovcf
fiv KQ%YIV dia inova ra roiavrcc ttyv JtQO
SVVOIKV ccvrovg AccfaZv, r^dri dl Kara TT\V (p%fig &&- 10
xccl ta hoiita tovtoig Kxohov&cc xccravoiiGcci
catAcbg r&v (pccwo[iVG)v ratg TQodo%oig iv-
voicug avriiiaQTVQOvvt&v.
cpQ yccQ, i rig vjrdOwro rr^v x&v atiTSQ&v tpogav
it v&iag ywoyLBvviv rt' aitiQOv (pQ60-cc^ xa&dttQ 15
ndiv 'do%v, rug ctv zmvori&GCri TQoitog, xcc& ov ditb
', 3iK><$ y&Q dvKxdujtruv edvvaro T<X CC
lit axt,Qov 60/w.o>^i>a; rj n&g dvccxd^ytroyrK OVK
', rj jtcbg ovyl XKT;' bkiyov ineiovyievwv rcbv ^ye- 20
avrolg rolg d(pavi6[iolg,
xccl &63t
Ma p,r\v xal rb dvd7tr6&a r avrd x ri\g
xal Ttdfav fig ravryv ttTCoGfisvvvG&cu, r&v d^oyo- 25
rdrcov av (pccvftrj itccvrfhcbg. LVCC ydg rig
3. ds
] Ss D. aTrcoTepco] tincozEQcot, AC, KHOTEQCIJI B,
ccno)TQa> D 3. 6. asl CD. 8. <T] mut. in ds D 2
. anaj&sv D 3.
14. KGTZQOJV] corr. ex >QCOV D 2. 16. s^o|f D. 18. sdvvaro]
s- in ras. A, fidvvccro D. 22. xara] corr. ex v.u A 2. 24. aHa
pT]v xat] in ras. D. 25. ravrrjv] avr^v D. cdoyorccTOiv B.
12 KAATAIOT nTOAEMAIOT
rrjv ro6avrr]v rd^iv Iv re rots iiy&6w xal reels
3to06rr]6i,v avr&v^ n ds dia6rrj[ia6i,v xal ronois xal
%QOVOIS OVT&S sfaf} xal cos rv%v cutorefatedai,xal
rods pv rtav TO ^iOOs rrjs yfjs avaitrwriv %iv yvtiLv,
5 r6de df 6fte0ri,xtjv^ fitUAov ds rb avrb rots psv avdx-
rsiv, rots ds Gpsvvvvcct,, xal r&v a6roa)v ra avra
rots 1*>V r^dri avrjiifieva rj sGpsGiisvcc rwy%aviv, roig
ds ^dfjccj, el' riS) WP^ ravrcc xdvrcc 6vy%G)Qij0i,ev
ovrcos ovrcc ysAoTtt) ri wv jtSQi rcov aiel (pccveg&v
10 Sftoijisv siTtsZv r&v iiijrs avccreMdvrcov ^itjrs dvvovr&v;
rjdi Ttoiav alriccv ov%i ra psr dvanro^isva xctl Gfisv-
vvpeva Jtccvra%fi xal avarshfai, xal dvvsi, ra $ [if}
3td6%ovTK rovro itavrcc^i] 6nv atel vnlo yijg; ov
8^ y ret avra rots y&v akl avaq)%"Yi6rai KOI
15 Gfrat,, rots $ ovdw ovdJtor rovr&v Ttutizrai, Ttavrd-
vaoyovs ovros rov rovs avrovs u
T xal
xccv bjfotov Ti
20 rrjs t&v ovgavtcov fpooas V7t6%"rirai TtMjv rov 6<pat,-
QOfidovS) avfaovs avdyxq yiyvtG&ui rag anb rils yrjs
till ra iLQrj r&v ^rG)QG)v a7to6rd0iSi ovtov av avrrj
xal cos &v vrtoxfyrai,) cadre Qytiteiv xal ra r ^a^fO1
^xal ra nobs AA?JAov dia&r^ara rtov adrfocw avi6a
2. 8ictGxrin,ctGi C. 3. ut$] slv.- in ras. D. 4. i'^ftv] corr.
ex %ei B 1. 8. GVYXCOQSLGBISV C, sed corr.; -QTJGSI,- in ras. A.
9. &d CD. 10. dvvovrajv] alt. v ins. D 2. 13. &s D. 14.
&si D. 16. oi>rog] corr. ex ovtag D. 19. S'~\ Ss D. 20. Post
ovQuvtwv ras. 1 litt. D. tpog&s] corr. ex cpcoQ&g D; similia
posthac non notabo. vnoTLfttTui D, -ri- eras. 21. yivfG&at. D.22. onov 23. vTrox^rjrai] in mg. sup. add. D, mg. D 3
.
23. xca (pr.)] fjveil CD 3
. vsroxfijTat] corr. ex vTroxaiTjrca C 2,
D.'
xi[ om. D. 24. &Ur\la D.
MA0HMATIKHS STNTABE&S A'. 13
tots CCVTOLS xcc& xd0Tr}v itSQicpOQ&v fag KV
7toT ^v itl pei^ovos, nore d' iitl IJTTOVOS
ojfQ ov% bqaxai Gvppccivov.
TO TtQOS TOIS bQi&VGW pit,OVK Ttt
ov% fj dnodTccGis eAdrrcw ovcfcc noiei,
rov vygov rov Ttegifyovros rv\v yv\v
vfjs rs fiascos fip&v xccl ccvr&v
xccl ra slg vd&Q suftA.rj&svra ^is^ova cpccC-
V8TCCI,) XCCI 00CO CCV XCCT&T8QG) %COQf}) TOtiOVTG) pSlloVCC.
itgotidyst, d' sis tv\v GcpcuQMriv SVVOIKV xal tec 10
TOICCVTCC TO Tft?)
dvVCC6&CCl MCCT* aMrjV VJCO&SGlV TCt
TCOV G)QO6X07ttC3V XttTCCtfXSVKS GVfKpCOVSlV Y} ^OVYJV TCCVTrjV^
xcdf
6ri Tils t&v OVQCCVLCW (poacts dx&hvTov TS xccl
evxivrjTOTaTrjs catccGcbv ovGys xccl r&v GjffliidTcov svxwrj-
TOTttTOV VTtdQ%l T&V ftV STtMe'd&V TO XVXfaxdv, TCOV 15
6e 6TSQSGJV TO 6tpCCl,Ql,x6v, d)0CCVTG)S & OTl) TG)V
6TIV TO. 7toA,VyG)VlG)TQCC) TCOV ^V 7fi7Cdo3V 6 XVX&OS
TG)V $ 0TQO)V ^ GCpCCtQCCj ^^COV $
6 OVQCCVOS t03V aMcOV 0G)[ldTG)V. 20
ov [lyy dMa xccl ditb (pvdix&v tivov k'GTiv dQ[ir}-
OLOV OTi TG)V
1. yuivfG&ai] corr. ex cpsQSG&ai D 3. obs] inter o> et s
ras. parua D. 2. d'] dt D. yivopwa CD. 3. SIKGT^-
OS] corr. ex Siaazriiidrcov D 3. ov%] corr. ex ovx D 3
. Antea ras. 1 litt. D. 4. OQI^OVGI D. 7. rs] om. D. yivo-
CD. 9. yiutoo-ceQcoi, BC. Z00?]?] corr. ex %<OQSI D 3.
psi&vcii BC, corr. B 1. 10. 8'] 8 CD. g^g] ins. D 2
.
11. KUTU D. 12 OJQOGHOTtfav] C 2D 3, UQOG*Onid>V ABCD 2
,
OQOGKOTCI&V D. 14. fuxn/TjxotraTTjs C, Bvv,ivi]riY.(ora,Tr]$ C 3.
xat] corr. ex KUTO, D 3. 15. v7C<xQ%i\ mut. in v7taQ%eL D 3
.
r&v] corr. ex TO C 2. sitmsdmv] corr. ex tnin&wv C 2
. 18.
sen B. TtohvytovoTeQK D, corr. D 2.
14 KAATAIOT IITOAEMAIOT
A7irO[lQ6rEQOS XOl b[lOlO[lEQE6rQ6s
ftirw 6 ai&ijo, rcbv ds b^ioio^o&v bfioio^Ots ai sxi-
s $E faitpdvfiaL povai ijr xvxho-
v rots faiJtdoi,s xal v rots 6rOEOts5 rov $ al&Qos p? ovros frtiiiEdov
,
Karafaiiisrai avrbv dvai GcpaiQosidri. xal oftotog, on
^ <pv6is G&Httra ndvra ra [ilv iitiytiu xccl
X 3t
,ra d
5
iv rcS al&sQt, xal &la ndvra itdfov
10 $; 6iLOio[iQ(bv xal GyaiQixcctv, 7ti7CQ sitiTtsda ovra $ovx av Jtatii, rots $x ditttpOQ&v rijs yrjs
V7tb rbv avrbv %QOVOV bowGi xvxfaxbv iv<paivsrodid rovro ff fvAoyov swat, xal rbv itEQifyovra
avra al&BQa rrjs biotas ovra (pvGfcos Gtpaioofidil re
15 sivai xal dia rrjv b^,oioiiEQiav fyxvxMws f
xal
'. "Ori, xalfj yfj GyaiQOfidtjs 6riv nobs
f'On df xal
YI yv\ 6(paiQOidijs <3nv
20 cos xati' oha por] Aaiij$avo[ivr] , iidkiGr av ovr&s
xaravoriGaipfV rbv ijfoov yao italiv xal rrjv 6J.?jvr]v
xal rovs aMovs d0roas 0rtv Idftv ov xard rb avrb
rots fat vys T^S dvar&Aovrds r xal dvvovras,
1. xal 6[ioio[jiQ(>TQ6s GTLV~] A, supra scr. D 3,
om. D,BC. 2. 8s] $' D. 3. -vf-icci, fjrtgja-] mg. D 3
. 4.
si>(alt.)] om. D. roig arsQfois] r&v crsQE&v D. 7. xat] xat rd D.8. ccvofioio^E | IISQ&V D. [isvroi] ds r&v D. 9. d'] 8 D.11. ccn&Gi D. 12. roncov'] corr. ex ronov C 3
. 13. 8'~\ re D.15. lyxDx^tcog] ivwAkl(o$ D. cp^QS6&Kt] -8Q- in ras. D. 17.
B, om. A CD. OTI 18. JU^TJ] on 6cpKiQ08i8i]g v.a.1r) yfj
mg. sup. D. 19. \(paiQOidr)s D. 20. ovrco D. 22. %6tiv\ins. D 3
. 23. n&ci D.
MA0HMATIKHS ZTNTASE&2 A'. 15
XQOtsgois y>v aid tots agog avarokag oixovtiw,
v6rQoig ds rots ngbg dvGyidg. rag yap vjtb rbv avrbv
dytor^.ov^vag exAfmrwas (pavratiiag xal
rocs GfAyviaxag VQi6xo^iv ovx iv reels avralg
-)
rovrttinv rats tb foov ait%ov6aig ri\g iisGyjiflQias,
itaGiv dvayQccyoiisvas ,cUAa itdvrors ras
rots ccvccrohxtQrsQOis rcbv rr^Q^avrco
COQCCS v6reaiov6ccs t&v Ttaga rots dvnx&rsQOis. xal
rys diacpoQKS ds r&v GSQ&V dvahoyov rots ditt6rrm,a6i
rcbv %coQG)v evQiGxoiisvrjs GcpcciQixriv av ns efaor&s 10
rqv rrjs yils sitHpdvsiccv vitohdj3oi rijs xara rr\v xvgro-
rrjra xa,& oka pegy Aapf}avoiivr]s d^oio^s^Siccs dva-
Adyog aid rag eitMQOG&riGsis tots ecpstfis xoioviisvrjs'
EL ds ye fjv rb ^%r\^a srsgov, ovx av rovro Gvvtfiaivev,
&g i'dot, rig av xal BX rovrcov. 15
xottyg ply yap avri]g vitaQ%ov6rjg jtQorsQoig av
eyaivero dvarsMovrcc ra atirga rotg
STtmedov ds itaGiv apa xal xara rbv avrbv
rotg iitl rijg yijg avsrsMsv rs xal sdvvev, rgiy&vovds
T) rergaycbvov ij nvog akkov 6%tj[ictros r&v itokv- 20
y&vav TtaGiv av ttdkiv b^oiog xal xara rb avrb rots
eitl rijg avri\g v&iag oixovGiv, 07tQ ovda^icog yaivsrai
or i, de ovd xvkivdQOidrig av /'^, ivar\
7tQL(pQr\g 7ti<pdvia jtQbs rag avarokag xal rag
rj rrQa^vrj^ rcbv d 7ti7tda)v fiddfov at 25
1. det D. 3. XQOVOVOV C. ccnoTElovptvccs] corr. ex ano-A 3
. 6. rdg] ins. D 3. Ttctgd] om. D. 7. <xva-
ToliKOTSQOis BC, corr. B 2. 8. VCTSQ^OVCCCS] v- ins. D 3
. 13.
ccst D. 17. "tec aGTQCc uvarsMovra. B (notas adpos. B 1
).
19. ccvttetev C. 20. de] corr. in rs D 2. 21. av] om. D.
22. ovdapr) D. 23. ort] inter o et n ras. 1 litt. C. 25.
e- in ras. D. snLTtsdmv] corr. ex STILTCS^COV D 3.
16 KAATAIOT HTOAEMAIOT
TtQQg TOVg tOV XOtfftOV tfdAoUS, OJtEQ CCV TlVSg
ifv cog 7ti&avG)T()ov ,Kid"v dqhov' ovdevl
av ovdsv atsl tpavsgbv iyiyvsro T&V
T&V 7tl TY\g xvQTY\g Iniyaveiag ofaovvT&v,5 itavra Jtatiiv xccl avsteMev xccl sdvvev, T)
ra avra xai
TO i'0ov aysGr&TK r&v xoAcov exaregov n&Giv del
atpavi} xa&fataTO' vvv d' o<?c} civ paMov agog r&g
KQXTOVS TtaQodsvCOlLSV, V060VTG) VGDV [IBV VOTKOTSQ&V
atitQcov KTtoKQVTtrovrai ra ntefova, x&v ds poQeiotegoiv
10 avayaivstai,, cog drjAov elvui, diori xccl svTav&a ^
^g yr^g xccl rag iitl ra ithdyia pdgvi iiti-
avaMy&g Ttoiov^wi Ttavra^&ev to
TO 6<Cd,Olda7todMVVGl,V lTCC TOi) XCCV
15 Kal agog fivdr}rtOT) Kara yuKQov CCVT&V av,6[iva ra
cc&KJtfQ % avrijg
, 3tQOTQov $
Trjg TOV vdarog sitiyaveiag.
'. "On ^.0rj TOV ovgavov
20 TOVTOV 81 &G)Qrid'VTog) l' Tig
av
1. onsq] corr. ex onev C 2. 2. nfi&avwreQOV C. 3.
fat CD. iysvsto D. 5. avsreUf D. Post r? add. -AUTO. D 3.
6. TO] ra D. nolcov] corr. ex TroHojv D. 7. $'] dt D.
OCTCD] o- supra scr. D 3. av] om. D. 8. nccQoStvcofisv] corr.
ex TtaQoSsvopev A 2,mut. in naQodsvofisv D, na^oSevo^isv C.
votetOT^tov D. 9. ^Trox^'ujrTfTat D. T] om. D. $e]
supra scr. D 3. 10. dfjlov] $fj- e corr. D 3
. 11. [tegr}] -rj
in ras. D. 13. aTtodsinvvGi D. 7r()0(>7rZfa)jw/v] corr. ex KQOG-Ttteoptv D 3
. 14. XWQIOIS] corr. ex jjo^otg C 2. 15. rjvSrjnors]
-v- supra scr. D 3. 16. ftaldcaris D. 19. e'] B, om. ACD.
ort yfi\ mg. sup. D.
MA0HMATIKH2 STFTAgEfiS A'. 17
fiovog 6vvrte6dri66iJiSVK ra tpcd,v6(iva xsgsi ii0rjv rov OVQKVOV xa&djtfQ xwroov Gyaioccg vito-
6rrj0ai[id'a. rovrov yao drj [irj ovr&g %ovrog fdsi,
ijrot, rov plv a^ovog xrbg elvai rfjv yrjv, MCCXSQOV ds
rav noA&v foov aitfysw, $ sitl rov a%ovog ovdav agogrbv srsQov r&v jrdAcov naQax%G)Qr]xsvai, ty ^r inl
rov a^ovog ivai ntfrs xaroov r&v itoA&v faov
agog y&v ovv rfjv itg&fYiv r&v roi&v &t6iv Xtvcc
on, t [iv lg rb avor}
rb narco rivcbv 10
oqd'ir], rovroig av 6v[i7ti7troi 7tl
6()d"fjg rrjg GycciQccg rb pqd&oirf faijfUQfav yCvs-
ig avitia 7tdvror dicugoviiwav vnb rov boi&vrog
rov r vitQ yv\v nol rov vnb yrjv, iitl $ rijg
yxx^vrjg rbirj py yivG&Gt.i naUv oAog farmeQfav 15
7) [if)v rr\ iittcfev Ttaoodo) rys * &Qi>vijg roonijs
xccl rr^g %i>[iQi,vrjg KVIG&V rcbv dta^rrj^idrcov rovrov %
yivoiiev&v dice rb \iYi%Xi rbv iGrmeQivov xal
rcov TtccQccMrjAcov r&v rotg 7t6Aoig ri\ 3tgi-
tpogag yoci^o^vcov xvxAcov 8i%oroyiZ6&ai vitb rov dot- 20
Jovrog, AA' f'va rcbv TtaQK^^cov avra xal ijroi
vori,a)rQa)v. cbkitoA(fy>t?Tca de y vitb
,ore ra dta6rtf[iara ravrcc faa rvy%dvt,
3. ^17] om. D. s%6vtos] corr. ex E^OVTOJS C 3. 4 sq. a,
(j, y, d mg. D 2. 9. ngmr^v] -co- e corr. D. 11. Tra^axf^aj-
Qr]Y.vLav C, -v del. C 2. vorj&fir]] -i- e corr. C 2
. 14. xat
yfjv~\ supra scr. D 3. 15. 6y*niJUfKri}0] -t- inter duas ras. D.
r|] supra scr. D 3. 16. T] om. D. 18. iGr)[tQiv6v'] -i-
ins. C. 19. T&V nccQccllriK(Qv'] om. D. Supra rav rots ras. D.
nolots] corr. ex TcoHHoig D. Supra TtsQifpoQ&g add. ccpKiQag D 3-
21. a-uto5] corr. ex ccvtoiJv D. 22. VOTLCOTBQCOV] corr. ex
V(OTKOTQ(OV C, 6X VOTIOTQ(OV D 3. ta/U-oA-OyTJTat] COIT. CX OfiO-
Aoysirai D 3. yg] om. D. 23. rvy%dviv D, -v eras.
Ptolemaeus, ed. Heiberg. *2
18 KAATAIOT UTOAEMAIOT
l)rat xccl tds Ttagd tqv i6r^LQiav av
jiiSQccg iv rats ftsQivaig tgoitalg L'6ag elvai
rats [ii'(b66i tcbv Aa%i6tG)v fipfQcov v rats
5 tw&v Ttdkiv rj rtccQccx&QrjGis vjroT^O'fn?, xccl
av Gvpfiaivoi, to [iijt TK [t'y&r] xal tec
T&V aGrgov l'6a xccl ta avta xcctd rs rbv e&ov xal
tbv 6XQi,ov OQ%ovra <paCv<5&a,i ^itjt rbv fat* avaro-
ti] p>%Qi> [i6ovQKvtf<30)s XQtivov faov djtOTffaZGd'ai,
10 rip djfb ii6ovQavtJ6(QS trii> dvtiiv, artQ tvaQyfbg navrd-
CCVtiKltttl tOiS CpKiVOyLBVOlS-
tfy dVtQCtV t&V &0G)V, Xa& 7JV 7tl
tOV CC^OVOS OV6K 3tQOS tOV tQOV t&V TtohcdV 7CCCQK-
X%G)Q'T)xvla vorj&iJ6tcct,) itdkiv av tig
15 si tovft' ovt&s stysv, Haft' f'xadtov av t&v
to tov dgt&vtos 7tiitdov avi6a diatpoQcss 7toii
jtdvtote to te vitfQ yrjv xal to vitb yijv tov ovgavovxat' ciMyv xal aA,A.r)v ttaoa%G)()r]6i,v xal
xal xgbs aMrjAa, itl plv iiowqs "*
20 8i%otoyiiv avtr^v dvvaptvov tov oQi&vtoS) iitl $ tils
ys rtoiovGrjs rov tyyvtfQov t&v xoh&v ddto plv v7tQ yv\v 7tdvtot iiiovvtos, to dt
V7tb yfiv av^ovtos-) &6t 6v[if}awiv to xal tov did
[i6G)v tcbv ^Gjdi&v xvxkov psyiGtov
25 <5o)m vicb tov tov oQi&vtos titntsdov, 07tQ ov
1. rag itccQcc rrjv] TO. sit' uvrijv seq. lac. 8 9 litt. D,corr. D 3
. 2. ev reefs] in ras. D. 3. TKL$ (alt.)] r corr. ex i D 3.
13. Tro/tcov] -o- e corr. C. 15. sl%Ev~\ corr. ex i%s D 2. 16.
TOV] bis D, sed corr. diacp&oQcos A, y^>. diKcpogoos mg. A 2,
17. TF] om. D. yfjv (alt.)] y corr. ex r D. 18. natd D.
TtQog] -s e corr. C. 21, atft D. 22. 8s] S' D. 23. rov]corr. ex to C 3
.
MA0HMATIKHS 2TNTASE.QS A'. 19
ovrog %ov O'fopfnrat, | p,v del xal TtaGi (paivo-
pVG)v v7tQ yrjg dcofifxarrjiiogtoV) ds r&v Aoiitcbv
dcpav&v ovr&v, sir' av ituKiv XWG)v [ilv ohcov xara
TO avrb (pawoiiBv&v V7CQ yv\, r&v ds hoirt&v apcc (li)
(pcuvoiisvcov CDS dyAov rvy%&veiv, on xal ta rfiri^iara 5
rov ,G)8iaKOv di%OTO[isZTcu vjtb rov b^C^ovros sx rov
rcc avra fi[iixvxA.i,a oA# nors iiev VTISQ y^v, TCOTS dl
vnb y^v oatoA.aiipdveGd'cci,.
xal xa&oAov d' av 6vveflat,vV) sfasg ^r\ i)it
avrbv rov l6r^iQivbv sl% ryv ftfaivfy yi} 5 legos 10
CCQXTOVg dfrj 7tQOS [L6r]llpQlKV (X7txA,lVV TtQOS tOV
STSQOV T&V jrdAov, TO [trpdri [tyd^ ngbc; afadytiw v
rats farjiiAQtais rag avarohixas r&v yvo^iovov
rats dvrixatg in v&ias ytyvsGftai xara r&v
aMtjAwv t& oQi&vri, ^xut^dmv^ fiitSQ avrix^vg Jtavra^ 15
&G)Qirai TtaQaxohov&ovv. yavfgbv d' avr6&v, on,
rp> rgfayv r&v &6G)v oiov r 7tQO%a)Qtv xa-
v r&v v rats ngarais wavn&ndrcov yt'
Gvvshovrt, 6^' slitEiv 7ta6a av 6wy%v&ir] rdfaov 20
rag av%0[iiK>6is rcbv w%fh](iQG)v
fari V3toxi,[ivr]s rrjg yfig iira rov
rag ryg 6Arjvrig txtefyetg xara ndvra ra [iQr]
rov ovQavov TtQog ryv xara dtd^r^ov r& ^Mc) 6ra6iv
dvvaG&ai, ryg yijg noMaxig pf} iv ratg 25
1. cthi D. 4. fatsQ 5. vpawoiisvmv] supra scr. D 3. 6.
(pSiccKov] -a- supra scr. D 3. 7. oAa] seq. ras. 1 litt. D.
11. AnEiiHivs D. 12. Post pride eras, xi D. 14. si)9sug\corr. ex ev&eicas D. ytvsG&cti D seq. ras. 4 litt. 15. Post TGJ
eras. 81 D. tmTtfdav] corr. ex snntidai D 3. 19. Gvpfirjoo-
fisvmv'] ante -o- ras. C. 20. *'] Ss D. avvxv&eiri C. 21.
rat-is] corr. ex S B 1 G*. ccv^o(iLo>G8is AD, corr. A 2. 23. sv.-
-t- in ras. D. TO} om. D. 24. xara] om. D.
2*
20 KAATAIOT HTOAEMAIOT
dia[iTQOv6cci,s ttagod
V rots &dTTo6t, TOV
v koyov %!> itgbc; ra
ri yij.
xal 6r^iiov loyov e%si
i\ yij agog to p%Qi> rv\ t&v catkav&v xahov-
6<pKiQtt<5 efordtfn^a, iieyct jilv rex^tjgiov TO
ocjtb TCKVXOV ccvrils tcbv psgcbv rd rs [isysfrri xal ra
dia6tyJiiKTcc r&v a0rQ(Dv xara tovg avrovs %QOVOVS10 face xcd o'ftota cpcctvsd&ai, jravra^i}, xafrccrteg ai dnb
diayoQ&v xA,i[idTa)v 7tl r&v ccvrcov XYIQ^SLQ ovds
ro sA.K%i,6tov svyfaxovrcci, diacpcovovdat,. ov pr^v
AA xaxstvo nccQa^Ttreov TO TOVS yv&novas tovg sv
CpdtJTtOTS [ISQSt, TilS yilS TI&SIISVOVS, Ti d TK T&V XQl-
15 XG)TG)V 6(pCCl,QC()V XVTQK TO CLVTO dvvaG&at, T& XKTK
cdtfd'fiav Tils yflS XWTQO) xccl dia6&t>iv Tag 8i07tTv6is
KKL T&S T&V Gxi&v 3tQt,ayG)'yas OVT&S biioAoyovs Tats
V7fOd'06i T&V (p(UVOllVCOV) O)g &V i til KVTOV TOV
Tils yns pfaov tiypstov yivbpzvui Tvy%avov.
20 tvuQyss $ 6rj[ilov TOV rav-0-' OVTCOS %i>v xal TO
TOV OVQCCVOVj Q7tQ OVX CiV 6VV^atVV^ i TO
2. sUdzroaiv D. 3. g'] om. A CD. on 4.yfj'j
iov hoyov %r) f) yr) TCQOS tec OVQUVIU mg. sup. D. 7.
QLOV D. 11. wXrjftaToov A. 14. H^ixcor&v] corr. ex
rwv A 2D 3. 15. SvvuGai A. %ar' D. 17. rat's] t corr.
ex i D 3. 18. vTto&fGfGiv A. cpKivopsvojv] cp- in ras. D.
dt
21] 7) St,' D, xat Si' D 3
. rov] om. BC. 20. IvuQyaSs C.
. &] supra scr. D 3. 23. et] corr. ex sis D.
MA0HMATIKHS 2TNTAEE&2 A'. 21
rijg
povov
agog rr\v rcbv OVQCCVL&V
av rb diet rov Kara rb
dt,%orop,lv ,rd ds 6Y
KV
'. "On ov KivyGiv riva
n yn-
Kara, ra avra d rots k'yiTCQOG&w di%d")J6Tat,, diott,
iivrwovv nCvYiGiv fig ra TtQOEiQqiisva TtAdyicc 10
rfjv yv\v oi6v r Ttoitfti&ctiij 6'Acog nf&faTciG&Ki
7tox rov xarci ro ndvrQov roitov ra ccvra yap 6vv-
i xal rv &6t,v ftMrv Ttaa TO
KV rig Kal rijg 7tl TO [teGov cpoQ&g rag ccfaiag iici- 15
fyirr^0Lv a7tci% y TOV, on,ij
t y^ rov [i6ov sits^i
roTtov TOV xoGpov xal ra fidor] TCCCVTK irf avrriv
,, ovr&g ovrog wccyyovgJ
| avr&v r&v yaivo-
7tQO%iQora,rov av ig rty
yivoiro TO 6(pcu,ooi,dovg xccl 20
g rov itavros, &g k'cpatim, djtodfdfLy^svrjg ryg yijg
2. TO (alt.)] om. EC. 3. TTJS yfjs~] om. C. ffTjfm'ov] corr. exD. 4. fjcdrjTtorovv] corr. ex fjGTtorovv D 3
. 7.'
\
om. A CD. cm 8. y?)] mg. sup. D. 7. Ttoistrai, [iszcc-
patLHijv D. 10. rd] seq. ras. 1 litt. A. 12. HSVTQOV] corr.
ex vJs\r^ov A 2. ccv Gwifiawsv D. 14. epoi C. TtegiGaJs D.
15. qpopag] mut. in cpoQctig C 3. fjrt^Tjrrjffftv] mut. in im-
tw^Gtuv D 3;fort. ini^riTfiGKL. 16. TS
yfj~]e corr. D 3
. TOV]corr. ex TCOV A 2
. 18. ivagyovg] supra scr. D 3. cpcuvopk-
v(ov\ seq. ov D, corr. in cbv D 3. 19. /taxftvo] seq. ras. 1 litt. A.
de] supra scr. D 3. 20. yivoizo] corr. ex ysvoiro D 3
.
vs C, v del. C 2.
22 KAATAIOT HTOAEMAIOT
ev aitatiiv ebdrag rots iiQ0t>v avrr^g rag re
xal rag rcbv ftdgog fyovr&v cfo^drov cpogdg, A^yo ds
rag Idtag avr&v, Jtgbg ogfrag ycovtag Ttavrore xal
7tavra%fi ywEGftai ra did -rife Kara rv\v
5 itaq)ijg dixpaMoiiVG) axhvsl sitins'da)
rb TOV&' OVT&S %W'> on XKL, si ^ avxexomovro
vrtb trjg emcpaveias ri\s Y^-) ndvtG)<$ av Bit avrb rb
KBVtQOV XaWJVT&V, 7td Xttlfj
7Ci TO XVtQOV CCyOVffK
v&Za Jtgbs OQ&as ycoviag ad ywftai t& dt,a rijg
10 Kara TTJV iitatf^v roftijg cpartro[iVG) rr^g Gcpatgag iti-
0601 $ Ttagadofcov ofovrai rb ^itjr fafiyxwai, TCOV
lirjr <pQ6ftai rb rrjhxovro fiagos rifc yijg, doxovGi
H,OL TtQog ra xa&' Zavrovg ita^r] xal ov 3i(*b$ rb rov
15 oAov i'diov djtoftt,3tovrs rty GvyKQiGiv jtoiovpwoi,
dia^aQrdvELV. ov yag av ol[iai, davjiaGrbv avrolg k'rt,
<paviri rb roiovrov, i 7Ci0rtj^aiv ,ort, rovro rb rijg
o/lw rc5 7tQid%ovrL G&iiari,
Ttabg avrb koyov %i' dvvarbv ydg ovro
20 d6^i rb Kara koyov kd%iGrov VTtb rov
T xal
rov ,v xrco
1. n&civ D. ft^><jn>] corr. ex (ISQEGI D. IIQOGVKVG D,? D 3
. 2. d] ^7? D. 4. yt'yvfff-9-at BC. f^nrcoGLv]corr. ex ntwGiv D 3
. 5. Sis^a^o^isvcp] 8 corr. ex a D 3.
cbdtvT? BC. 6. TO] om. D. 7. Post yfjs add. at yogaCmg. BC (pro scholio). ctvrb TO] utrumque -d in ras. B. 8.
%fVrpoi>] -ov in ras. B, nivrgov at tpoQcci D. 10. roft^j] -g
add. D 3. sniTtedav A, sed v eras. 12. nccQaSo'^ov] do^ov C,
mg. yQ. naQa.8o(^ov} C 2, Ao^ov B. Btfafajiiiftti D, sed corr.
13. TTjZtxoiJTo] mut. in TqJiiKovrov D 3. 14. avrovg D. 16.
av] supra scr. D. ?rt] supra scr. D 3. 17. sf] corr. ex ij C 3
.
19. ovrco] e corr. D 3.
MA0HMATIKHS 2TNTAgE5i2 A'. 23
av(o prjdwbs ovrog iv r& xoGpG) agog avrtfv,
vds V GtpaiQa Tig CCV TO VOlOVtOV 7tiVOt]-
r&v d iv avr<p 6vyxot,^idro)v rb ocfov eitl rij
idCa xal Kara yvtiiv savr&v yoga rcbv pv xovcpcov
xal A,iiTOicdv ig rb %& xal cos o? rv iii- 5
$ r
rqv OQ^V TtoifZGd'at, di,a rb xal ndvrcov
rb VTtQ Ksyakris, avo $ xaAovpfvov xal avro,
vViv fog ngbs tt\v itQi,%ov6av 7tt,cpdvi,av, r&v $
flaQa)v xal xa%v[iQG)v 7tl rb p6ov xal ws ngbs rb 10
xswsgov <pQOtiVG)V) doxovvrov d LS rb xdro
dia rb xal Ttdvrcov Jtdfav rfticov rb ngbs rovs
xakov[ivov $ xdrO) xal avrb vViv ftgbs rb
rijs yils tiwtffttiiv T flxor&s 7tQl rb pfaov Aanfi
vnb rijs ngbs AAi?Aa 7tavra%6&v fays xal opotas 15
dvnxoitils T xal dvrQi6G)S' roiydgrot, xal' ixoro3s
xaraA,aiif}dvrat, rb oAov Gr^s&pa ri^s yfjs pfyiGrov
ovr&s ov C3Q XQOS Ta (pQo^va en avrqv xal vnb rr\
Ttdvv Eka%i6rG)v pag&v op/iifc ar dij 7tavra%6^vxal &^itQ ra ^v^Tciitrovra xd%o^vrj. si 20
da y xal avr^ f)v rt,s yoga xowr} xal pia xali\
avrr\ rots ahhois pdQ6iv, Zcp&avw av itdvra
did rr^v roGavrqv rov yLsyd&ovg vjtQ(loA,riv xara(f>Q
xal v7tteiitTO fiv Ta re (pa xal ra xard pfyos r&v
1. ^Q'svog D. ctvxr\v\ ccvrov D (corrigere uoluit D 8).
3. a-urw] CCVTOLS BC. avvKQifidtav A. td] ins. D 3. OGOV]
mut. in OGOJ D 3. snl TJJ ISCa] corr. ex snuijSsicci. D 3
,STIL
rr\ Stai C, 'iitl rfj tSiai C 3. '4. avt&v D. qpo^a] corr. ex
cpOQoct D 3. 5. TO] corr. ex rov D. cptgeiccv C. 6. &VCCQQI-
7tio[iEvcov A 2 C 2 D. 7. IxadTotg] con*, ex gjta<7T7js D 3- 13.
civto] corr. ex ccvr& C 3,avrb vsvs A, cavtb VZVEI, A 2
. 14. ts]corr. ex ye D 3
. 18. cpcciQ6[ievcc D, corr. D 3. 21. cpogd] ante
$ ras. 1 litt. C. 22. alois C.
24 KAATAIOT IITOAEMAIOT
ficiQ&v o%ovpva 7tl TOV efe'pog, avrfj de Ta%i6TK rsfaov
av xit7tTG)Xi, KOI ccvTOv TOV ovQcuvov.
{lev xccl povov siuvoq&evzK TCCCVTCCIV ccv
g y oi'ovTcu, iti&avG)TQov, TOVTOIS
ovx %ovtS) o, xi avri7Coiv, Gvyxcctccrtd'fvtcii,)
ovdv ccvTolg avxiiiciQ'tvQYiGeiv, t rbv {isv
ovQccvbv axivrjrov vnoGruJGccivro Aoyov %KQW, rfjv $
yv[v 7CQl TOV ccvrbv
10 lit avatoAas xa6Trjs
T)KCil (X[l(p6TQCC XLVOtV 060vdtJ7tOT^ [lOVOV
rbv avtbv cc^ova, wg (pa^iv^ xal Gvjjip&Q&g rri agog
$ ccvrovg^ on, t&v [iv itgl ra
15 (pCClVO^lBVOV VXV OV$V CCV /'(?(0g XCoAvOl XKTtt}> TrjV
a7tA,ov6rQav 7tt,pohr]v toi>& ovrcog %w, eforo d r&v
yt()i fipag ccvrovg xal r&v v asgi GviMtrcotiKT&v xcul
Ttavv av y^OLOTarov dcp&fLr] TO TOIOVTOV. LVCC
^vyic3QYi6o^v avTolg TO naga q>v6iv omog to,
20 A7tTO[lQ6TaTCC XCil XOV(p6TKTtt ij ^d' oAo?g XWi<5%'Ki t)
adiag)6Q(og Toig Tijg wavTiag (pv6cog T&V y nQl TOV
(XQa xal tfTTov A,rtTO[ii,$G)v wccQycbg ovTcog Tcc%vTQagTG)V yG)d6TQa)V ItdvTGZV (fOQag 3tOLOV^VG)V^ TK $
3. snivori&ivtu] corr. ex snovori&svTcov D. 5. y'] om. A.
6. GvvKaraTi&svrciL D. 7. avroig ovdtv D. zbv (isv] corr.
ex (isv rov D 3. 9. rov] bis C. 10. in''} sni D. ntgi-
crQocprjv] -otpijv in ras. D. 12. GvpsrQcos D, corr. D 3. 13.
nsQinarulri'tyBi] post -r\- ras. 1 litt. D. 14. MJ.rj&ev BCD.avrovs] -s add. D 3
. 15. ovSsv] corr. ex ovSs C 2,ov&tv D.
ncohvoi] H- corr. ex K in scrib. D. 17. TCSQI] nsgi rs D.rcbv sv CCSQI] A, rbv CCEQCC BCD. 18. ccv] corr. ex c:y C 3
,
om. D. 20. (ir]d'] -73- e corr. D. 21. adiucpoQcoc;] corr.
ex tftafooog C 2D 3. f corr. ex rs D 3
.
MA0HMATIKHS ZTNTASE&S A . 25
xal (layvrara Kivritiiv idiccv o%iav
ovr&g xal o^ia^v TtoistG&ai, rcov yead&v ndfav 6fio-
e JtQos rfjv vn dM&v xivrjtiiv sm-
sviors %6vr&v, dW ovv bpokoyriGKisv av
rqv tfrpogp^v rijg <yrjg yiyvsG&oLi KitKG&v 5
anlag r&v Ttsgl avryv xivrjGecw cog av ToGamyv ev
av ra pvi pspyxora Bit avrils yiiccv asl rqv svccvtiav
ty yri xivrjGw zyaivsto Jtoiov^isvcc^ xccl ovr' av vscpog
note edetxvvro Ttagodsvov TCQQ/S avaroAas ovrs aAAo 10
n rtbv LTtTa^isvcov tj ftcc^o^iVG)v (pftavov6ri ael Ttdvra
nod 7tQo^a^avov6^s r^v 7tQO<s dvarohccs
)&6ts rd AoiTtd jcdvra et$ rd 7tQO$ dv6[ids xal
si y&Q nai xov atQK cpijtiaisv avrf} GvyLitsQidysd&ai 15
xard rd avrd KOI l6ora%&g^ ovdsv forov ra xar
avrbv yivopsva (jwyxQijiara Jtdvrors dv sdoxst rv\
6vvan(potEQG)v xiviJGs&g v7toA.L7t6d-ai,) rj i'jt() xal
avrd co6XQ f}vco[iva rc5 aQi 6vyL7tQiriyro, ovxr
av ovdrQov ovrs TCgo^yov^Bva ovrs vnohsinonsva 20
syoiivsro, psvovra $ dsl xal ntfrs sv ratg itx^s^iv
v ratg (tohatg itoiovyisvd nva it\(ivrp> r) (j,rd-
1. ncc%v[iQ6t<xTa] -at- e corr. A 2. Q&LCCV] post 6- ras.
1 litt. A. 2. r&v] -v supra scr. D 3. ytood&v] -d- corr.
ex "k D 3. 5. yiyveG&cii xj]g yfi$ B. yivEGfi'cti D. 6. ccvrriv\
-77- in ras. D 3. 8. sW D. <m'] supra ras. scr. D 3
. TTJ'V] r-
.e corr. D 3
. 9. ovr'] ofcs seq. ras. 1 litt. D. 11. T) (3aHo-
j^fvcov] supra scr. D 3. 12. TtQoHafipccvovGrjs] post -o- ras. 1
litt. B; 7tQOG).cc[ifiavovG7]g C, sed -G- del. C 2. 13. stg\ si's rf D.
17. yevoiitva D. 19. av/Li7rf(irjyTo] -r\- ins. C 2. 20. ovSt-
TfQov] ovdrfQK A 1
,mut. in ovd&eQct D 3
. 21. <J] d' D.
nrriGfGiv] irtrJGSGi B, cpogccis D, ^olaig D 3. Deinde ins. ftTjrf
v rarg cpOQuis mg. BC (pro scholio). 22. ^o^ar?] mr^GBGi D.
7t\a.vi]v\ ABCD, mg. yp. Tra^aA^wyrjv C 2.
26 KAATAIOT HTOAEMAIOT
,ayieo aTtavra ovrog tvaQycbg oo&^iev dxorekov-
p,eva cog nyde poadvrriTog nvog oh&g rj ra%vri]rog
avrotg KTtQ tov pri etirdvai rqv yv\v
rj
f
. "On dvo diayogal rcbv nocarav
5 si0iv ev ro5 OVQCCVG).
Tavrccs [iev dfj rag vitod'6i,$ avayxai&s
sis tag xara pe^os XKQccdfaeis xai ra$
dxohov&ovGac; ayxsctsi, xccl ^B%^I rcbv rotiov-
tcov ess sv xecpcdafois vnoTsrvTCcbGd'ai, ^s^aicod'rj^o^svKS
10 re xccl ETtinccQTVQrj&rjGoiievag rsfoov e% avtijs r^g r&v
axohov&(o$ xal scps^rjg ci7todi%d"ri6o[ievG)v TCQOS ra
cpai,v6[isva ^v^fpcoviag. XQOS ds rovroig f'fi xaxstvo
r&v xa&oXov n av Yiyritiawo dixatas yt^o^aftslv^ on,
dvo dittyooal r&v itQ&x&v xwtJGsav sitiiv ev rc5
1.5 ovQctvK), IILK per vy i\s (pegexai JCCCVTCC ano dvccroh&v
del aGavrcog xal i6ora%cbg jtoiov[ievrjg rfjv
xara nccQccMrjk&v dMtfAoig xvxA&v t&v
rotg ravrrjg rijg xdvra diicd&g
jrdAotg, d>v 6 pfyitixos xvxfog
20 farmeQivbg xcdelrcu dia TO povov avrbv VTCO peyidtov
ovrog TOV bat&vrog Siya jtdvrore dicuaeiG&Ki, xai rrjv
xar' avrbv yiyvQ^ivr^v rov fyCov iteoi,6Tao(priv farjueoiav
Ttobg afofrrjO'iv navra%ov noielv, rjde ereaa, xa& ty
4. rj'] om. A CD. on 5. OVQCCVW] mg. sup. D. 5. slew]supra scr. D 3
. 6. TtgoGkapflavofisvas D, sed corr. 8. &Q-corr. ex CCQ-H^GI, C 3
. 9. sv~\ sy C. vTtOTSTvnoG&cti C.
C. 10. re] om. D. 13. fjyrjGairo] -i-
ins. D. nQokcifiBiv] TO rtQokcefisiv D. 15. ftta] seq. ras. 1
litt. C. 16. Ante ini ras. 3 litt. D. 18. T7)g] -$ e corr. D.
19. Tro/lotg] corr. ex Tro/Uoig D. 22. yivopsvriv CD. 23.
7tccvra%fi D. ^] corr. ex at D 3.
MA0HMATTKH2 STNTAEE&S A'.
KI TG>V a6rQG)v 6<palQKi xccra ta
[ivrj (poga TtQiQvvtai nvccg tiTctxt,vrJ6i,g itsgl itohovg
xccl ov rovg ccvtovs tots Trig yfQOJttjg nsQicc-
xccl rccvrcc ds ovrcog EJJBIV fator&fys&cc dia
rb K pv rils wen \*>iuv sxccGrrjv qpSQav O-fo^tag 5
jtdvta djccdzaitAcbs t& iv r& ovgavti Kara r&v dfioei,-
d&v Kol jtKQa^^cav r& farftiSQwa) KVK^G) toncw
itgbs afa%"ri6w bg&G&Ki 7toiov[ivcc rag rs
KCil T<XS [isGovQccvriGsis xod t&S dvGsis idfov ovros
rotovrov rr^g ttQarys fpoQccg^ sx $ Tijg tystfig KOI 10
[lV ttMcC TCCCVTCC
KOI to,
xal tec TtQog roi>s oinsiovg r
xoitovg 7tl Ttheitirov td^coftara, xbv df ijhov xal tqvKeel TOVS JthavoiiEvovs aGtEQKS [lErccfidGEig 15
jtoiEZG&cct, Jtoixttag pw xccl
& &g ngbs ity xcc&ohov xivrjGw els ra
avccrohag xal vjto^L7to^Lvcc {JLEQV} t&v
aAA^Aa diKOttj^iara xccl &6itQ VTtb
ttQl>tt'yOllVG)V CCtfTQCOV. 20
ovv xccli\ Toiavrrj [lErdfiaGis r&v
xara itKQa^in^ov xvxA&v Eyivsto tat
TtEQi Ttohovs rovs inv ^g^nv
avrccQXES ccv EyCvEro \Liav %\yEl6ft&.i xal
2. noKovq] corr. ex noMovg D, ut saepius. 3.
-rov- e corr. D. 4. ds~\ d' D. Sid] -d e corr. D. 6. 6(io-
Lda>v] -et- in ras. post ras. 2 litt. A, opoiosid&v D. 7. xvxiw]om. D, comp. BD 3
,del. B 2
. roitoov] -v euan. D. 9. tSiov]corr. ex IStovc D. Idfov ovros] corr. ex tdiovvtos C 3
, mg.ovxog. 12. (paivetcct, D. 18. avvrriQOvvTcov] pr. T ins. D 3
,
post rjras. 2 litt. 19. aU^a] e corr. A. 20. CCGTSQCOV D.
21.17] supra scr. B 3C 3
. nlavo^vcov D. 22. xara] corr.
ex xal rcc BC 3. iy^vsro C, corr. C 3
.
28 KAATAIOT IITOAEMAIOT
rr)v avrrjv Ttdvr&v Tteoiyoodv axokov&ov rrj
m&avbv yap av ovrcog ecpdvrj Kal rb rr]v
avr&v nerdfiaGiv Ka& vnohefyeig diacpdoovg Kal
Kara dvri,KeL[ievr]v KivrjGLv ditorekeiG&ai. vvv de
5 ratg xgbg rag dvarohag [lerapddsGi
del yawovrai, 7tQ6s * agxrovg xal
ScoQOv^isvov rov iisy&ovs rr]s roiavrys
&6re do^au di ^cod'^scov nv&v rovro
rb 6vii7trG)[ia yiyvsti&aL itSQi avrovg, akX avo^d^ov10 [lev &$ agog rqv roiavryv vitovoiav
, rEraypevys ds
&S bxb xvxhov Aolov JtQbg rbv far][iQi,vbv dnorshov-
fiEvrjg' o&v Kal 6 roiovrog xvxhog sig re xal 6 avrbg
xal r&v 3tAavG)ii8VG)v i'diog xaraAajjipdvsrai, aKQifiov-
psvog ply Kal cbtiiteQ yQaydpsvog vnb rrjg rov i\Uov
15 Kivri6G3$) TtSQiodsvopevog ds Kal vito re rrjg <5ehi]VYjg
Kal r&v nAavcoiiev&v itdvrore itegl avtbv dvatirge-
q>o[ievG)v Kal [irjde Kara rb rw%bv eKTUJtrovrcov rrjg
djtore[ivo[ievr]g avrov Ka& sKaorov etp' eKdreQa ra
pegr] jtaQaxcdQiJGe&g. enel de Kal [leyiGrog ovrog 6
20 KVKhog fteogetrat, did rb rc5 fccp Kal (toQeioregov Kal
voncSregov rov faypeQivov yiyveti&ai rbv rjfaov, Kal
jteol eva Kal rbv avr6v^ fog etpapev., aC r&v Tthavco-
lievcov Jtdvrcov xobg rag dvaroAdg iierafiddeig dito-
reAovvrat,, devreoav ravrrjv diayogav rrjg Ka&6Aov
25 KLvrjGe&g dvayKaiov i]v v7tQ6rr\<5a6&ai rr)v iteol nohovg
2. OVTCOS] corr. ex ovzco D 3. fcpavrji, A. 4. %ar' D.
anorsifiG&aL] -n- e corr. C 3, post n ras. 1 litt. A. 5. tag]
om. CD. (iETKcc686L D. 7. oficdov] post a ras. 1 litt. A.
8. &jco<ibj(yoov] ^oQ"tJG(ov C, post -f- ras. 1 litt. D. 9. ytW-0-9-at CD. 10. to'] d' D. 15. T] om. BC. 20. xw fato]
corr. ex rb i'aov C 3. 21. yfofcd'ai D. 22. nicer ofievcov CD.
25. mvr)6(os~\ -c- corr. ex "k in scrib. D.
MA0HMATIKHS ZTNTASE&S A'. 29
xov xaxt,hr}H[ivov Aojov xvxhov xal sis t& IVKVXLK
av drj vo^o^iev xov dice xcbv 3t6A,&v d[icpoxQG)V
XG)V 1tQOLQr]llVG)V XVX&G)V yQCCgJO^LSVOV llfyltiXOV
xvxA.oV) os f| dvdyxys xdxQov sxsiv&v, xovxfaxw xov 5
re far]iiQt,vbv Kal xbv JCQOS avrbv eyxexfaiisvov ,
TS xccl XQOS OQ&as y&viccs vspvzi,, ttGGuQa plv
Gr][ilcc xov Ao^oi) xvxhov, dvo plr xa VTCO xov
xccxa did{iXQOv dMrj&ois yivoyiev
Qivd) G)V xb [iv KTtb [i6rj[jif$Qias ngbs ayxxovg 10
k'%ov xqv nccQodov saQivbv kiytxai, xb $ IVCCVXLOV
yLxortG)QLv6v',dvo d x& yivopwa vitb xov di a[i(po-
XQG)V XfbV JtoAcdV yQCC(pO}lVOV XVX&OV,
XCCl CCVXK 6^-
Aovdrt xccxa didjjifXQOV aAA^'Aotg, xaA,ov[ivcc d xgoTtixd^
G>V xb tiv Kitb p&cttfli$QfaQ xov foffli(>tvov lEiyLEQwby 15
xb d ait' CCQXXCW &Qivov.
i\ ^lv pta xccl TCQCSXITJ <poga xccl
3tQl%OV6CC X&S CtMaS JtddCCS 3tQl'yQCCCpOllVTq XCCl
XOV dl d^l(pOXQ(DV XCbV 3t6A,G)
xvxhov 7tQiayo^ivov x xccl xa 20
a rtdvxa 6v[i7tQi,d'yovxos ditb dvaxoh&v itl
itsgl xovg xov forjpfftvov nohovs fepqxoxas7tl xov xahoviivov iisGripfiQivov, bs XOVXG) povG) xov
2. yogas] corr. ex niv . . . D. anoTJiov[ivr}v] corr. ex
ccnorelovfisvcov D 3. 5. Ante xvjdov eras, xv D. endrsgov]
-o- in ras. D 3. 7. reaoccQo] corr. ex rscasgcc D 3
. 12. ysvo-D. apoTcov -tov e corr. D. 13.
, -yiGTOv in ras., D. xat 20. xvxAov] mg. D 3
in textu supra scr. tefasi. 21. GwrcfQidyovros AC. sni]els D. 22. fop^-KOTocs] BCD, mut. in ^f^xora A, in
P^TJ-xorog B 3
. 23. pfGriiipQwov, og] corr. ex fifGr](iQivovs C. os]in ras. B 3
;corr. ex tog D, ut saepius. TOVTOJ] rov- e corr. B 3
.
30 KAATAIOT IITOAEMAIOT
naoi,ar}iivov diatpto&v rcli pf} xal dia rcbv rov
KVK&OV rt62.o)v jtdvrorf yodcpfG&ai, tn xal did rb nobg
ycoviag rco bgitpvri, 6vv%cbg voslG&ai, Katelrai
roiavrr) &6is xdroov r6 rs
5 V3to yv\v KOI rb vitb
Xttl T&V VV%Q"YULQG)V TOVg [l00VS %QOVOVS
3tQl%OHVr] [lV VJtO
a$ t&v
vxb r
10 <pa[iv, ttvti'jitQia'yoyisvri dl fig ra ivavtia 7tQ\
rov Aoov xvxhov jrdAovg, 01 xal avrol fofirjxoTfs adKara rov rqv XQ&rrjv itfoiyoafpriv Ttoiovvrog
rovrfart, rov dt' dfig)orO(ov r&v jrdAcov,
r fixdr&s 6vv avra) xal xara rr^v i$ ra evavria
15 dvroas <pooas Kivr{6iv r^v avr^v &&6W a\rov yoa<poivov <Si' avrr Lsfarov xal
rov
rcbv Kara
'H ply ovv
20 roiavryv av %oi ri\v K&6iv rcbv oyfMvr&v noovno-
aQ%6&ai rcbv Kara [ifyos dxo-
v7tdQ%iv fiyov^&a, Si jjg ^
1. diacpSQcov rov itqoiQr}yivov D. rw] corr. ex x&v C,
supra scr. D 3. ta>v\ corr. ex TO D 3
. 2. n6l(ov~] supra scr. D 3.
4. rffjin ras. D 3
. 5. yfjv (alt.)] y corr. ex r D 3. 6. vv^j]-
us'^cov] --91- ins. D 3
. %Qovovg] %QOV- e corr. D. 7. nsgi-
%o[ievrf\ fj 7tQi%oiJivr} D. 9. gjf^oju/fVrj] seq. ras. 1 litt. D.Ante cog ras. 34 litt. C. 10. Ss et$\ corr. ex (isv C. TOVS]
corr. ex TT)S C 3. 13. x&v] corr. ex xov C 2
. 14. ri\ seq.ras. 1 litt. D. 15. cttst I). GVVTJIQOVGIV] GWTriQOvGiv 01
noioi A. 16. avr&v D. 18. #'] om;ACD. 19. ngo-
didlr}tl>i$~] corr. ex TtQOGSid^fii^LS D. iv\ y C. 22. ^]corr. ex ot C 3
.
MA0HMATIKH2 2TNTASE&S A'. 31
r&v TtQoeiQriiLsvGdv jrcUoov rtSQHpSQeicc rov i
ccvr&v ygacpoiisvov iisyfarov xvxhov ityMxr] rig ov6a
rvy%dvi, xcctahcc[ifldvTai,) dvayxatov OQ&jiev Ttgofx-
rrjv ngay'pax siccv rr\ 7tr]A.ix6rr]Tog v&v iv rco
i. Tlsgl r^g TtrjAixoTyros r&v sv r& uv
sv&si&v.
ovv rv\v % EXOL^OV %9n0iv xavovixijv
nvcc psta ravrcc x&6iv itoiytio^d'cc xi\<s ytrj^xor^Tos 10
v 3tQi[iTQOv fig t
d rag vitb tag xccd''
t&V
lv r^irj^drcov &s rf}s dicc^iBtQOv dia r e
avr&v r&v 7Ci^oyt,6^G)v cpavrj6o[ivov v rolg aQi&[iotg 15
tg QX Tfitj^iara foyJQrjpivrjg. Ttgorsgov ds
nag av cag evi [idhdTa dt' oUyav xal r&v
ccvt&v &&Qrni&tG)v vn&6dvrov xal
STiipokriv ri]v xgbg rag m^^Lxdrr^rag ccvr&v
ojtcog ^ povov xr^L^ivcc ra /Ltfye'O1
^ t&v v&icbv 20
1. fifra|v] in ras. D 3. 2. ftsyi'tfrov] supra scr. D 3
. m\--TJ e corr. C 3
. 3. rvy^dvsi] om. A. 5. a?ra|] -n- e
corr. C. yf] corr. ex TS D 3. jLtfUTjcov-rsg] -a- e corr. C 3
,
CD.jnut. in iieUrjGcivTfs B 3D 3. 7. t'] om. A CD. rfjs
off] om. D. TW] om. D. 8. sv&fi&v] fv&si&v v.a.1 SK-
Ka.voviY.ri D. 12. ra$ vnb rds] scripsi, tag ABCD. l
f]p>i>-
v D. nKQccv^asig] mut. in TtccQccv^Giv D 3. Deinde
add. xal rag B 3. 13. vnorBivo^vu?] corr. ex vnonvo^vccs A.
rovrectLv C, comp. B. 14. noGO)v\ OGCOV BC. slai D,
comp. B. 17. fta/Uffra] -i- et -T- e corr. D 3. 18.
SEVTOV] -fi- et -^=- e corr. D 8. 19. rr]v\ om. D.
-a? in ras. D. 20. oncos] -it- in ras. D 3.
32 KAATAIOT UTOAEMAIOT
tG)S) AA xccl dice
odixi avrcbv 6v6tcc6G)g tbv
t&v
tG)V
v ecpodoig Kara rbv tij$ Qyxovtddos tgoitov
5 diet to 8v6%Qri<5tov t&v [lOQicuSiicbv ti t rolg
xal nQi,6[ioig axoAovd"tj(5oiiv rov
ccsl xata6ro%a6[ivoi,) xccl xa& o<5ov civ to
tov yt^bg
10 "EtitG) dr\ TtQ&tov fiiiixvxfaov to ART ml
tQOV t^g AAT 7tQl XVtQOV tO Z/, XCCl .KttQ tOV
tfj AT Ttoog oo&ccg ycoviccg
BV
YIAT xata to E^ xal
15 Ttt,V%&G} TI EB, Kttl XL0d"G)
avtfj l'6rj TI EZ, xal ETt^v^G) ^fjZB. A.y(O) ott,
TI pv Zz/
dfxay&vov ftitlv
dlBZ20 V&Zci
Kata to E, xal 7tQO<5Xi,ta tig avtfi t
,tb V710 t&V FZ XCCl Zz/ 3tOl%6[lVOV
1. Ij^oofifv] %oo- e corr. C 3. t&v} t- e corr. D. 3.
] lHftCt%lQl6ll%'K B, COrT. in [LSTCC%lQioilld'Cl D 3.
Zgriaope&'a] corr. ex j^TjacbfisO'a: C 2. 5. STL] post e- ras. 1
litt. D. re] r- ins. D 3. 8. SLCC^QSL C. 10. 8j] eras. D.
11. AJT] e corr. D. ^(pr.)] corr. ex A D 3. 13. dufc&a D.
15. &reev# >
a> rj]mut. in ini&vi&tiGriis rfjs B 3
; tTtt&vx&siGrjs
r^g, -si- e corr., D. xca] om. D, eras. B. 16. avx^\ u>v\ttvxfn. A,corr. in ravrrjt C 3
. xat 17. ZB] supra scr. D 2. 16.
corr. ex m&v%Q'cQ C 2. 17. ZB] Z in ras. A.
seq. ras. 1 litt. A. 17]in ras. D 3
. 18. dwaymvov]e corr. D 3
. 19. EZ] B- in ras. BC 3,ZE D. 21. E] seq.
ras. 1 litt. C. 22. FZ] F in ras. D 8. o^otycbvtov A.
MA0HMATIKHS STNTASESS A'. 33
VLOV {isra rov ajtb rijg Ed TETQaycnvov i'6ov
TG) ano rijg EZ rer^ayava) [Eucl. II, 6], TOVTSGTIV
t& aitb Tijg BE, fasl fay 0rlv % EB T% ZE. dUaT& ebro Tijg EB tsryaycovG) face i<5xl ret aitb r&v
E4 xal 4B TSTQaycova [Euel. 1,47]' TO ago. VTtb rCbv 5
JTZ xal Zz/ 7CQie%6^svov oQ&o'yawov pera rov
tfi /IE rsTQayavov foov ttixiv rotg CCTCO t&v
4B TSTQay&vois. xccl xowov oupcuQS&svrog rov aitb
rijs EJ rergccyavov Aoinbv TO vno r&v FZ xal Zz/
faov i<5tlv TK> aitb Trig z/5, rovrsGriv T& aito rijg 10
jATf)ZF ago, &KQOV xccl pzGov Aoyov rsr^rai, xara
TO z/ [Eucl. VI def. 3]. licel ovv % rov Qayavov xal
$1 rov dsxay&vov nkevQa r&v slg rov avrbv xvxkov
fyyQacpo^isvov Inl rr\g avrfjg sv&stag axoov xal [istiov
Myov TfyvovTai [Eucl. XIII7 9], ij
ds FJ sx rov 15
XZVTQOV ov6a rr^v rov sfcay&vov xeQi,8%i nkevQav
[Eucl. IV, 15 coroll.], % JZ aga 6rlv fay ry rov
dexaytivov itfavga. b^ioicog de, eitsl ^ TOV TtevTaya)-
vov TckzvQa dvvarai, rr^v rs TOV s^aycbvov xal ri\v rov
dsxay&vov r&v sig TOV avrbv xvxhov syy^acpo^svov 20
[Eucl. XIII, 10], rov ds B4Z ooftoycoviov TO anb
1. (Ltsra rov &-] in ras. C. EJ] 4E D. SGTIV] iozi B,om. D. 2. TOO Tovrf'trrtv] ins. B 3
,om. C. rovrsGri B.
3. TW] corr. ex TO C 3. ITISL] mut. in snsiSijnsQ D 3
. 19 EB]supra scr. D 3
. 4. TW] corr. ex TO C 3. ZGTLV D. TO] corr.
ex TO C 3. 5. TfTQccycovct] comp. supra scr. D 3
. 7. z/E]Ed D. sGxi B. 8. JB~] noil JB D. xvcQuywvoi,<s. xat]supra scr. D 3
. 9. TSTgaymvov] ins. D 3. TO] seq. ras. 1
litt. D. vno] v- e corr. D 3. r&v] corr. ex r& C. Zzf| Z
ins;C.
?
10. Tw(pr.)] corr. ex TO B 2 C 3 11. ZF] corr. ex ZI C 3.
O.QCC] &QCC fv&ffa D. 12. ^] z/. V.KI IGIIV TO [iiov TfifjfJia
TO 4T D. ^J supra scr. A 2,ins. B 3
. 13. elg] e corr. C 2,
corr. ex iv. B 2. 14. yyQ<xcpo[iva>v] pr. y supra scr. A 2
. 17.
i'cri EGTLV D.
Ptolemaeus, ed. Heiberg. 3
34 KAATAIOT IITOAEMAIOT
BZ rerodycovov fcov i&r\v rip re anb rrjg
ijris etirlv e^aycbvov ntevQK, xal red ccnb rrjs
[Eucl. I7 47], iJTis e6rlv dexcry&vov Tttevgd, j]
BZagcc fay etirlv rfj rov nevrayavov TtAevoa.
5 Inel ovv, fog Etpyv, vitori&e[ied'a ri)v rov xvxkov
didperaov r^^idrov (w, yiverai 8ia ra
ftfi/ JE riyLfasia. ov6a rijg ex rov KBVXQOV
A xal rb an' avrfig % % de BJ ex rov xevraov ov6a
rpyiJidrcov | xctl rb cutb avrfjs y%, rb de anb r^g EB,10 rovreGnv rb anb rijs EZ, r&v enl rb ccvrb ficp' prjxet,
aacc etirccirjEZ riirjpdr&v % d Ise eyyidrcc, xal Aomf]
ijz/Z r&v ccvr&v AJ d ve. y aoa rov dexccyavov
vitoreiVovGcc de xeoKpeoeiav roiovr&v AST, ot'ov
6 xvxAos r%, roiovr&v etirai AJ d ve^ oicov ^15 diaperyog lyx. ita'kiv eitel pey z/Z r^rj^idrcov e&rl
AJ d ~ve, rb de Kitb Kvri\g proe d If, eGrt, de xal rb
anb rijs 4B r&v avrcbv y%, a Gvvre&evrcc noiel rb
anb ri}s BZ rerodyavov fi^oe d If, prjxet, ccoa
1. foov] supra scr. D 3. 2. ^aycovov ntevQa] in ras. A,
3. sW B. 4. for] icTiv D. TOV] supra scr. D 3. 5. fW]
inc. fol. 15 alia manu D.I'qprjv] mut. in scpcciiev B 3
,sed
euan. 8. &n'] ano B. BJ] J P, A in ras., C 3. OVGCC]
om.D. 9. <bro(pr.)] A, an BCD. 10. EZ] corr. ex E D.11. ma] A, l<nv BCD.
?j] ins. C 3. EZ] corr. ex ESJ D.
Post fyytdro: add. / C, mg. (pro scholio): '/ $6ri ds noif)
4E A,''. 12. ^Z] corr. ex z/S D. 13. TOIOVTCOV] -a>v e
corr. C. orcov] -to- corr. ex o C 3. 14. TOWVTCOV] corr. ex
roiovTOV C 3. I'ffrat] conip. B, omnibus litteris mg. B 2
;simi-
liter saepius; seq. ras. D. d] ins. D 3. ol'wv~\ corr. ex otov C 3
.
15. SidfjLerQos] ante p ras. 1 litt. A. ndliiv 16. Vs~\ BD,mg. A 3
(xElfievoy) et pro scholio C. 15. fast] ds ind A 3.
serf] IGTIV D, comp. BC. 16. ccno] an D. if] inter t
et s ras. A, mg. yp. xiF A 2, supra c scr. # B 2
. ^CTtv D. 17.
4B] BJ D. TWJ/] corr. ex TW A 2. tVMf^wa] alt. v supra
scr. D 3. 18. BZ] supra Z ras. D. If] supra e scr. tf B 2
,
in ras. D. Supra fiTy/tft ras. D.
MA0HMATIKHS STNTAjEjE&S A'. 35
fjBZ rprjiadrcov o~ A/3 y fyyitira. xal
r\rov itsvra-
yCOVOV aoa ItkeVQK, V7COrlVOV0a ds [lOlQag Oj3, OICOV
i6x\v 6 xvxhog T|, roiovrcav 6rlv o A/3 y, otoi/17
did[iroog (W' cpavfobv ds avr6d"sv, on xalr\
rov
thevQa, vitorsivovda d poioac; |, ^tftfiy 5
roi) xevroov r^rj^iKrcov stfrlv |. o^ioicog
fti/ TOV TSTQccyavov TttevQK, vitorstvovGa
ds poiQccs 9, 8vvK[iei, diithccGLa edrlv rrjs & rov
xevrgov, % ds rov roiy&vov ntevocc, vitoreCvovtiu de
[loioas ^jc, dvvd[it, rrjs avrifc fanv rQnthatifaV) rb 10
ds outb rrjg IK rov xevrgov rprjfUxTtov 6rlv j
6srca rb psv ccnb rr^Q rov rsroccycovova
rb $ alto ri]g rov rgiy&vov Mw. codrs xal
ply rag 9 poiQag vitoreCvov6a sv&slcc roiovrcw
3rd va I iyyitircc, oi&v $ di,d[isrQog ^3c, fjds r&g ~QX 15
r&v avr&v ~gy ve wy.
aids [isv ovr&g J][LIV sx 7too%iQov xal xa&' avrag
sttri<pd'C()6av.lxal 6rai, cpavfobv svrsv&sv, on, r&v
didoyiVG)v sv&fi&v | v%oovg didovrai xal ai vytb
rag 2,iitov6ag eig rb fj[juxvxAiov itSQicpfOfiag vitorsi- 20
1. o A|3J ol|3
C. 2. o|3] supra rasuram D 3. 4. to'] ^s
xat D. xat] om. D. 5. [taigas] n AB, ut saepe; [tD semper
fere. 8. [taigas'] ft ABC, ft D. 9uf3Laelcc] mut. in dmlaGicovB 8
,8inlK6ia>v D. 9. TOV] TO LGontevgov D. 12. roi)] om. D.
13. d^] d' D. TOW] om. D. rgiymvov] rgi- in ras. D.
M] C, corr. ex MAB 2, jt corr. ex
ft- post ras. 7 litt. D 3;
a'eo
add. mg. C 3. 15. fyytora] -ffra add. D 3
. 17. Post pe'i; add.
ovv comp. C 2. 18. Ante Y.CCL ras. 4 litt. D. carat] corr. ex
(m D 3,
mut. in fWco B 2. ^vrcD^ev] avto&tv, supra auro-
ras., D. r&v 8i8o^v(ov] Si8oy.v(ov r&v edd.; sed genetiuusreconditiore quodam modo a Hfinovoas TtsgiysQeias pendet.
19. af] supra scr. B 2 C 2.
36 KAATAIOT 11TOAEMAIOT
vov6ai did TO TO. an* avT&v 6vvTLd~^va itoiiv TO
dnb Tils diayiETQOV TfTgdy&vov olov, %id^ f]{)7tb
Tag AS: [loigag v&ia T{ir][idTG)v fdffy&r] Af d v xal
TO dri* avTfjs aTO dZ*f,
TO $ dnb Tfjta
5 T[ir]iidTG)v 6Tlv Mydv, 6Tai xal TO ^iV dito
TCCQ foiitovdas iS to YULIXVX"a
TKIV koiTt&v Myxd v ^i, avTri dl[IYJXEI, TCOV
avt&v Qid Af fyyiGTcC) xal itl T&V cckk&v oftoto^.
OV $ TQ07COV CUtO TOVTG3V Xttl CCi AoiJtCll T&V XCiTK
10 llQO$ dofrtflSOVTCil,, dl%OllV Cp%iiS 7tQOXd'[lV
IICCTLOV fVXQqGTOV ttdw JtQOS tV\V TtCiQOVtiaV
TV%OV TO ABT/1, xal 7t^v^G)6av KL AT xal
15 8iXTOV, OTL TO VTtO T&V AT XCil B4OQ&O'yajviov i'Gov Ifal 6vvct[i<poT()oi,s TK> T vitb xCbv
AB, 4F xal T<p vnb T&V Ad, BF. xffa&o yag TTJ
vitb T&V 4BF y&via l6r\ % vnb ABE. lav ovv XOIVYJV
TtQoG&Gbiiw xty bitb EB4, <5Tai xal % vito AB420 y&via fay TT} V7tb EBF. 6Tiv dl xal % vnb B4A
2. olov] corr. ex otcov B SC. 4. is] supra s scr. S B 2
. 5.
JVf] corr. ex ft A, IIVQL e corr. D 3. 6. /notices] ft mut. in ft A 2
.
a od1. M] corr. ex ft A 2
, ftv^t e corr. D 3. j] corr. ex d D 3
.
jiff] supra scr. s B 2. 8. /l] supra scr. g B 2
. 9. Jioiicat]
-01- e corr. C 2. r&v~\ om. B. 11. navv] om. B. 13. Mg.
ZT^/LUX BC. 14. -cv%6v\ om. D. AP~\ corr. ex AEP D.
15. deiKTSov --Bdi\ supra scr. D 3
. ort] ovv on D 3.
16. TC^ corr. ex TO C 2. 17. A B, z/f
1
]e corr. D. rw] corr.
ex r&v D. xc^^ca 18. AET\ supra scr. D 3. 18. x&v]
om. D 3.
17] supra scr. D 3. Post ABE add. Inel ovv icy
sc-clv r) (supra scr. D 3) vnb 4BP ymvlu ty vnb ABE D et mg.
pro scholio BC; V- add. C 3. ovv] om. D, del. C.
MA0HMAT1KHS 1TNTASE&2 A'. 37
TTJ vnb BFE fay [Eucl. 111,21]' TO yap CCVTO
vnoTtvov6iv' faoy&viov KQK etirlv rb ABATO) BFE TQiytbvoj. coGxe xccl
avcttoyov i6nv, &s n BF ngbg
Tr}v FE, OVT&S YJBzJ ngbg iv\v 5
z/A [Eucl. VI, 4]* rb KQCC vnb
B4, FE [Eucl. VI, 16].
sitsl far} 6xlvfj VTCO ABE yavia
tri faito 4BF ycovitt) S&TIV ds xal 10
v]vnb BAE fay tr\ VTCO B4F, Itioy&viov CCQCC farlv
ro ABE rgCycovov ro5 BF^d TQiyavc)' av&KQyQv
6Tiv, K>S i\BA XQOS AE) f)
B4 Jt^bg 4F' TO
vnb BA, AT faov farlv T& vnb B4, AE.de xal TO vnb BF, AA foov r& vnb B4, FE' xctl 15
[Eucl. II, 1] &QK TO vnb AF, B4 faov
rc5 TS vnb AB^ 4F xal T& vnb
BF' onsg sdfi det^cu.
TOVTOV nQOXT&VTos 6TO r}^ixvxhov TO ABF4Inl dicc^LTQov T^s AA, xal anb TOV A dvo dirftftca- 20
3. ro5] e corr. D 3. 5. ryv (alt.)] om. D. 7. ET] T&V
FB D.'
8. BJ] 4B C, r&v BJ corr. ex rb BJ D 3. 10.
ycovia] om. D. 11. -no BJF -- 12. TQiycovov] mg. B 1.
11. tcoymviov 12. T^tycbvw] mg. C 3. 11. tari C 3
, comp. B.12. ABE] BAE C 3
. rwj'corr. ex no B 1
,ex TO D 3
. EFz/]BdP BC 3
. rptycbvra] TQiywvmvou etiam in textu C. 14. AnteBA ins. r&v D 3
. Jr] TA D. leti B. rw] corr. ex ro D 3.
AE] EA D. 15. to] corr. ex TW B^ 3.
"
vno (pr.)] vnbT&V E 1 D. EF vno] om. C.
'
BF TE] mg. B 1
,in
textu ras. 4 litt. ET, AJ] B4, FE B 1 D. IGOV\ -ov in
ras. A 2. TW] corr. ex ro D 3
. Ez/, FE] T&V BF, AJ B^.16. AF] T&V AF D. taxi D. 17. cvvcc(i(poT^QOtg] G- corr.
ex v in scrib. D. J F] F4 D. 18. BF] FB D. 19.
TOVTO rb ftemQrjiJicc Y.CC&' vn8QO%r]v tiyercci. mg. B pro scholio^,
y mg. D. 20. A] seq. ras. 1 litt. B.
38 KAATAIOT HTOAEMAIOT
<5av ai AB, A F, xal 6TG) xaT$a avT&v do&ftGa
^t, oicov-Y] did[iTQOs do&t<5a pjc, xal
BF. Af'yo), OTI xal avTri dsdoTai.
ai Bz/, FJ'5 aga sltilv dyhovoTi
dia TO keCrtsiv BXBLV&V sis
sjtsl ovv iv
0TIV TO
TO aga VTCO AB, JTz/ [iTa TOV
10 vrtb T&V A z/, BF foov IGTLV
TG) vnb AF, Bz/. xaC i6nv TO
T vnb T&V AF^BJ do&ev xal TO vnb AB, F4' xal
hoinbv aga TO vnb Ad, BF do&v itixiv. xai
A z/ didpfTQOs' do&i0a aga i&tlv xal ^ BF15 xal <pavQbv fj[itv yfyovsv, ort, av doft&Giv dvo
(pBQiai xal ai vn avTas vd"ia^ 8o%~i6a k'GTai xalf]
iv\v vnsQOfflv Toby dvo TtfQHpfQsicdv vnoTsivovtia sv&ia.
drfiov df, OTI dia TOVTOV TOV ^C3Qr^iaTog aMas T ovx
v&ias fyyodipoiiw anb T&V v Tats xa&
1. CIVT&V] om. D. 2. px] supra scr. D 1. 4. Bz/] corr.
ex BA C 3. 5. CCQCC stow] om. D. 8. xstQd.nte'VQOv] -ulvv-
supra ras. 2 litt. D. 9. &QCC] supra scr. D. Post vno add.
T&V D 3. 10. r&v] om. D. BT] B e corr. B. 11. BJ]
B4 d C, 4B D. V.KL 12. Softtv] BD, mg. C 3,
om. A.
11. SGTLV D, comp. B. 12. ]om. A. r&v AT, B4]
AB, TA D. xat] So&sv -AuC AC, doftsv & %ca A 3. AB,
AT, B4 D. 13. ^0-9-^ KGTIV] -v del. C, SGTLV SO&EV D.
t] ins. D 3. eariv] mut. in txi B 3
,Iti D. 14. Post
add. dofrsiGa B 1 C 2. fffrtV] EGTCCL D. 16. ai VTC']
corr. ex en' D 3. do&eiGcc tcrcci] do&siGcci &GIV tGrca do-
&EIGK D. SGTCCL] mut. in cofft C a. 17. vnsQo^riv] post 9
ras. 1 litt. A. 18. ort] on KCLI D. TF] mg. B 1. ovx] in
ras. B 1. 19. 6Myu$] -U'y- in ras. D 3
. iyy^dipo^v'] pr. yin ras. D 3
. need' ccvrdg] xar' KVTCC$ D.
MA0HMATIKHS 2TNTASE&S A'. 39
vnEQO%G)v xal dy xal ryv vnb rag
EnEidynEQ E^O^IEV ryv rs vnb rag f xal ryvvnb rag o/3.
nahv ngoxEfad-G) do&Efayg rwbg Ev&eiag EV xvxAa) ryvvnb rb ypiGv ryg vnorsivopEvyg nsQupEosiag svd'Etav 5
svQEiv. xal 0ro ypixvxfaov rb ABF snl dtapEroov ryg
AT xal do&Eltia ev&eia y T5,xal y FB nQi<pQt,a 8%a rs-
^J tpijtid'C) xara rb d, xal ine-
^Evyfiodttv at AB, Ad, Bd, 10
EZP dT, xal dnb rov d Inl r^vAT xd&srog y%&n y JZ.
onr\ZF ruiiGEia i6ri ryg r&v AB xal AT VTCSQ-
xefa&G) yap trfjjAB fay % AE, xal site-
17AE. STtsl i'6rj farlv
r\AB rfi AE, xoivri 15
derj Ad, dvo drj ai AB, Ad dvo ralg AE,
Ad faai, sfalv ExarsQa sxarsQa. xal y&vta % vitb
BAd y&via rfi vnb EAd fay 6rw [Eucl. 111,27]-
xal fidtiig aga % Bd flaGsi rfi dE fay idriv [Eucl.
I, 4]. aUa % Bd ry dP fay itixiv xal y dT aga 20
ry dE fay iGtCv. litsl ovv faoGxEfovg ovrog rQt,y&-
vov rov dET aito ryg xoov<pyg litl ryv fi&Giv xd&Erog
1. dedofitvoov] dedopevais D, -atg eras. dcbfoxa] t|3D.
2. floras] ^ vTtorsLVOVGUV D. 3. Post o{3 add. o D, onegi'du Ssi^ai D 3
. 4. 8 mg. D. e&Q-efag nvog D. 5. vno\v- e corr. D. 6. xat] om. D. 7. 8v&efa r) FB xat] ins. D 3
.
FB] BT D. 10. at] om. C. 13. lanv D. 16. AB]BA D. dvo] Svel D. AE] EA D. 17. frca] COIT. exi'scc D. SKCCTSQCC] seq. ras. 3 litt. B. 18. BAJ] corr. exABT D 3
. SGTLV 20. SGTLV] mg. B 1. 19. xat] om. D.
I 20. IGTIV] om. C. 19. IGTIV i'cj} B. 20. &Ud]-AKL BD. JT] rj D. faq SGTLV] A, tcriv IGT] BD.
Seq. v.a.1 17 JT KQK xy JE IGJ\ SGTLV mg. B 1
,del. B 2
. J F]J D. 22. JEF] FJE D.
40 KAATAIOT UTOAEMAIOT
fyrai % z/Z, fay farlv % EZ if} ZT [Eucl. I, 26].
dU' $ ET <tty fj vnQO%ri <snv r&v AB xal ATv&i,G)v fj agcc ZF fififaeid &6nv rijg r&v avrcov
avro&V dsdorai xali\
fatnovtia fig rb
f] AB, fa&ifocmu, xal % ZJT rmfaziK ovtia.
T&V AT xal AB V7tgo%ri<s. aW fad iv op-O-o-
TCO ATA XK&&OV iigftf&tyg rijg z/Z faoycbviov
rb AAT QQftoy&viQv t& z/TZ [Eucl. VI, 8],
10 KKL <5TiV) ag % AT xgbg TA, rjTd JtQog FZ, TO
KQa vnb r&v AT^TZ, 3tQi%6iJivov ogftoycbviov faov
<5rlv r& anb ryg TA rsTQay&v(p. do&lv dl TO vnb
r&v AT, FZ' do&v KQK 6mv nccl TO anb ri\g JTz/
tsrQdy&vov. &6r xul [IIJXM f) Td v&Za. do&
15 rv\v rjiii6i,av vnoTfivovGcc tr\g BT 7tQi(pQiag.teal dia rovrov drj ndhv rov &coQtfiiaTog
re Arjcpd-ujtiovrai, nfatGrcci, xata rag ruLi6eiag rav
toV) xal dq xal anb ri\g rag t/3 {lOigag vitorei-
vvfruag ijre vnb rag g xal $ vnb rag y xal
20 ^ vnb rv\v \iiav r^iiev xali\ vnb rb ijiiuSv rsrccgrov
x rcbv
2. ccUd D. 4. v&Las~\ f-v&sius do&eicris I 5. vno-
xetftfVrjg] del. D. Supra scr. 77701 dfdo^vris B 2, Ssdo^svrjs
mg. C 2. dsdoTca] corr. ex dtdorai, D. 6. Ante pr. 7)
ras. 1
litt. D. xu] postea ins. D 3. 7. &m'] om. D. 8. TW
ATJ] vgiymva TOO AJF D. 9. A AT] ATJ D. z/TZ]FJZ corr. ex JZ D 3
. 10. FJ (alt.)] mut. in 4T C 3. 11.
Vcov] add. D 3. 12. do&sv d -- 14. TeTQctytovov] om. A.
12. fo'] dt 86TIV D. 13. rZ] FZ m^Mf^HNK)* D. 15. TTjVJe corr. A. BF] e corr. D 8
. TteQicpeQfias] -g e corr. C T
7CQl(pQiag 07tQ $81, Sti&l D. 16. mg. D. 17. 7tQOK-n&fufvcav D. 19. ?] ?| B. 20. ijpLGv (utrumque)] comp.BD. TO] rrjv D. T^TQI^TOV] d' D (similia posthac nonnotabo).
MA0HMATIKHS ZTNTASE&S A'. 41
ti\v plv vnb T^V ^Cav ij^iav poigav roiovr&v a Atf Is
tyyiGta, oiov failvv\ diaperyog px, T^V ds vnb TO
i' d' T&V avT&v o ^ ^.
TtdkiV 6TG) XVX&OS 6 ABF4 1tQl dlK{lST()OV [LV
TYJV A/l, XSVTQOV $ TO Z, XCll KltQ tOV A CC7CeL^(f>^G)- 5
Gctv dvo itSQKpeQficci, doftstGcu xara rb ^rjg ccC
AB, BT vn' ccvrag
xal ccvral ddo^f
vat.
OTi, CCV ltt&V%G)llV TJJV 10
AT, 8o&Yi<5TUi xai avrij.
y&Q dice TOV B did-
TOV Kvxkovri BZ.E,
xal iit^vffiKttiav ai
^ KVTO&W, OTL dice
FE, dice d rfv ABxal dia Ta avTa
15
TO
FE, 4E' d^ovTyv BT do&rj<5Tat, xal
0Taiij
TS B4 xalYJ
[HtQ06&V ,fad V XVX&G)
BF4E, xal diriyyiBvai ffolv aC B4, FE, TO vitb T&V
diyyiLWCOV 7tQi%6n,VOV OoftoyCOViOV I'GOV (5T\V 6VVa[l- 20
(poTQOig Totg V7cb T&V artfvavTiov &6T, fjtfl dfdo-
[ivov TOV vjtb T&V B4, FE dsdoTKi xal TO vitb
T&V BF, 4E, ddoTai aoa xal TO vxb BE, F4. $-
1. Supra a scr. tvog B 3. 2. TO] tr\v D. 3. /_']
in
ras. A. o] A, o BCD, ovdev comp. A 3D 3. 7. tni&vi&co-
CKv BC; 7ti,&v\ D, -05" add. D 3. 8. ev&stca] corr. ex ev-
&SIKS D 3. 12. did] KTCO D. 14. tm&vx&coGav BC. 15.
JT] TA D. Sri] ds D. CCVTO&SV] post -6- del. i C. did]in ras. D 3
. 16. doQ"r\GtTcu (alt.)] SoQ-ijcovccci D. 17. rd] corr.
ex T D 3. 18. lv\ -v in ras. D 3
. 19. BJ, FE] in ras. A.20. lathi] -v eras. D. 21. vno] v- in ras. D 3
. 22. BJ]BT C. direct] corr. ex dCSorcti D 3
. 23. BT] mut. in B4 C 8;
BE, PzJ supra scr. D 3. dsdorca (pr.) FJ] om. D.
$s-] mg. A 1. SsSorai (alt.)] dedovrca D, sed v eras.
42 KAATAIOT DTOAEMAIOT
ds xalfjBE did^TQog, xal Aowr?) rj
F4],
xal dia TOVTO xalrj
tefaovGa ig TO
FA' tiers,
eav dofr&Gw dvo itQi<pQiKi xal
at vrt' avTag ev&stKi,, dod-tfGsrcci, xal ^ 0vva^i(poTQag
5 rag TtfQiyfQfiag xara GvvfttGiv vnorswovcfcc sv&SLa
dt: rovrov rov ^sco^^aros.
(pccvsgbv df, on Gwriftivrts ad psTa r&v xgoex-
T&l[ieVG)V 7tCi<55)V 1T]V VJtO tfjV CC [_'
6vvcc7tTO[ivcts STtikoyi^oiisvoi, TtccGag c
10 otiai dig yivoyisvai tgCrov [ifyog f|ov(?tv, xal \i6vai h'n
at ^,ra^v rcbv ava a [_'
dvo xa&' ZxaGrov i^Q^Bvai^ f
lOV^B^K t^V ty'yQKyijV. K)<JT, KV
TJJV VTtO TO fllLllLOlQlOV V&iaV VQG){lV, KVTr] KttTtt
15 TB xv\v 6vv&<5iv KOI tv\v vit^Q^v t^v agog Tag Ta
diaGTtfiiaTa 7tQL%ov6ag xal dtdoiiwag i>&iag xal
Tag hoiTtag Tag pTav TtaGag iftLw GvvavaitkriQ&Gsi.
7ti df dofafarjg Tivbg v&iag &g Tijg vitb TYJV a i'
{lOLQaV i\TO TQITQV Tf}g aVT^g 7tQl<p()iag V7COTlVOV0a
20 dia T&V yQa^iii&v ov didoTcti Tt&g' i de y dvvaTov
i\v, l'%0{Lv av avTo&v xal TYJV vitb TO
1. 8s] corr. ex SL D 3. AotTrrj] r\ loinri A. Deinde add.
KQK D s. 17] BC, rj vTtb rfv AD, vnb rrjV eras. D. 3. FA]
AT onsQ fSst, dsti-ui D. 4. vno D. do&iJGETtti] corr. ex
SoQ"f\60vi;cii D 3. 6. rovrov] rov rovrov C, om. D. roi;] rov
roiovrov D. 7. H mg. D et in textu D 2. 8s] mut. in Stf
B 3D 3. nQOwri&Epsvcav D. 9. cvvaTtro^vccg] -n- in ras. D 3
.
^yypai/)Ofifv] pr. y in ras. D 3. 10. ooui] corr. ex oa ai C 2D 3
.
ysvopevat, D. 11. 7ieQifaicpd"}J6ovr<xL] corr. ex neQdr](pd"i]-Govrcci C 2D 3
. r&v] post ras. 3 litt. D. 13. xa^'] %al xa-91'
D.
14. ccvrr]] BC 2, avrfi A et corr. in avrri D, avrij C. 15.
rag] corr. ex rd A. 16. dsdo^vag] -fte- supra scr. A 1.
17. rag (alt.)] xcu rag corr. ex xara D. 19. fioiQav] sic AC.
7) TO] corr. ex r\roi D. rfjs ccvrrj?] corr. ex rfjs D 3. 20.
SCSorai] dsdorai corr. ex dsdcorui D.
MA0HMATIKHS ZTNTASE&S A'. 43
rqv V7to ri]v cc {LOLQCCV onto rs
vnb rqv cc // JIOIQCCV xccl rr^g vitb // d' vno^l^evoi
o, xav pr} ytQog rb xa&ohov dvvrjrcci, rag
6(Hn/, iiti y rG)v ovrcog &a%farcov rb
off rag G)Qi6^evag aitaQdMccxrov dvvair' av 6vvrr]Qtv. 5
hey& YKQ, on, lav v XVX^G) dta^wedvo fv-O-ftat, rj H,%G)V nabg rqv ikaGGova
%i r[itQ $ 7tl rijg [ifftovog v&Lag
ri]v 7tl ri\g fhaGGovog.
6 ABT4, xal dt,tj%&G)6*av iv avrci) 10
dvo sv&siai aviGoi, ttdtiGov {ikv fj AB, ^ifi^cov dfr\
BF. Af^o, on,i\FB v&ta
6ova Aoyov %i, rjrtfQ r\BF
\ T~J
itQicpQi,a itgbg rr^v BA TCSQL- 15
tpQi,av. rfriitJG&G) yap rjvnb
ABF y&vCa dC%ct vitb ri\g
B4, xal 7t%v%d'G)6av r\r
/i AEF xai $ Ad xalr\
T4.
xal 7tdj]
vjtb ABF ycovia di%a rr^irjrai vitb 20
1. fJLS&oSsvGo^ifv^ corr. ex [if&odfvGaiifv C 2. 2.
om. D. vno] vnb TO D. 3. Iri^drtov] -n- in ras. A.
corr. ex ju-ot C 3. 4. nr{Liv.orr\ra.^\ corr. ex
f^a^tdrajv] corr. ex iKd^iGtov C 3. 5.
corr. ex ci)Qi6\[iva$ A 1. _ SVVUIT' &v~] dvvarai D. 6.
mg. BC. avtaoi, 8vo~] |3&VIGOL D. 7. slaGGova (pr.)] ante v
ras. 2 litt. A. ^CCGGOVK (alt.)] AD, om. BC, add. C 3 et mg. B 1.
8. (Ltf^ovoff] -g in ras. D 3. 9. 7rt] ccito B. sldrrovos D.
11. KViGOi ev&stccL D. 12. FB] BT D. 13. KQOS 15.
7CQL<pQicc] mg. B X C 3. 13. fv&fLccv] om. B*D. sUdrrovcc C.
14. i]7tQ] r\ C 3. Br] FB B X D. 15. TCQOS 7tQi(peQi,av~\
et in textu C et in mg. C 3. 16. ? mg. D. 17. Sfya ycovi'a D.
20. Y.ai fTTft 7CL OVV D.
44 KAATAIOT HTOAEMAIOT
A /I [Eucl. Ill, 26, 29], JWI&DV 6*rjTE tfg EA
[Eucl. VI, 3]. %<& d?) arco TOV z/
T?)f AEP 1] z/Z. rfl roivvv ^et'fwv
v4z/ T% J5z/, ^ 6* .EJz/ Ttjg z/Z, 6
5 TCO z/, 6^<m?fi<m ds ro5 z/.B
xv\v i&v A z/ r[iet) tinsgnzGstreet, ds r^v z/Z.
y&G) dij 6 HE, xal sxfiep^&G) i\ z/Z@. xal
6 /ni> 4E Topsvs iizifav <5rlv rov
TO ^ 4EA tQiy&VOV ILlt,QV tOV 4EH TOllS&g, TO
10 (>a z/JZ tQiy&vov TCQOS TO 4EA TQiycovov skdti-
tiovcc Adyov ^t ^() 6 4E Toptvs JCQOS rov /IEH.AA' wg f*v TO z/Z T^t'/covov ^po^ TO JEA r$iy&-
vov, ovr&g $ EZ ev&stcc agog r^v EA [Eucl. VI, 1],
cbg df 6 /IE ro[ivs agog rbv A'EH TOftf'a, ovr&s
15 ^ vnb Z.4E y&via Ttgbg r^v bito EA A'r\ aga ZE
sv&sta agog ryv EA &K<56ovK hoyov Zyjti iJ7tQ 17
VTCO Zz/.E y&via itgbs ryv vitb EA A. xal 6vv&vri,
aga i\ZA ev&ia itgbs rqv EA hd06ovcc koyov %t,
r^nQ YI VTCO Zz/A y&via 7t$bg rr^v vnb AAE' KOI
20 rCbv fiyoviLW&v roc diTthaGicC) f]FA v&tcc ngog rr\v
AE ttaGGova Myov %i ijjtfQ i]vnb TAA y&via
4. 6 ago] 6 a- e corr. D 2. ju-fV] om. D. 5.
8ii] Y.a.1 8i.a6Triu.an D. 6. re(ifr] corr. ex rspvei D. zf Z]corr. ex AZ B 1
,AZ C. 7. HE] corr. ex E<9 D, supra
ras. 1 litt. xai tnEi] end ovv D. 8. iaxCv 9. jLtfi^ov]
supra scr. D 3(fcrt). 10. To Z/EZ a(>a TQiycovov KQOS rbv
4E@ rofiEcc skdrrova koyov %i ijnfQ rb 4EA rgfycovov KQOSrbv JEH rofiscc
'
IvaUa.!- mg. pro scholio B et nonnullis uerbis
recisis C. JEA rQiyavov] A? arQiycovov D. 11. Ante Adyovras. 1 litt. A. 12. rgCycovov (alt.)] om. D. 13. EA} AE B,corr. B 1
. 14. rofif'a] om. D. 15. Post pr. VTCO ras. 1 litt. C.
16.?)]
add. D 3. 17. Zz/E vno] supra scr. D 3
. EJA]E4A ycovfav D. 20. FA] FA &QCC D. 21. FJA] seq.ras. 1 litt. A.
MA0HMATIKHS STNTABE&S A'. 45
vnb EAA' xal diMvn17FE v&ta jrpog rrjv EA
koyov %t, ijjfQ f)vito FAE yovicc TCQOS xr\v
vitb EA A. AA' &$ {ilv ^ FE ev&fiK itgbs rqv EA,ovras rj
FB ev&etcc TCQog rr^v BA [Eucl. VI, 3], o>g df
^ VTtb FAB y&vCa TCQOS rr\v vitb BAA, ovt&s i\FB TISQI- 5
<p$Lcc xgbg rv\v BA [Eucl. VI, 33]' r\FB agcc fv&tfa
agog ryv BA IkaGGova Aoyov %i, i]7tQ i\FB TISQL-
BA 7tQi(pQl,CCV.
rovrov drj ovv vitoxt,[ivov
6 ABF, xal di- 10
iv CCVTCO dvO V&tai
ijT AB XCil
f} AF, V7tOXL6&0)
$ 71Q&XQV fj {LBV AB VTtO-
Tivov6cc [nag [IOIQCCS [_' d', fj
dl AF polQav cc. fad % AF 15
5? rriv BAf\AF
, 1]$ AF 7tQl(pQl,a faiTQlTOS StiXlV t^ AB, fj
FA ago, v&ia ri]g BA ttaGGcov 6rlvTI sitiTQirog.
aMai\AB v&ia dL%&r] roiovT&v o ^ ^, oi&v 20
0TtVYj dld[JLTQO$ ^' fj KQK FA V&lC
i<5xlv r&v avrCbv a/3
v' TCCVTCC y&Q fatrQitd
xGbv o 7.
1. E4A] A4E D. SiflovTi 1^] Sielovrrii D, i suprascr. D 3
. 3. E4A] A e corr. C 2. ev&eiK] om. D. 4.
tv&Eia] om. D. 5. rj (pr.)] om. C. BJA]-Be corr. D 3.
6. TTJV 7. TtQOs] mg. B 1. 6. r]
1. EA} add. C 2. 8.
TtSQLCptQSWV OTttQ dtl (Hdtl D 3) SfL^Cii D. 9. ^ mg. D. OVV^
om. D. 13.TJ jLteV] [isv i] D. 14. fuas] supra scr. D 8
.
15. a] mut. in ar D 3. 17.
TJ] supra scr. A4,om. C. Mg.
TO IfipiLu pro scholio BC. 20. o] o C, ut saepius. 21. PA]AT D. 22. snuQicTu C. 23. rj] supra scr. D 3
.
46 KAATAIOT HTOAEMATOT
Ildfav itl rrlg avri]g xarayQayfis r\ plv ABsv&eta vitoxeiG&K) vitorswovtia potQav a, ^ de ATyLolgav a l_'. Kara ra avrd d^ iitsl
$\AT iteQuplgEia
rtfg AB <5riv ^fuoAla, r\FA aga SV&SIK r^g BA
5 &d66G)v 6rlv rj fiiiiofaos. aM.a rqv ATTOIOVTGJV oi)0ccv a Ad tf, otcov 6rlv
v\
f] aga AB sv&stcc [isifcv stirlv r&v avr&v &($!>'
rovr&v yaQ i^iMid sdnv rot TCQOXS^SVCC a Ad Is.
attire, sjtsl r&v avt&v edsfyftrj xal {istfav xal
10 ^ Tfjv \iiav \HQigav vitorsCvovtia i>&ta, xal
dri^ovon f^opsv TOIOVT&V afi
v fyyiGTa, oicov 6rlv
rj did{itQog ^c, xal dia ra nQodtSsiyptva xal r^v
vitb rb fitiiiioiQiov, rjrtg VQi6xsrai, robv avr&v o A,a xs
lyyiGttt. xal 6vvava7tA.r)()K)d")]<)rai, ra Aoiitd) cos
15 diatirtfiiara x y&v rijg TCQQS rr^v yiiav rjiiitiv
Aoyov svXv cos snl rov TtQ&rov diaGrtfiiaros 6vv-
rov fuiiyioiQiov duxvvyiBvris ryg vnb rag ($
x d rijs vnQO%ijs rijs XQOS rag ~y fto^a?
xal rfjs VTtb rag /3 L' didop&njs' caGavr&s dl xal 7tl
20 rcbv koiitcbv.
% [itv ovv TtQayparsCa rfbv iv rep xvxAa)
ovrag dv oi[iai gatira iira%eiQi6&siYi. iva df, cag
3. nsQLCpSQSia 5. AP] mg. D 3
(ttc^teyop).4.
lanv D 3. FA &ga\ AP D 3
. B A] AB D 3. 6. ovoav] supra
scr. D. 7. AB] BA D. 8. 5 Ad I?] corr. ex ^1 dls D 3.
9. coffr' D. 12. TtQOvnodfSsiyiiEvci D. 14. tog f'qpa^ev TCC
loiita. D. 16. itQwrov] corr. ex a D 3. cvvftsofas] I) (-? e
corr.), TVJS 6vv&s6(o$ ABC. 19. xat (pr.)] eras. D. 22. <Jf]
8' D. Iqprjv] corr. ex f'qprj C 2, I'qprj B.
MA0HMATIKH2 STNTASESS A'. 47
ExaGTrjg T&V %QEI&V f'J Itofyov rag
TG)V EV&El&V EXXEljJLEVCCg ,XCCVOVHX
dva 6Ti%ovg [IE dice TO GVJJLHETQOV, (bv TCC [IEV Tt
i, Tag nyfaxoTrjTccg r&v rtQi,(pQ(,G)v
7tccQrjv%rjHEvccs, ra de devrsga rag t&v 5
TQircc TO X iifyog Tf}g Haft1
ExatiTov tyupofyiov T&V
iva E%OVTS xccl Tyv TOV vbg
adiayogovGccv TCQOS ai'6d"rj6iv 10
vs xcci T&V ^ETCC^V TOV
Tag 7ti,f:lccM,ov6ag
aiiEd-a. EvxciTavorjTOv d\ ort dia T&V KVT&V xai
)XCCV V dltiTCCyilGJ yEVG)^L8^(X,
itQi Tiva T&V iv T& xaroviq) nagcc- 15
xfipEvcov V&LG)V) QttdCav TCOirj^o^fQ'a TIJV TE s&xal Tr\v EitavoQ&coGLV T^TOI catb Trjg vitb T^V
Tijg Eiti,r}TOviiEvr]g 7) Tqg TtQog aMccg Tivag T&V
vx()o%ijg tj Tijg Tr\v faiTtovGav eig TO
EQHpEQEiaV V7tOTEl,VOV6rjg EV&ELCCg. KKl 0TIV fj20
TOV XCCVOVIOV XCCTayQCCCpfj TOlCCVTlf]'
1. %QeiO)v~] mut. in wqastov D 3. 3. ava] ins. D 3
.
,-i- corr. ex o, D. 5. r]iii[i6
l
Qiov D. 6.
-is e corr. C. 8. i'] I ABC, TQICCKOGTOV D.
D. 9. LVO.f^ovrfg]
bis D, sed corr. 10.
QOVGCCV] mut. in adiacpoQOvs &v A 2. ccl'ad"r}6iv] -GIV in ras. B 1
.
11. e etoifiov] om. C. 12. ETCi^aUovGccs'] -ni- in ras. B 2.
13. dvvd^u BC. *'] 3s D. 14. ysvo^cc C. 16. rijv]
TJ extr. lin. A, T^V A 4. 20. nut IGTLV] tonv ds D. 21.
ij D. XUVTJ] D.
48 KAATAIOT HTOAEMAIOT
ia'. Kctvoviov
TT
MA0HMATIKH2 2TNTABE&S A'. 49
tp /
50 KAATAIOT HTOAEMAIOT
Q81WV
MA0HMATIKHZ! 2TNTABE&2 A'. 51
A
52 KAATAIOT HTOAJEMAIOT
*W -
MA0EMATIKHS STNTAEESS A'. 53
vt.ll
54 KAATAIOT HTOAEMAIOT
QSl&V
MA0HMATIKHS A'. 55
It
56 KAATAIOT HTOAEMAIOT
Qfl&V
MA0HMATIKHS A'. 57
tflL'
58 KAATAIOT HTOAEMAIOT
QGiiov
MA0HMATIKHS ZTNTAgESS A'. 59
QXS
60 KAATAIOT HTOAEMAIOT
TtfQMpB-OiO)V
MA0HMATIKHS STNTASE&S A'. 61
9PtL'
62 KAATAIOT HTOAEMAIOT
QfLtOV
MA0HMATIKHZ STNTASE&2 A'. 63
P
64 KAATAIOT HTOAEMAIOT
Tils iiTa%v T&V TQOTCLX&V
r} Trjs TtqfaxoTrjTOs T&V iv Tip
7CQ&TOV KV ^ XK&KltGQ /JtO^
6 Ao|6g xal dta [ifa&v T&V Jradtov xvxhos
5 XQOS rbv far][iQiv6v, rovrfarw tCva Aoyov %i, 6
a7toha[ipccvo[ivr]v afaov [iTa%v r&v
rtQi,(pQiav, fi fcr]v CCTC^L drjAovori, xal rcov
XCCTQOV <5riiLeiG)v rb xara rbv fariyiQiv6v.
10 d9
fiinZv rb roiovrov dgyavixcbg xara^cc^ftccvrca
TWOS ccrtAij
&l, TTOQVV[lVOVo5 xQrjGonf&a [i6r]ii{lQiv(p dt,&6vTs CCVTOV fig TCC vito-
15 Xl'[lVCC TOV [lyi6TOV XVX&OV T[MJlt,CCTa T% Xttl TOVTCOV
) 1$ 00K tyx&Qft ^Q^' 7tlTK TQOV XVX-
TOV lQrj[lVOV VKQll66aVTSCCVT&V 7tl /Lttg [lVl,V
)A,VTG)S VTtO TOV
20 dvvaG&ai TOV &d66ova xvxhov iv red
7tQOS ttQKTOVg T
dvo TLV&V xccTa did^TQov TprjuccTcov TOV
XVX&OV XCCTCC TfjS TOCiS TG)V
1. t^'] om. AD. Ti]s] corr. ex r&v D 3. 3.
corr. ex slnco^sv B. 4. t&v] om. D. JyK&dijrca C, corr. C 3.
8. J] r/ A. 9. TO] mut. in td D 3. 10. diuKa^KVsrai D.
12. TTE $1 Karcc6H8vfig mg. B, xaTaaxfu^g mg. C. 14. w] e
corr. B, T77g TCSQicpegsfas <j>D. 18. (isv jtitag]
bis C, sedcorr. Post psveiv del. B. 22. xara] r&v Kara D, r&vins. B 8
. 23. XVH^OV] xvxZtffxov D. TCQLGfidna] mut. in
C 3, Trqy^arta corr. ex nQiypaxiK D 1
.
MA0HMATIKHS STNTABE&S A'. 65
fact vEvovrcc itobg ccMrjAcc re xccl rb XEVTQOV rcbv
xvx&cw axQificag itccQa&EVTEg Kara peGov rov rthccrovg
ccvr&v yvojiovicc keitrcc Gwdrtrovrcc rr\ TOV
XCCI dlTlQ^EVOV XVX&OV TtkEVQK. 0V dij XCcl
GCCVTEg CC6<pcdG)g ETtl TG)V TtttQ SXCCtira %Q(,&V Eltl 5
Grvkfaxov GVIIIISTQOV xal xarcctirriGavrss EV VTtcci&QG)
rr^v rov Gxvkfaxov ficcGiv iv axfovst agog rb rov 6^t-
Ertfasdov edutpei 7tccQa(pvhtt%oiisV) o'jrcjg rb iiti-
rcbv xvx^cov 7tgbs [IEV rb rov do^ovrog OQ&OV
f],Tc5 df rov iLE6ri^QLVOv TtccQaMqhov rovrcov ds rb 10
IIEV TtQOTEQOV tilCl XCC&ETIOV ^E^odEVE
pV Kitb rov xara xogvyviv EGOJJLEVOV
IIEVOV df, ECOS av EX rijs r&v V
ETtl rb xccra diccpEroov itoiijd'rjTat, ri\v nQoGvEvGiv^ rb
$ dEVTEQOV ILEGyilflQLVilS yQCC^l^S V6^^l(DS f^A^ftftfV^^ 15
EV r& vnb rbv 6rvM<5xov EitiitedG) xccl Tt
fts ra itkuyia, r&v xvxAcov, &$ civ
'yQa^fl rb EitiTtEdov avrcbv diOTtTEvrjrcci. roiavrrjg d^
rijg &E6E&S 'yivo^iEvrjg rr]Qov[iv rr\v ytobg ccoxrovg
xccl [i6r]ii(}QiKv rov r\Mov 7tccQcc%c()or]6i,v TtaocccpEQOvrES 20
iv rcclg (lEGyppQicug rbv svrbg xvxMdxoV) Ecog av rb
vTCoxccro TtgiGiidriov oAov vcp' oAov rov
1. L'GK] xal i'aa D. 2. fifoov] corr. ex (iscov D 3. 3.
ovLcc Isnra GVV-] supra scr. D 3. 4. IvaQfioaavrss] corr.
ex svccQii6ovi;$ D 3. TctQi ftsceoog mg. BC. 6. xaracrTjaav-
rsg] KccQ'iGTdv'tEs D- 7. &^ivsi * et mg. ^? (h. e. nccQ-
ccUrilG)) B. 9. TO] supra scr. D 3. 10. Post $ ras. 1 litt. D.
11. y.QT]pvKiLvov\ B 2D 3, KQi(jLva[iEvov ABCD. 12. arHietov]
corr. ex Gr\\isiov C 2. 13. &v\ a extr. lin. A, corr. A 4
. vno-
BD, corr. B 2. 15. svc^fifjioos C.
16. 7tCCQ<X(pSQO[lVa)v] CD, TtSQICpZQOllSVOOV A XB. 18. TCSQL
^Tjcecog mg. BC. 21. (iG7](iQivcas D, sed corr. 22. TtQiGpd-
riov] mut. in m^y^d-ciov C 3; nriy^driov , r\
e corr., D. TOV]corr. ex r6 D 8
.
Ptolemaeus, ed Heiberg. 5
66 . KAATAIOT HTOAEMAIOT
xal rovrov yivQ^ivQv disdrjucuvsv r}{iiv ra
rS)v yvwiiovicov axoa^ notice r^j^iara rov xara xoov-
tpriv xa6roT rb rov r\Mov XWTOOV acpsGrrjxsv 7cl
TOV urtqiipgivov.
5 ri> ds v%arj6T6raov ertoioviie&a xv\v roiavrrjv
xaTcujxsvKticcvres ccvrl rcov KVK^CDV
xfav&idcc TeTQccycwov xal a
xccl
10 nvl Ttgbs ifi [M& i&v y&vi&v fyQK^a^ifv xvx&ov
cbro TOV xara rb xwrgov
tQi(pQ{ccs rag tr^v
vn r t^agtri^oQLOV OQ"\v ycoviav itQL%ov6ccs
v&iccs xal diA6vtg oiioi&s r^v 3tQt,q)Qi,av slg rag
15 9 poiQag xal ra rovrav [iQr]. pera df ravra 7tl
yuK<$ T&V v&i,G)v rfjg [iA,A,ov6r]g oQd"f}g re
Ttgbg rb rov OQ^ovrog 7tfadov xal TtQog
rv\v &<5iv ^LV [i7toA,faavTg OQ&a xal L'6a
dvo xvMvdQiK jjuxaa xara rb OJIOLOV rToovv^iva^ Tb
20 /iv 7t avrov rov xara TO XBVTQOV Grftisiov Jtol avrb
TO pfaov axQip&g, rb $ Jtgbg ro5 xdro nsQan rijg
1. 6mK6&j}~\ 6- euan. A. difcrjpavsv corr. in
vsv D 3. 2. yv(o\n6v(ov D. 5. Ttegl HUT<x6KSvfi$
mg. BC. 8v%QT]GTOTQKv D. 6. Aifi"t]vr]v B. 7.
BCD, corr. D 3. Kid.6'tQoyov~\ A, add. sv (om. D)
Ttldrsi y.al fidftu itgbs to ^f^Tjx/vat KKTK ngoTKcpov BD, et mg.pro scholio C (offica <jqpa/l/ta add. eadem manu). 8. ano-
r\TET<xiLvr]v D. 10. lyQcctyKiisv] 79- in ras. A. 11. xfV-
TQOV D. 12. Grjfjisiov] corr. ex Grjptiov C. rag] suprascr. A 1
. 14. dif-ttvTsg] corr. ex. diEl&ovres B 2C. 15. enl]
Kara. D. 16. [iehov6r]$ D. TE eaec&cci] ri&eG&ai D. 17.
3rpdg(pr.) yiat] om. B, mg. C 3. 18. fynoliiGuvTEs] mut. in
EV7toUGK\TS B 3,
SVETlQlr\6&.\LW D. 19. Y.vMv8QlCi] post Veras, n D. opoiov] o- ins. D 3
.
MA0HMATIKHS STNTASEaS A'. 67
rv\v secr
ttfavgav itaga xv\v ev rc5
rr\v ft&iv TG> TOV
V EitiTtedcp, xal XK&STIG) dice t&v
ts xal 6^-9-^v XQOS TO snfaedov rov
jv di' avt&v ev&etav axgiflovvTsg VTto&spaTi&v ita
kem&v TO svds'ov diOQ&oviisvwv Tr]Qov[iv
iv Talg }i6rj^ftQLCCLs Tr\v aitb TOV agog rc3
KEVTQCp KvklvdQLOV yiVQ^ivY\V 6KLKV 7tCCQaTl,d'VTg 11 10
/
yQK^svrj ytQi<pGQ8ia XQog TO xaTadr}-
TOV T07COV <p(X,lV6d'ai KCcl TCCVT^g TO
6ypwvpevot> TO HUT' KVTOV TH^CC Tqg TOV
itl TOV ii6rj[ipQivov nagodov 15
TOV fjMov.
in drj T&V TOIOVT&V jrccQCCTrjQiJGfcav xcci iidAiGTct
TCQV itol Tag TQonag avTag V\\LIV KVCCKQWOIISVGW iitl
nteiovag 7tQiodovg TO, face Kai TCI CCVTCC T[nj[iaTcc TOV
v nvxhov ncd XCCTK Tag &Qi,vag TQOitag xal 20
Tag %iiiQivag T^g 6rj[iid)6G)g cog iitiitav anb
TOV xaTa xoQv<pf}v dTtoAappavovGrjg 6r^iiov xaTfAafio-
[i&a TYJV dnb TOV POQMOTKTOV TtBQUTog iitl TO VOTLCO-
TCCTOV 7tQlCpQiaV, iJTig 0TiVf] [IfTa^V TG)V TQOTtM&V
1. TtEQti &GCQS mg. BC. 3. yQcc^iijv C. 5. KvMvSqmv D,
deinde del. KKQifaZ TS xat. 6. unlivf)] &y.UvftH
D. ra]
postea ins. D. 7. ndUv" riv&v B. 8. ten-lav] in ras. D,JiSTtrov BC. itQi %gr}G(o<s mg. BC. 9. wGavtoog] o^otoog D.
rb y.tvxgov D. 10. xvMvdQOv D. 13. avrov] avro seq.ras. 1 litt. D. 14. dicca^atvov] d- in ras. A. 17. dij] posteains. B. 20. xara] supra scr. A 1
. 21. cog] supra scr. A. 22.
v]t A.
corr. ex arnistov C, supra scr. D 3. 24. TteQitpfysiv A.
sett A. rj] supra scr. A 1. T^oTttxwv] r- postea ins. C.
68 KAATAIOT UTOAEMAIOT
,Ttavrore yivQ\Livv\v ^ xctl peC&vog [lev TJ
arog, elaGGovog de fjiifoovg rerdgrov,
dt ov tivvayerai 6%edbv 6 avrbg Adyog rc5 rov 'Ega-
roG&svovs, c5 xal 6f
'IrtJtaQ%os 6vve%g^ato5 yap TOiovtcDv 1^ psto&V r&v tQOTtiK&v Ice
OLCOV 6Tiv 6 n,6rjit,($()ivbs ivy.
ds avro&sv ex ri^s itgoxsLiisvrj
Keel ra r&v oiMJ6(ov, v cclg av
rag rriQt]6i,s^ fyKJUpaxtt ^CC^KVO^VCOV tov re
10 percc^v Grftieiov r&v dvo nfyccrcov, b yiverou, Kara rbv
,xal rijg ^era^v rovrov re xal rov xara
ov TteQicpeQeCag, i] fayv d^Aovdrt nal ot
7t6Aoi, rov bgt&vros a
eig rag
15 'AKokovftov d' ovrog ajtodet^cu xal rag xccrcc
rcbv a7t
V percc^v rov re l^rj^eQivov xal rov dia
r&v Jcadtov xvxAov rcbv yQafpo^e
dice r&v rov farnieQivov nohov
20 paria pQa%ea xal ev^ri^ra^ di' cav rag itkeitirag 6%edbvrcbv GcpaiQM&g fteooovnevcw, &g em
xal iie&odix&reQOV TCoirjGope&a.
eig dvo di) ev&eCag rag AB xal AT
2. Se] Ss ij D. 3. TOT] TO C. 5. peragv] -|- posteains. C. 13. Trolot] TroHo/C. 14. ty'] C, yt B, om. AD.
15. ovros] -v- ins. D 3. 17. pscov D. 21. GcpaiQiK&v
D, supra scr. ccpSQM&g &ea>Qov[iva)v D 3. 23.
eig dvo dij] postea ins. D. a' A^/u-^cc evftvygauiiov KKTCC ovv-
mg. BC.
MA0HMATIKHS 2TNTAEE&S A'. 69
dvo sv&slai,
TO Zrs BE Kal
r\TA rspvsrcoGav a
on, b rijg TA jtobg AE Adyog Gvvrinrai SK
rs vov tils Td TtQog 4Z Kal rov rijg ZB JtQog BE.
yaa dice rov E TTJ TAefaw ai TA Kal EH, 6 rijg FA
itabg EA Adyog 6 avrog s6nv r&
rijg TA xabg EH [Eucl. VI, 4].
sv $i]ZA' 6 aoa rijg TA
EH Adyog 6vyKi[ivog sGrai, 10
SK rs rov rijg TA Jtgbg z/Z Kal
rov rijg A'Z nabg HE' &6rs Kal
6 rijg FA itgbg AE Adyog
Ksirai SK rs rov rijg TAz/Z Kal rov rijg z/Z itobg HE. 15
ds Kal 6 rijg z/Z Ttobg HE Adyog 6 avrbg ro5
ZB xabg BE [Eucl. VI, 4] dt,a rb naoaMrjAovgslvai rag EH Kal ZA' 6 aga rijg FA itabg AE
Adyog (SvyKSirau SK rs rov rijg TA Ttobg z/Z Kal rov
rijg ZB Ttabg BE' oitsa xaosKSiro dsl^ai. 20
Kara ra avra d dsi^^srai, on Kal Kara diai-
Q6iv b rijg FE agog EA Adyog Gvvrptrai SK rs rov
rijg FZ Jtobg A 2, Kal rov rijg AB nabg BA, dia rov
A rri EB jrapaAA^'Aov ^O^tfiyg Kal itQO<5eKfttri&siting
sit avrr^v rijg F4H. sitsl yag ttdkiv TtaQa&hrjAog 25
1. FJ] AT D. 7. EA\ AE D. 9. ilfr&w SE] wlD. 10. TCQOS] corr. ex TTQO D 3
. 11. zfZ] Z4 D.
12. z/Z] Zz/ D. HE] EH D. 15. HE] EH D. 16.
HE] EH D. 17. ZB] E Z D. 20. ZE] BZ D. 21.
l7)ti[ici vccra Siuigtaiv mg. BC. 23. z/Z] Zz/ D. z/E] Ez/JB mg. D 3
. 24. rfj] seq. ras. 1 litt. B.
D. 25. Fz/H] corr. ex Fz/ D 3
70 KAATAIOT HTOAEMAIOT
Z47 AH Tfi EZ, eGTiv, cog i\
FZ xabg ZH [Eucl. VI, 2]. aUa
Aaiifiavo[ivrig 6 Tijg FZ itobg
ZH Adyog Gvyxeircti ex re rov
5 Tf}g FZ rtobg Z4 xal rov Trjg
z/Z Ttgbg ZH' 6nv d 6 ri\g
4Z rtQbg ZH Ad/og 6 avrbg
TK> Trig 4B nabg BA dia TO
fig Jtaoahkrjhovg rag AH xal
10 ZB dirjx&ctt, rag BA xal ZH'6 aga rrjg FZ agog ZH Adyog Gwrptrai ex re rov
rrig FZ TtQog z/Z xal rov Trjg 4B nobg BA. akka
T& rr^g FZ ytobg ZH koycp b avrog etiTiv b r^g FEagog EA' xal 6 Trjg FE aoa Jtobg EA Ad/og Gvy-
15 X(,TUI, x re rov rrjg FZ JtQog 4Z xal rov ri}$
JiQog BA' ojfeo edei det^ai,.
Ttdfov e6TG) xvxhog b ABF,ov xe'vraov TO z/, xal ft'A^'gpO'Gj
ejtl Tr^g ftSQiysQsfas uvrov rv-
20 %6vra, TQia Grftifta ra A, 5, P,
&6rs exaTs'gav T&V AB, B F7tQi<peQei,(bv &a66ova eivca f]p>i-
TO
25 opoiov vTtaxovsGd'G)' xal 7t&v%d'G}6av atAFxal zJEB.
QOS] bis D. 3. la^avo^ivr]?} corr.
"D. 6. JZ] ZJ D. 12. JZ]
D, JB mg. D 3. 14. Mat EA] om.
rr. ex A D 3.
1. ry\ rfjg BC. 2.
ex laiijlapoiisvrig B 2. ngo
ZJ D. JB]BC. EA (alt.)] corr. ex A D 3
. 15. TZ rfjs] mg. A 1.
TZ] ZT D. 4Z] ZJ D. 16. faeg ?8ei d%cu] om. D.
17. y' JUjfApa wAlwov mg. BC. 20. id] om. D. 24. Za^t-
^avo/n^ajv] ^, corr. ex f D. 25. ofioiov] avro corr. ex avrS) D.
at] bis C.
MA0HMATIKHS 2TNTASE&2 A'. 71
cog
rtQt,(p()iag ftgbg rr\v vjtb r^v diTtAijv rrjg -B-T*,
ngbg rrjv EF sv&etccv.
KK&STQI aitb rwv A xccl Fre AZ xal % FH. exsl
AZ rf) FH, xal diijxTcci, stg ccvrag sv&elcc, ^
AEF, l<5tiv, cog % AZ agog r^v FH, ovrog % AEagog EF [Eucl. VI, 4]. aU' 6 ccvrog tenv H6yog 6
rrjg AZ agog FH xcci tijg VTCQ r^v ntKv\v rqg ABagog rr\v tinb tyr diitlr^v rrjg BF' ^(i- 10
arQcc xccrQccg' KK\ 6 rilg AE CCQK agogEF k6yog 6 avr6g 6nvAB Ttgbg rr\v bitb r^v dirtkrjv rfjg BF' ortQ
on, xccv do&G)6iv ijrs AF oArj 15
7tQlCpQl,K KOi 6 Ad/0? 6 Tljg
rr\v 8iitfa]v rijg AB itgb$
vnb rrp> diTthijv r^g BF,ca xccl BKKTBQK r&v AB
KOI BF 7CQl,(pQL&V. XT&t- 20
faet&tybm % Ad, xccl
rov z/ xa&Tog 7tl xr\v AEF rjz/Z. on
ovv rr\g AF TteQicpegsiag do&i'6yg ijT vnb
1. rfjg 2. BF] mg. BC 3, rf]s BT etiam in textu BC.
3. KOS supra scr. D 3. 6. ev&Efa] con*, ex SV&BLKS D. 8.
6 (alt.)] om. D. 9. rrjg (pr.)] corr. ex
supra scr. D. 12. ET] trjv EF D.13. EF] FB D. oni-Q t'dsi de^ca] supra scr. D 3
. 14. #']
comp. ins. D 3. 15. AT] corr. ex FA D 3
. Post oKj] del.
17D 3
. 17. tjv] r- e corr. C. 18. BF] corr. ex FB D 3. 19.
%ca] ins. D 3. 23. ^4EF] corr. ex z/EF BC 2
.
EF] xj\v ET D.
tr\ D 3. 10.
72 KAATAIOT HTOAEMAIOT
ia rr\v f)[ifaiav avrr\g vnorftvovtia
xal o'Aov to A4Z TQiycovov, dijjAov 7tl d\ TTJS AFi)&as o'A^g ddo[ivr]s vitoxsirai xal 6 rfjg AE TCQO<S
EF Aoyog b avrbg G)v TG) rijg vnb tr^v dt^Aijv rijs
5 AB Ttgbg rrjv vnb rr\v dntki]v rrls BF, ijT AE
6rai do&t6a [dat. 7] xal Aomr} ijZE. xal dia
rovro xal rijg z/Z dfdo^vr^s So&ritiexai xalij
t vitb
E4Z y&via rov E4Z ogfroycovtov xal 6'A^ ^ vnb
10 hoiJtii i]BF' 07tQ fdft, dft^at.
6 ABF 1tQtl XVTQOV TO ^/,
avrov tttjg)&G) tgCa Gr]iiia
A, By .T, &6t XaTQaV t&V AB^ AF 7tQl,<pQeiG)V
r
dvai rmixvxMov' xal 7tl T&V
15 fiavo[iVG)v jtQKpQi&v to opoiov VTtaxovfa&G)'
Im&vx&tfGai, ijT dA xal % FB
0V[l7tl,7CTT(06aV XaTfX TO E 6rj[ltOV.
xal
xal
1. seq. ras. 1 lilt. D. 2. zgiyavov] TQiycovovD. Se] Ss nat D. 3. 6] supra scr. D 3
. AE~]seq. ras. 3 litt. D. 5. BT] PE D. 6. ZE] EZ, E in
ras., D. 7. dedo[itvr)s\ alt. 8 supra scr. D 3. 8. yeoWa rov
Ez/Z] om. D. 10. oneQ I'^t de%ai] om. D. 11. ABP]ATE D. Mg. TQLTOV tcbv Kvy.foH&v B 3
. 12. cr\^icc\ 6r]\[Licc,
post r\ras. 1 litt., A. 13. &GXE 15. vnanovsGO'ca] om. D.
13. Supra AT scr. ET C 2. 16. tnifcvtd'Bfate D. FBI
BTD.
MA0HMATIKHS 2TNTASE&S A'. 73
,on iGtiv, cog j]
VTCO r^v diitkifo rijg PAagog x^v vitb r^v diTt^v rife AB, ovrcog
rjrE v&tcc TtQbg rfv BE.
opoicog yo\Q TOO itgorspG) A^ftftarlip, lav cbto tcbv Bxccl F a'yd'y&iisv xa&srovg enl rrjv 4A t^v rs BZ 5
xal rrjv FH, serai dux rb xaQKMrjAovs atiras elvai,
<&g ^ FH rtQO$ xrp> BZ, ovt&s r\FE it$bs rrp> EB
[Eucl. VI? 4] CO&TS xcu', cog ^ vitb iv\v dtjrAijv Tr^g FAXQOS rfv vnb ryv dnt^v ri\g AB, ovrcog % FE vtgbg
ity EB' oitQ sdst, defeat,. 10
xccl VTav&cc ds ccvrod-sv TCccQaxo^ovd'
j]FB 7tQi(pQicc ^oV?; do&rjj xccl 6 Adyog 6 rijg v
rijg FA TtQbg xr\v VTtb rv\v
AB do^, xcclr]AB 7iQi(pBQia dod"rJ6rai.
pay ml rfjg o^otccg xccTCfyQCKprig &tt{&vg$E40tyg rijg 4B 15
xccl xcc&tov a%&far]g iitl r^v BF rijg z/Z ^ plv
1. FA] AT D. 2. ovTcog] corr. ex ov-coo A 1. 4. yap]
om. BC. 6. IWat] om. D. 7. cog] yivsrai cog D. 17 (pr.)]ins. D 3
. BZ] ZB D. w^og tr\v\ TCQOS corr. ex JT^O D 8.
8. cbg] supra scr. D 3. 10. onsg i'^ft ^i|at] o>: AC,
7tQicpQiciv comp. B, om. D. 11. ?' mg. A.<5e']
^' D.12. ^] ^ Tf D. ^o^^] Sod-sir] D. 6 (pr.)] om. D. 13.
rryg (pr.) SmJLfjv] ins. B 3. FA] -A in ras. A. FA -
14. ^B(pr.)] supra scr. C 2. 13. TIQOS rijv] con-, ex TIQ < D 3
.
14.^JB(pr.)]
etiam in textu C. ^o^] del. B 3, do^Tjafrat D.
doQ"iJGT<xi] om. D.
74 KAlATAIOT nTOAEMAIOT
V7tb .Bz/Z y&vi'a rrjv rjufaeiav vnoreCvovGa rijg BF7tQi(paiag farat dsdo[ivr]' xal o'Aov CCQCC rb B4Z
7Ci df %al O r rijg FE TtQOg rfjV EBdtdorau xal ert % FB v&eta, do&?j6rat, xal
ij
5 r EB xccl f'rt (U?? ^ EBZ' nets xat, fad % z/Z
dfdorat^ 60fhfott& xcclij
rs V7tb E4Z YGWLK rov
avrov oQ&o'ycDviov xai Aown) ^ vnb E4B. G)6T xal
f\ABrovrav
10 iitwpv.VBt<t peyfatcdv KVX&COV ttQMpfyucu, &6T fig dvo
rag AB xal AF dvo ygcKpffaag rag BE nccl
Tiiviv aMtffag Kara, rb Z 6qiitov' fara) $
avrcbv ttaGGcov f][iixvKMov' rb d$ avrb xal iitl
r&v uarayQatp&v vitaKovfa&G).
15 AS'^GJ drf) on, 6 ry\g vnb rqv diTt^v rtfg FEcpQiag rtgbg ryv VTCO rr\v dnt^r\v rijg EA Aoyog
GvviJTtrai, ex r rov rijg i)ttb ryv ^nt^v rijg FZagog ryv vnb r$\v diithriv rrjg Zz/ xal rov rijg VTCO
rr}v dntkriv rijg 4B xobg rty vnb r^v diTt^v rijg BA.20 fttrjcp&a) yaQ rb Kwrgov rijg GtpaiQag xal faro rb
H, xal riffiotiav aitb rov H 7ti rag jB, Z, E ropagr&v KVX&CW
ijr HB xal % HZ xal
i\ HE, xai iiti-
A4 MfcfttiJGd'G) ual 6vu,7tiittrci) rri HBxal avrr] Kara rb S GrjUEiov, b^,oiG)g df
2. ago] supra scr. D 3. 3. oQ&oyojviov] Tglycovov D. 5.
0>CT KCCL, STCEi] &Gt' STtSl %CCi D. 7. OQ&OyCQviov] TQiydiVOV D.9. 'frfcbjji^a Kuta, dicciQEOW mg. B. 11. y^aqoftWg] corr.
ex yQK<p&i6ag C 2. 12. GT^JLBLOV'] om. D. 13. sldrrcov D.
] d' D. 14. vifaKovtG&G)'] vnci-Aov^cQ-co T\\LIV D. 16. rrjg- 17. dmtfiv] D, mg. A 4BC 3
, KSL'HI-VOV add. B 3. 16. EA]E4 B, y. so. B 3
. 18. vnb r^(pr.)] bis A. 21. ccnb rov H] an'ccvrov D. B,Z,E]BEZ D. 22.
rj (pr.)] om. BC. xat (tert.)]
$' Y.KI D.
MA0HMATIKHS STNTAJSEBS A'. 75
at 4F xal AT r^ivr(D0ccv rag HZ ncii
HE Kara rb K xal Ara 6> K A
7tl
dia rb v dvtilv
ivai l-jtumdoLS r<p r
rov AF4 roiy&vov 5
nal r(p rov BZExvxkov
, ijns Xi-
fev%&l6a 7tOll t<$
dvo Ev&Mag ras A%al FA diiyyiizvas 10
ras A xal
xata rb K Gyiietov' 6 CCQK rijs FA 7iQO$ AA6vvi\7trKi K r rov rijs ^K TIQOS K4 xal rov
rris 4 TtQbg A [p. 69, 21]. AA' fog [tv ^ FA 15
agog AA, ovrcog f] vrtb rrjv di7tA.ijv rijg FE ngbvitb rqv dinkey ri}$ EA 7tQi(pBQiag^ &$ ds ^ FK
, ovr&s n VTTO rr\v dirtArjv rife FZ 7tQi<pQCa.
vitb ryv diTt^v rfjs Zz/ [p. 70, 17], cbg
, ovrog 3}VTCO ryv dnt^v rfjs 4B 7tQi(pQLag yfQog 20
vjfb ryv dinkey x^BA [p. 72, 11]' xal 6 Ad^o? KQK 6
rijg VTtb r^v 8ntkv\v rijs FE itgbs rrjv vitb rrjv diithijv
rijs EA Gvvijjtrai, X r rov rijs vitb r^v dmAijv rijs FZ1. at] supra scr. C 3
. AP] corr. ex AT C 3. 2. TO]
to. D. GruieiK D. 8v&ia$ yivstca D. 3. Sid] coinp. B,di B 3
. 7. txievxfatocc] ante G ras. 2 litt. A. 11. A]corr. ex OA D 3
. 15. FA] corr. ex Fz/ D. 17. vno] suprascr. D. TTJV] supra scr. D 3
. EA] EA corr. ex Ed B,EA mg. B 8
. 18. K4] corr. ex KA B 3C 8. 19. Zzf]
AT. D. J] AC, corr. ex 4 B 2,A C 3 D. 20. AE -
21. r?)g] om. B, mg. C 3,8(ft mg. B
3. 20. Trfetg^tag] om. C 3
.
21. TTfc] corr. ex TT) D 3. rfjg BA] mg. C 3 alio atramento. 22.
Tfj? (pr.)] om. D. vTto (alt.)] e corr. D 3. 24. Ante E^
ras. 1 litt. A.
76 KAATAIOT nTOAEMAIOT
nobs rr\v vnb rrjv Si7tki]v rr}s Zz/ xal rov rijs vnb rrjv
dinkey rijs z/JB nobs rrjv vnb ri\v dinAijv rr^g BA.xara ra avra drj xccl (otineo enl rijs smnsdov
xara'yQcc(pijs r&v sv&si&v [p. 68, 23] dsfavvrai,, on5 Keel 6 Tifc vnb rv\v dnt^v ir\<$ PA TCQOS tv\v vjtb xv\v
EA A.6yos 6vviJ7tTai, x re rov T^S vnb
rijs F4 nobs tv\v vitb vfjv dnt^v r^g
xai rov rrjs vnb rqv dnt^v rijs Z5 ^6? ryv vnb
rqv diJt^v rijg BE' OCKZQ nooexeiro
10 id'. JIs^l r&v [israkv rov itiqiisoivov xal rov
Ao|oi) KVKhoV 3tOl(pQSl,G)V.
Tovrov dij rov frscaorjiiaros rtoosxrs&siiisvov noirjGo-
K itQcbrrjv rqv r&v noox6i,[jLSva)v TtsoKpsoEi&v ano-
ovrcog.
15 farm yao 6 di'
rcbv jt6A,G)v rov rs
xal rov dice yitG&v r&v
xvxhos 6 ABF4 xal rb
rov farjusoivov rj[it,xvxA,t,ov rb
20 AEP, rb ds rov dia [isticov r&v
%GtdiG)v rb BE4, rb dsEv\
xara r^v ICCQLV^V
avrcov roily, &6re rb pey B %iinBQLvbv rgonixov ELVCU,
rb ds 4 &Qiv6v, efaijy&a) ds Inl rys ABF
2. TTJS dB 8nt\i]v} supra scr. D 3. ij\v vno] postea
ins. A 1. 3. dij~\ de D. xal co<>-] in ras. A. 4. on] corr.
ex 8i6n D 3. 7. dutlrjv (alt.)] -i- corr. ex
7]A. 8. //Z] Z4 D.
9. TtQQSMiTo] corr. ex nQOHSi-cai TO D 3. 10. i'~\ C, dt,
~
om. AD. nsgi 11. 7teQicpQi&v~\ mg. D 3. 10. rov (pr.)] TOV
re D 3. 12. dj] om. D. 13. rr?Y] om. D. 23. TO] xai to D.
elvui roniKov D.
MAOHMATIKHS STNTASE&2 A'. 77
6 ;rcUo TOV AEF l6r]^i0ivov xal eGto TO Zxccl aitfiA.rjyd'G) r)
EH 7tOi(pOicc rov dice [leG&v rcov
XVXkoV T[ir][lKTG)V VTlOXEL^BVYl A, Oi&V 0TiV 6
xvxhog T|, dice ds TCOV Z, H yfypagpO'ca yLsyfarov
XVX&OV JtQi(pQiCC fj ZJFf, Xdi JtQOXi6&G) 1T\V H 5
sv^elv. jtQOi^cpd'oo dq xai Bvtav&a xccl
7tl Ttadcov r&v d^oiov dsC&ov,f
iva
tavrokoywyiGv , oVt, orccv tag
1tQi(pQiCOV tyV&iG)V
,00G)V
7tl [lV TC3V 1tQiCpQiCOV TOiOVT&V (pa^lSV^ 10
fjrov peyfarov Kvukov rtQi(pQia r[ii][idra)v
T|, 7Ci d r&V V&iG)V TOiOVTCOV, QlKtVJ] TOV XVX&OV
7ti tOiVVV V KCCWyQCCCpfi {IfyiGTCOV KVXk&V iS
dvo ras A2> xcd AE 7tOi(pOiccs y^Qcc^^vca efal 15
dvo ij re Z xai i\ EB rfyvovGcci aMtjAccs Kara TO
H, 6 rils VTtb rr\v dnt^v rr\g ZA Myog Jtobg rr\v
VTtb ri\v diTthrjv r^g AB (SwiJTCraif
x r rov rijg vjib
rr^v diTtAijv rfjg Z ycobg rr^v vito TTJV dirthijv rrjg
&H xal TOV Trjg V7tb tr\v diTt^v rijg HE ycobg rrjv 20
vnb TTJV dixMlv Trig EB [p. 76, 3]. odXr\ [iv rijg
ZA 7tQiCpQlttg SiltM] U,OiQK)V 6TiV ~Q7t XCCir]
VJt
avrr)v v&icc T^^idTCov ^c, ^ d ri]g AB dirtki] xccra
TOV 6v[i7t(pa)vr]ii8'vov [p. 68? 4] v\\jiiv r&v ny ycobg ra
Ta k6yov poiocbv [i ft/3 ^ ? r\d' vit avTr)v Ev&sia. 25
~iwj ha v, xal itdfovr\ pev ri]g HE
6. 8r\] ds D. 9. dctv\ slot in ras. 1 litt. B 3. 10.
ij]
supra scr. D 3. 11. 17 T^Tj/Liaroov] 6 [isyiGTos KVK!,OS
. B, om. C.~
mg. B, om. C. 15. sla~\ comp. B, tfafo D. 16.
EB] BE D. 17. TtQbs vf\v\ Tr^oJarV D>, post 6 add. G D 3
.
19. <9Z] A, Z9 BCD. 24. nqog] corr. ex n$m C 3.
78 KAATAIOT IITOAEMAIOT
xa17
VTC avrr^v
fjtdrcov , r\ds r^g EB dntkj] ^LOLQ&V ^r xal
i] vii
avryv v&ia r^irj^drcov QX' ear aga dub rov r&v
QX rtgbg rd ^ Aa vs Adyov dtps^ca^sv rov r&v f ftgbs
5 ra QX, xaTafafastai, 6 Adyog r^g vTtb rr\v diTC^v TY\
Z agog rr^v VTtb rrjv dinkey rr\^ H 6 r&v ~QX
Ta xd Is v. xcct iGiiv 17 plv dmAij xr^g Z
pOlQ&V ^3T, V]$ VII
xalf)
vitb ri\v SuiK^
10 avr&v i6tiv xd Is v. &6rs xalf) psv dinki] rfjs
cbv 6nv xy t-91 v-01
, ccvrrj $j]&H
CCVTCOV Tajit eyyiGrct.
TtdhlV V7tOXl<3&G)fjEH XQl(pQLa
rfbv aU.G)v {IWOVT&V rcbv avr&v rrpj
15 EH yivstifttti UOLQ&V QX, r^v dl viC uvrriv ev&elav
vscy. sav ago, ndkiv dnb rov r&v QX
rd^irj K&. ve hoyov dq>^G)^Lv rov rcbv ^y vs *ty
rd ^Xy xara&i,(pd"tJ6rai, 6 Adyog 6 rijg VTCO ryvZ ngbs ryv vnb ryv dutlijv rrjg H 6
20 r&v ~$x ytgbg rd pf} d ^. XKL 6nv ^ vjtb rr\v
rrig Z r^rj^tdrcov QX' &6rs xalr\
vnb rr\v
rf)g H r&v avr&v 6rat,ft/3
a prj. xal17 p
aga rijg H nsgicpSQsias yioiQ&v iGtiv ^id oTrj,
H r&v avrcbv x A -9"
2. git] Q- corr. ex o D 3. vn'] vno D. 3. T^^arcov] -v
supra scr. D 3. 5. xara/Ut'nrfTtu] /tfnrsrat D. 6. Z@] corr.
ex S& D. 7. Is v\ corr. ex iv ~vs D 3. 8. nsQupsQeiccs] -$
supra scr. D 3. d] d' D. 9. T&V] rov C. 10. vgj xg BC,
mg. v B. 11. v&~] vj] D. 12ji] A-9
1 v& in ras. D 3. lyytcra]
in ras. D 3. 15. S] d' D. 18. 6 (alt.)] corr. ex v C. 19.
(9H] 6>- e corr. D 3. 20. ngbg rd] con*, ex n$b GTU D 3
. 21.
mut. in sxarbv SMOGI D 3. 24. T] in ras. A.
MA0HMATIKHS 2TNTASE&S A'. 79
rbv ccvrbv di) TQOTIOV xccl lid r&v xara [iQO$
xavoviov t&v xov rsrccgryiioQiov poiQ&v 9
twv oftotov rats &'
KKl S0TLV TO KCtVOVlOV 5
roiovrov '
2. sTtdoyiadiisvoi, sec. -i- corr. ex -rj-, D. 5.
A.
80 KAATAIOT HTOAEMAIOT
2-
p-aa- as 3. ~J
, .
o o
IS 3.
15^
fl rto to
-8 S.
^ 1? v^cd o So'if ^ '
(M <M ^J^
CQ
1QPM ~ao ^
>XJ3 VfiX ,
|S^^|^
3 53.
'ri
rH W **- "^11
<D <?*. lg
5 ^^
ifV _J . R"j ,H 3 X . 41
%r-, n-.fiP H_>>03 CO
a . 2 ^
MA0HMATIKHS STNTASE&2 A'. 81
*u,x
CJQ.CQ.QQ.5i X X xxx
o a CQ.B-jr? ft"
^ CO.
15r sr xI.
CQ.CQ.CQ.~i
IP IP IP
.XXX II: 1:1
sstS
Ptolemaeus, ed. Heiberg.
82 KAATAIOT HTOAEMAIOT
xa
L<5
f
. IIspl r&v fV og&ijs rijs 6(pcctQa$ avacpoo&v.r
E%ijs dy
av sl'rj6vvanodefeat, r&v rov farjHQi,vov
nQi<pQi&v tag yivoiivas nr]favoryras vnb rcov
yQaq)0[iVG)v xvxAcw did te rcov n62,ov avrov xal r&v
5 di,do[iVG)v rov Ao|oi> xvuhov t[ir}[idTG)v ovro yap
f|ofti/, sv 0716601$ %oovoi,g fayjiEQivois tec rov dice
[isG&v rcov t,G>diG)v rpriiiara diA,ev6rai, rov r ^is^rj^i-
PQWOV 3tccvra%ij xal rov 7t' o^ijg rijg GycciQas doi-
ovrcc di& rb xccl avrbv ror p6vov dia r&v noh&v
10 yQKyfG&ai rov fayiifQivov.
roivvy % 7t
tv rijs EHA dov k'tirco
rr\v E rov faypfQivov itQi-
15 Cp0LCCV VQLV.xara ra avra dy rolg k'p-
7tQo6&v 6 rijs w^o tfiv dt,7tki]v
rf}s ZB JtQog r^v vnb rr\v 81-
itK^v ri]S BA Aoyog Gvvvptxai gx
20 r rov rijg &*o r^v dirthijv rijs
ZH xgbs ryv vnb r^v diJtAijv rijs H xccl rov rijs
vnb rr\v dmhijv rijs E itgbs r^v vnb r^v
rijs EA [p. 74, 15]. jAX_ji ^V rijs
dmhij poiQ&v itiriv ohfi 1% y, xal % vnb ccvrrjv
25 r^ri^idrov o& /Ltd vy, 17$ rijs BA poiocbv ^ ft/3
st B, om. ACD. GvvctvacpoQ&v D.ov KVV.I.OV A, KVKJ.OV mg. pro scholio BC.. -v sv OJT-] postea ins. A 1
. 19. yldyog]-
1.
BCD, fcrmsQwov KVV.I.OV A, KVKJ.OV mg. pro scholio BC. 5.
ovrcos D. 6. -v sv OJT-] postea ins. A 1. 19. yldyog] -g in
ras. D 3, seq. ras. 4 litt. cvvfjnrcci] cvyKEtTui D. 20. t^g (alt.)
21. H&] supra scr. C 3. 21. ZH H&] mg. B 3
. ngbstr\v\ V.KL TTJS C 3
. rfjg H&] etiam in textu C, H0 in textu B.
xcu] yiccl s* D. 22. @JE] E@ D. 24. vno] A, vn BCD.25. BA~\ BA Sinl.fi V.
ft]corr. ex D.
MA0HMATIKH2 2TNTASE&S A'. 83
xalf)
vrtb avrqv ev&elcc r^irj^idrcov ^irj Aa v' xal
7tv,kivj] [isv rijs ZH TtsQiysQSiccg SmKv\ \LQIQ&V QV$ p IK
xal fjvjtb avr^v sv&eta r^irjfidrov pt hoc 7
5 17ds
rijs H poiQ&v xy t,& v& xalfj vjcb avrijv sti&stci
nd Is vj. sav CCQCC aito rov rcbv Q& pd vy 5
ra ^ ha vs k6yov fafdfaapsv rbv r&v ptf Aa is
agog ra xd Is vg, xaratei,(pd">j6T()it, v^nlv 6 rtjs i)Jtb
ri\v diic^v rils E jc^bg rv\v vjtb iv\v diTthijv xv\
EA Aoyog 6 rcav vd v$ x$ agog tec ptf A Is' 6
d' avrbg Aoyog 6zlv xal x&v v$ cc xs xgbg ra ^x. 10
xat iGtiv y [isv dwr/tfj rijg EA [IOIQ&V QX, % d' bit*
avrty ev&sla r[ir)[idr(DV 'QX' xali]
vitQ x^v diit^v
aga rrjg &E tpqp&iaw. rcctv avr&v etinv v$ a xs.
xalfj pev dinAij rijs E 7tQi(pSQias stirat, poi-
ve ft fyyitfcct) f]ds E r&v avr&v xj v. 15
TtdAlV VTtOXSlG&G)fjEH 7tQl<pQia IIOIQ&V |, G30r
rcbv ahkcov iievovr&v r&v avrcbv ri]v [iv diTthijv rijs
ZH tt$L(pQias yiv<5ftai iioiQ&v Qkri v& pf! xal TYJV
vjt avryv v&tav rinqiidr&v gift xy vg 9 ryv d
rijs H 7tQi<pQias [loigcov JLtao 7^ xal rv\v #' 20
avrqv sv&etav riirjpdr&v yifia
jil^.av aga aito rov
rtbv pO- |itd vy ngbs ra ft^ Aa v hdyov acp&G)[jiv rbv
r&v Qi/5 xy v$ rtQbg ra pfi a fZ^, xaraA,icpd"tJ6Tai 6
rijs VJTO rfv dntkriv rijs E ^oyos XQOS rr\v vjtb r^v
1. vno] A, vn3 BCD. 2. QV$ ft a] B, ipv s jta A, QVS Ji ft
B 3, pvg fta C, QVS ftg|5 D. 3. vno] AC, corr. ex vn' B, vn' D.4. H&] H nQicp()ia$ dinhcccicov D. vno] AC, vn' BD.
5. lav] bis D, sed corr. e-91
] corr. ex 90 D 3. 7. 6] in
ras. C. 10. %cu'] %al 6 D. xs] corr. ex vy D 3, vy in ras. B 3
.
11. vn'~\ corr. ex an' C. 13. r^rj^arcov] supra scr. D 3. xf]
corr. ex vv D 3. 15. Post p ras. 1 litt. D. 20. H} AB 3C 2
D,ZH BC. 7tQitpQEi<xs] om. D. 21. apcc] aga nuliv D. 22.
Id] corr. ex ^^ D 3. Adyovc, a eras., D.
84 KAATA10T ITTOAEMAIOT
rr\g EA 6 r&v $ ft p rtgbg to, Qifi ny vg' 6
$' txvrbg rovrcp Acfyog farlv xui 6 tcbv pa KTJ x
ra0jc.
Hat atfTtv ^ VJTO r^v diitH]v rijg ^cpQiag ev&sia r[ir][icira)v pit' entire xal
fybttb rr\v
5 diicKriv rijg E r&v avr&v fativ QCC mj x. KKI % [isv
E 7tQi(pQiag stitcci, [IOIQ&V gls MJds
v\E r&v afa&v v pd.
)on rb yfev a aitb rov
da)dxcctrj[i6Qi,ov rov diet [izG&v r&v
10 xvxAov 6wy%QOveZ rots rov farftisQivov xara rbv SK-
v r^tj^a^iv x~v, rb
x& vd, 7ti,dri3tQ a[i(p6rQa' xal rb rgfaov $ d^Aovdrt
rats Aomccis ffe tb
15 A/3 T% dt,a rb xai oAov TO rov Ao|oi) xvxhov rrao-
rrj[i6at,ov oAc? red rov far][iQi,vov
rovg dt,a
rbv ccvrbv d?) rooftov rr\ 7tooxi^,vrj defi^ei xar-
axohov&ovvrs &Vttoyt4<xp&m xal rag xa6r'fl dfxa-
20 (JLOiQiy rov Ao|oi) xvxAov 6vy%Qovov6ag 7tQt,cpQiasrov i&ftifQ&ov di& rb rag k'ri rovrcov [iMoo^afdrfyccs
Lv r&v itpbg o^a^v TCCCOKV-
ovv xai ravrag^f
iva
Kara rb 7iQ6%eigov fyopev, iv otioig %oovotg ccvrcbv
2. J<mV] -v del. C 2. x] D, supra scr. A 1
,in ras. B 3
,
^ C. 5. T&V 6. @E] D, om. A, mg. BC. 5. IGXIV\ecToci D. 6. KQCC] D, *. BC. 8. 8t8emxai\ COIT. ex ^e-
SfKZKi C 2. TO] supra scr. C a
. 10. rotg] om. D. 11. tie]
Om. BC. 14. Gvy%QOVLGl] BC, GVV%QOV16SI A, 6VV%QOVi]6i A 3,
cvy%()ovi]6t, mut. in Gvy%govit D. ^OLTtccig] fainovGcas corr.
ex iinovGKis D. 15. rot?] corr. ex TO C 2. 16. 6vy%Qoviv BC.
19. Sfna^oiQia] corr. ex dfxaTrjfiopta D 3. 22. TT^OS] corr. ex
D 3. 24. TiQo%iQoxov D, TT^o^st^oTaTov D 3
.
MA0HMATIKHS 2TNTAEE&S A'. 85
rov r [i6r][if}oi,v6V) 035 (pa^v^ itavra%Yi xai
rbv iit opoHjg rr}s Gtpcciocts boi&vrcc di^v6rai^ rrjv
riv anb rfjs TtQog r& farjufoiva tf^/m'co
flV OVV JtOCOrr] 1t8QiB%l, %QOVOVS & 1<, fj
$ $V- 5
& tf, fj$
ccvrb rov a'
'Y\$ teraQ
81 fxrr 6vov$ I Ig &6rs xcci rov
10
ds fid6[ir) %QOVOVS TAd,L ftj, fj
$ fvdrr) %QOVOVS i VE, fag
xal rov pey rofaov xal nobs tot$ raoitwols 6r][iioi,s
rovs kfi 7$ %QOVOVS., oAov d rov
rovs 9 (Jv^oavog. 15
avr6&v cpavfaov, on xal y r&v koiitfov
rd&s n VTI) rvy%dvi ovGcc, ndvrcov
xcctf Ka6rov r&v avr&v Gvuficuvovrcov diet rb rr\v
0(pcclaav oofi-qv vitoKtiGftai,,rovrfanv rbv i6^Qivbv
nobs rbv boi^ovrcc. 20
3. TO tGr}[iQivbv Grjpsiov D. deuceILOLQLCCS] post pr. -a-
ras. 1 litt. D. 5. nsQi^si] seq. ras. 1 litt. D. I 17] i'\j]
corr. ex\ii]
D 3. 9. ^ovovs (alt.)] -ov- ins. D 3
. tg] corr. ex
ic D. codrf] o>s D. 12. evdtr)] & C, v supra add. D 3. 14.
ScoSmcttriiLOQlovs, -g eras., D. TOVS] om. D. 17. OVGK]om. D. 19. rovrtcTiv] -v del. C. In fine: Klccvdiov
IlTotefiKiov pa.&riiLctXi"A&v (-bv C) a' ABC, T&O$ TOV
mg. sup. D 3.
B'.
Tads V6nv v rc5 p' rqg IIrofo[icciov
Gvvrd,G)g'
5 /J'. yt&g do&vrog rov rv\
aC K7toA,oc[ipav6[ivcii, rov
vito re rov i6r\[iQLVOV xccl rov Ao|oi) KV
avr&v vxoxi,[iVG)v rb ^KO^CC rov itohov
10 didorai, xal rb avdnccfav.
d'. it&s ZitikoyitirsoV) tiGiv xal 7t6rs nal TtoGdmg 6
ijUosf
yCvrai xara xoavytfv.f
. nag KTtb r&v KKi^iBV(ov oi /loyot r&v yvwpov&v
jtgbg rag farj(ieftv&g xccl raomxag iv rcclg
15 [ifGyiifiQfaig 6xi,ag Aaiipdvovrcu.
sr'. x&6ig r&v Kara, 7tccodMr]A.ov touopufaanr.
'. 7tol r&v iitl rrjgi
yxxhi,[ivyg Gcpcu'oag rov dice
r&v ^(pdicw xvx&ov xccl rov i6y[iQi,vov
20 vj. xs<5ig xavovi&v
avcctpoQ&v.
_ 1. B'] om. ABC; Khccvdiov nrotepaiov iiaQ'^cixiY.&v D,
{3add. D 8
. 2. rfjs 3. 6vvrdea>] QiQMtp r&v UTotefiaiov
paQ'JULoiTiKMV D. 6. o^t^ovrog] OQI^OVTOS V-DU rov D. 11.
riGi D. 15. (iscri^QLvats Gv.iu.is D. 17. lyttextafpfrijc AC.20. Hccvovfov D. SBKccpoiQiav] om. D. 7tccQciM.rj1.ov] -Hov
comp. in ras. B.
KAATA. HTOAEM. MA0HMATIKHS TNTAgES B'. 87
91
'. JtSQi rcbv xara {isgos rats avayogaisfrovvr&v.
t,' . itol r&v vitb rov dia peGwv r&v
Keel rov (i6r][if$()i,vov ywojievovIK' . 7tol rcbv vrtb rov ccvrov Ao|oi) xvxAov Keel rov 5
'. xsol r&v Ttobg rov avrbv xvxhov rov diu r&v
rov bgi^ovrog ywoyisv&v y&vi&v xal
r&v 7tgoxsi,[i8VG)v y&viGbv 10
XCCi TtSOiCpSOSiGJV.
a. Tlegl rijg xcc&6Aov ftstisas rijg
sv r& Ttgcorc) rij$ 6vvrK%s&$ roc rs
ytsol rrjs r&v oAav 6%tiG)s xara rb K<pKkcu,G>8$ 15
Kcd o6cc av ri rCbv 7t 60-iHjg
itgbs tv\v r&v v7toxi,iiVG)v
7tiQa66[Ji9'K Kara rbfijjijjs
xccl r&v
rqv lyxwliyizvriv Gcpccioav ^v^ccivovrcov ra
xvQi(brQcc ttukiVy <$$ Vi ndki,6rcCj Kara, rov sv^ra- 20
vravd-cc (^ ro {ilv 6ho6%QK>s otpatAov TCQO-
i, rovro <5nv, on rijg y^ ?$
1. itccQccKcdovd'ovTcov D. 7. T&V (pr.)] v B. 8. nut] D,xal r&v ABC, x&v del. A 8
. 10. Kara] r&v nurd A. yco-
via>v\ r&v ywvifav A. 11. In fine add. xeqpaXcaa ly D. 12.
ju-atbji^arnt c5i> ^ supra scr. B. a'] B, om. ACD. 14. rs\om. BC. 17. r&v vnoKEiiitvcov] vno%i^vriv D. 18. 177^-caro D. 22. ro] r- in ras. A. blo6%Qt<s B. 23. rovro
lortv] rovrecriv D. rsGGaga] t^GGSQa A, A D.
88 KAATAIOT nTOAEMAIOT
rraorrj^OQLa ra yivo^eva VTCO rs rov Kara rbv
KVK^OV Kal vbg r&v did r&v
avrov yaa(poiiva)v rb t% Ka
vnb rov sroov r&v poofi&v
5 rovro d' av ^idhcfra ysvowo cpctvegbv [snl [isv rov
rovrstinv rijs anb ^le^^^Qiccs yfQog r&g
ttccoodov., dia rov Ttavra^i] rag &v ral$ faq-
liQiat,$ rav yvco^ovcsv yiyvo^isvccs fU&rjufaiv&g Gxias
XQOS aaxrovs aisl 3toil6&cu ra xooGvevcfeis teal
10 pydsTtore agog [LetiyiipQiav, exl ds rov ntfxovs, rovrstinv
rtjg ajcb avarok&v nobs dvGp&s xagodov, dice rov rag
ccvra$ eKkeityei$, [idfoGrcc de rag 6eA,r]vi,ccxd$) TCCCQCI rs
rots lit* CCXQCOV r&v dvarohMcbv [LSQ&V TrjjgKCC& f}H>&s
ofaov[ivr]s oiKovtii uccl ttccQa rolg in ccxocov rcov
15 dvrincbv Kara rbv avrbv %$6vovitkeov dddsxa Ttyorsoetv rj
vtirsostv (ba&v
avrov Kara [irjxog rov rsraQrr^LOQiov dcodsxacooov
diddrrma itQie%ovro<2 , ETtsid^TtSQ v(p evbg rcov rov
i<5r][iQivov fjuwvxMcov dfpoot&rai,. r&v ds Kara
20 dtpsihovrcov &G)Qr]d'rivai [idfaGr av rig
xobg rr^v ytQoxi^vrjv XQayptctefav CCQIIO&IV ra
j5oaiorQG)v rov
v avr<p Kal ralg vaoxi,iivai,g ofarj66i Kara
ra xvQH&rfoa r&v tdiandrcov ^v^itiitrovra' ravra
5. ini\ e corr. D 3. 7. itugodovG D, G eras. 8. ywo-
,_,._.xs C. 9. ai D. 10.|u,f(77]fip(>tW]
-v e corr. D 3. 11.
ano] an' D. 12. pdhGra] ft- in ras. A. rag'] om. D.15. SVXM&V] Sv- e corr. A; UVTIK&V C, ^ supra scr. C 3
. 16.
OQtov C. 17. Post rov ins. r^g yfjs mg. pro scholio BC.
rTaQrr][JiOQiov] rraQrr]^OQiOV rf]g y^g A. Scodwdagov] corr.
ex ^fxacopov A4. 20. pdliGr' av] pdliGTa D. 21. ra\ corr.
ex TO BC 3. 22. TtvxZcov D. 23. xorTa] corr. ex v.a C 3
,xa
corr. ex xcu B 2.
MA0HMATIKHS STNTAEE&S B'. 89
6' ittiV) o^ov rs oi rtohoi rijg XQaryg (poQag rov dgi-
frvrog aysGrujxaGiv, i} o6ov TO Kara, xoQvtprjv 6rj[iiov
rov farjpSQivov xara rov (itfr][i{$Qi,vbv xvxkov, xai\
olg 6 ijfaog Kara xoov(prjv yCvtrai, icors xal Jtotidxig
rb roiovro GvpfiaCvGi^ xal rivsg oi koyoi, r&v farjiisgivcor 5
xal rgoitiKcov iv ralg [i6r][i{lQtai,s Gxi&v TtQog rovg
xal mjMicai, rcsv [isyfarcw rj &a%irag fariiLsgwas ai v7CQo%ai^ xccl
rag Kara HSQOS av^o^LG)6i^ r&v
In r itQi rs ras GvvavaroAas xal Gwyxa- 10
rov re foqiiSQivov nal rov Ao|oi) xvxAov xal
ra idico[iara xal ra psyiftvi r&v
vnb rcbv xvQiorQCov xal [i&yforcov
do&evros rov rijs iifyiGrrjs fjpSQag 15
ai aitokayifiav6iivai, rov dot^ovrog
7tQt,cpQi,ai vjto r rov l0r]^iQLvov xal rov
Ao|oi) xvxAov dudovrai.
nQoxffa&G) drj xa&oAov r&v vnodsiyiidrov VKv 6
dicef
P6dov yoacpoiifvog jtaodA.A.rjA.os r& far]iiQivG) Kvukos, ^Qitov rb iikv \aQ^a rov TtoAov [toiocbv fariv Ag; f)
df
1. <T] Ss D. Tf] om. D. rov] anb rov D. 3. PostM _
add. aqpf'ffTTjxfv mg. A 1
, aqptcrrj mg. B, ^ <xcpGri]Ka6iv
mg. C. 4. yfyvsrcii D. xca] xal nov V.KI D. 5. roiovrov D.
rives] rivsg re D. 9. avo[ieiwGeis] -v- supra scr. C 2, pr. e
ins. A 4. vv^rjfi^Qcav] corr. ex vv%Q"r\^eQiv&v D 3
. 10. GVV-
uvcirolas] corr. ex Gvvavuro7.LV.a,g C 2._ 12. nsQi'] oca negi D.
Post KCCI del. v.ctrd D 3. 15.
j3'J ^ B, om. A CD. 16. at]a- in ras. C. 19. xa-Oo^ov] inter duas ras. 8 et 3 litt. D.
20. *P68ov] 'P- in ras. A 1. nagdHrilog} 7ictgdl\r]lo<s xvxAog D.
KVY.3.G) D. 21. ILQI.Q&V} ras. 3 litt. A.
90 KAATAIOT IITOAEMA10T
G)QK>V fayiiSQivcov id/.', xal E&TCO
[lev xvxhog 6 ABP4, oo^ovTog de
XOV r][ll,XVXhl,OV TO
BE4, xal
5 VOV 116V
b[lOLG)g TO AEF,6 ds VOTIOS CCVTOV
TO Z. VTtO-
ds TOV dia
TG)V
TO
VOV TQ07CMOV
xvxhov TSTccgTrjiiOQiov TO
10
TOV H,15 dia T&V Z, HZH. dsdod&a) ds TtQ&Tov TO peyed'os Tr\$
)XCCl 7tQOKEi<5&G) TYJV EH TOV 6()%OVTO$ TtSQL-
EVQEIV.
7tl TOiVVV % TJJS GCpKiQag GTQOCpri 1tQl TOVS TOV
20 l6rm,eQt,vov it6hovg aTtOTefaiTai,, fpavsoov, OTL sv TG>
avTG} %QOVG) TO T H Grjiistov xal TO xaTa TOV
Qivov E^TKL^ xal 6 ^v ait CCVKTO^^
Tijs VTtQ yfiv iiEGovQavvJGE&s TOV H XQOVOQ 6
6T\V V7CO Tijs A TOV i6^^lOiVOV TtEQl-
25 <pQiKg, 6 d' aito T^g vitb yi\v [i6ovQavrj<5EG)g
4. xat 6. AEP~] supra scr. D 3. 6. ART] -P e corr. C.
13. ScvuTsMav C. 17. EH TteQicpfysiccv] HErov OQifrvros D. 18. EVQSIV] add. B 2C 3
. 20.
-st- corr. ex s A 4. 22. ABTJ] corr. ex Tz/, AB D 3
.
IWca] SGzai dr]Jiov6zi Kivovfisvrjg rf}s GcpctLQccg D. Kit']CCTCO D. avccTolris] -lf\- renouat. D 3
. 23. XQOVOS] comp. B,mut. in %o6vovg C 2
.
MAGHMATIKHS STNTABE&S B'. 91
rilS avccroAijs 6 7tais%6iivos vitb rijs F.ds scfnv, on xcci 6 fisv rijs q^oKS %Q6vo<3 6
6rlv rov vitb rijs A 7COi%o^ivov^ 6 ds rijs vvxrbg
6 diTthcctifav rov vnb rijs F TtQi%o^vov^ eyte^TCSQ
xccl x&gls tu t vitQ yi\v xccl ra vTtb yijv T[iri[iccta 5
rcbv jiaQaMtfAov red i<5rniQivG) xvxA&v rtdvrwv
lLlrai VTtb rov [i6r][if$Qivov.
dltt $ TOVVO Xaifj [lV E
ov6a rov diuyogov rij$ ifajjlkfii
nciQK rqv farjiisQivrjv fita? [iv &QO.Q xal d' ywrai 10
xara rbv vitoxiiivov JtccQaMrjAov, %QQVG)V d dyAovori,
Irj jilf, .fjds Aoirtrj fts rb rfragrrjiioQiov ^ A r&v
avr&v OK T. 7Cidri ovv xara ra avrd rotg
artoddi, /
y[ivoi,s i$ dvo [ifyfar&
rag AE Kal AZ dvo <
yiyoa^vccL ffalv ai EB xai 15
Z rspvovticci, aMijAccs xara rb H, 6 ri\g vitb rv\v
rrjs A jtQog rqv V7tb rrjv dutAijv rijg AEGvvijitrcii, x r rov rijs VTCO rr\v dt,itA.ijv rrjg
Z Jiobg rqv VTtb rqv diit^v rij$ Zif xcd rov rijs
vjfb ri\v di,ithijv rrjg HB TCQOS rrjv vnb r^v diyt^v 20
rfjs BE [p. 76, 3]. cUAo:f\ psr rijs A
ftirw opf} A xalf) VTtb avrqv
~Qi/y Ag vd, ^ ds ri\g AE poiQ&v ^r xali\
2. %QOVO$] mut. in %QOVOVS C 2. 4. Post 7tQie%o[ivov del.
7tiSr] TfSQisj^o^vov A. 5. t(n^fiaroi] corr. ex r^Tj^arcov D 3.
6. T&V~\ om. D. -Avnlau D. 15. AZ~] corr. ex ABZ D 3.
16. Z@] corr. ex ZH& D. 17. A] -A supra ras. 1
litt. D 3. T?)g(alt.) 19. dmlrjv] supra scr. D 4
. 17. AE~\EA CD 4
. 21. &U' B. Post iti-QL<pQeias una litt. (t?) ma-cula del. C. 22. UTTO] ABC, vn C 2D^ 23. rfji^KTcov
-
p. 92, 1. QX~] bis C, corr. C 2. 23. ]
in repet. corr ex
Jig C. AE] AE Sinlfi D.
92 KAATAIOT HTOAEMAIOT
VTt ccvrqv v&Za tftrflufacw ^, xal itahiv % plv rijs
,QIQ&V pjr %al % vTtb avirpt sv&eicc
ds rijs 2.H poiQ&v pA/3 it, % xccl % v
jv v&ta rprindr&v Q& ftd vy' sav &QO. artb rov
5 Aoyov n&v Qiy A vd agog ra QX acp&K>iiv rbv rCbv
Q% rtQos tec Q& [id vy, xccTafaicp&riGMcci, i]^iv 6
vnb T^IV dL7Cki]v trjg HB TCQOS rj\v V7tb rr^v
rrjS BE Aoyo? 6 T&V ^yy ^vs wy ngbg ta (M. XKL
r\ vrtb ryv dijt^v v^g BE tCSQUpeystegi fad
10 fjLOQiov rvy%KVi) xpvipcatav ^sc* xalfyvnb rqv
CCQCC rijs HB r&v avr&v faxiv ~^y v wy'
yS BHavrr] $
rjBH r&v ccvr&v *
xccl tomy KQCC
HE roiovtcov xatahsiiterai, A, oitov Itixlv 6 b
15 T
y'
'
. Hag T&V avrcbv vitoKi[iVG)v rb k'^ag^La rov
didorai xccl rb
dq itdfav rovrov ddo^ivov xal rb
rov nohov kaflelv, rovrs'tinv rr\v BZ 7lQi<ptysiav rov
20 ii6r]ii(lQi,vov. yivsrui roivvv Inl rijs avrijs
6 rvls vnb rfv diTtAijv rijs E nobs rr\v VTtb rr\v
1. T[ir)[ictTcav px] etiam ing. C 2. r^g] corr. ex rr\ D 3
. 2.
vno] A, vit' BCD. 3. QJL] corr. ex pop A. __vno]AC 2
,
V7f} BCD. 5. ply] -i- supra ras. 1 litt. D. vd] corr. ex
v\ D 3. 7. rfjs HB~] supra scr. C. 8. y] post 9 ras. 1
Htt. D. xy] B, xy?A, xs CD; sed cfr. p. 93, 10. 11. xy]
%y?A, xg BCD. 12. BH] HB D. poiQai D. 13. xat]
corr. ex i] D 3. 14. 69^001'] -v supra scr. C 2
. 15. OKSQ] suprascr. D 3
. owep ltf det|at] o):oo ABC. 16. y'] y B, om.A CD. 18. dr/ TfdHiv] corr. ex driniriv C. df
fteVov D. 19. BZ] ZB D. 21. E@] E D.
MA0HMATIKHS STNTASE&S B'. 93
rijs A Ao7>0 (fwrfpfdvos ex rs rov ri}s vnb rrjv
rrjs EH nobs rr\v vjtb ri\v diTtAijv rijs HB xccl rov rrjs
rr\v diithijv rijs BZ nobs rr)v vytb rr\v
ZA_ [p. 74, 15]. AA' fj plv dutMj rijs EBAf A xal
r\vnb avr^v ev&sta r^irj^drcjv Ay Ad
de diTtM] rijs &A ILOLQ&V Qpfi A not ^ vitb
T(ir}ndtG)v ~gi/y AJ vd, xal ndfov y per
rfjg EH poiQCbv % xalj\
vjtb avrriv evfteicc
|, ^ d diTthi) rfjs HB poig&v ^ xccl
sv&sta r^^drcsv qy w wy' lav KQO, anb rov Aoyov 10
r&v A^ Ad x/3 agog ra yip AJ i/d dtpeA&nev rov r&v
f ^6? ra oy ve %y, Karuhei(p&ri6er(x.i 6 rife v^o ri)i/
dmhijv Tys BZ ytobs r^v vito r^v dtTt^v rrjs ZA6 r&v o Ay syytfra Tfobg rot QK. KKI i<5riv
r\ vTtb rr^v diTt^v rijg ZA jtQiq)Qias r^rjfid- 15
r&v QK' xccl vrtb rrjv dm^v CCQK rrjg BZ rcbv
avrCbv itinv o Ay &6rs xcclf} pv dinki] rrjs BZ
rtZQMpSQstccs farcci noiQ&v o/3 a, rjde BZ r&v avr&v
Ag h'yyi&ra.
itdhv 7tl rrjs ccvrfjs xccrccyQcctpijs dvdrtccfovfj [isv 20
BZ nsisEicc rov s^accros rov it6kov
1. 6vvr](t[ivos] 6 cvvriyfitvos D. 2. EH] HB v.ccl rov rr]s
vnb XT\V dinlfiv tfjs EH BC^corr. B 2. n^og HB] del. C 2
.
4. rf)g(pr.)] bis D. 5. ^] -^inras.A1
. vn D. avrrjV]corr. ex nf C. fu-9-fta] in ras. C. 6. vwd] mut. in vn' C 2
,
v?r' D. 8. Ante f ras. 1 litt. A. vn6~] mut. in vxc* C 2,
vn D. 9. Post 1 del. H D 3. HB] -B in ras. B; #M C,
corrigere uoluit C 2. vn' D. 10. sav ago] bis D, corr. D 3
.
13. BZ] ZB B. 14. &7rw>] -v del. C 2, comp. B. 18. sarcti
\L iativ D. o|3 a] a in ras. A, corr. ex o |3a D 3.
20. TTeoff TOV s|a(^aTOff rov nolov do&svro$ rb ftgyf-d'Off rijs
(LifyiffTTjg r)(jiQKS SiSorccL mg. pro scholio B. 21. BZ] -Z in
ras. A, ZB D.
psgsias.
nb ryv
^ntKr^v
94 KAATAIOT HTOAEMAIOT
poio&v A, nQOKi<5&& ds svostv rb did-
A,a%i6rr]g T) ^Lsyidrrig fjfieoag nagd rqv
rovrstfriv rrjv dinhijv trig EroCvvv did rd avrd [p. 74
? 15] 6 rijg vnb
5 dinAijv rijg ZB nsoicpsosiag ngbg rrjv vnb rqv
rijg BA A6yog 6vvr}ii[ivog x rs rov rijg vnb rr^v
dinAijv rijg ZH nobg rr\v vnb rrjv dinAijv rijg Hxal EX rov rijg vnb ^v dinhijv rijg E nobg rrjv vnb
rqv dinAijv rijg EA. aAA' ^ VLGV dinky rijg ZB10 [loiQcov fariv oft xai % vnb avrr\v svftEla r^^drcov
o A/3 y, ^ $ dinhij rijg BA [toio&v ^ xalj] vnb
avrjjv evfrsta r^^idra)v ^ d vg, xal ndAiv
rijg ZH [loig&v stinv pA/3 1% K nalf) vnb
\v sv&sla rpyiidrcav ^^ fid i/y, 17ds
15 H [loiQKtv ftf ft/3 ji xalfjvnb avryv sv&sta
r&v^Ji/ij
A,a vs' lav ciga dnb rov rcov o A/3
9? d vs Adyov dcpE^co^isv rbv r&v pO1
^d vy ngbg
^ Aa v) xaraAsitpd'YJo'erai r^^lv 6 rijg vnb rr^v dtnJ
rijg E ngbg tv\v vnb rrjv dmAijv rijg EA A.6yog 6 ri
20 A Id wy nobg rd 9? d vs. KOI snzidri 6 avrbg
stirlv fyyiGra xal rcbv A^ Ad ngbg rd ^5c, ^ ^ V7t(-
6. >l6yog] Myos 6 D. 8. SinJUjv'] Si,- in ras. A. 10.
D. vn' D. vnb UVTIJV] vn' CCVTIJV corr. ex vnb xr^v
11. y] seq. ras. 1 litt. B, corr. ex A D 3, y 8 AC, 8 del. C s
-UTTO] mut. in vn' C 2,
-UJT' AD. 12. piv\ -i- in ras. A 3.
6nv\ om. D. 9^j3] Q- e corr. D 3. VTTO] mut. in vn' C 2
,
vsr' D. 14. pfl] corr. ex jlv D 3. 15. j*p] -|3
e corr.D 3.
jiZ]
^ D, (i add. D 3. -UT^] mut. in vn' C 2
,VTT' D. 16. y] corr.
ex A D 3, y ^ ABC, sed d punctis adpositis del. AC 2
,eras. B.
7T(>6s] ngbs TO. D. 17. $] postea ins. C. fid] corr.
vd D 3. 19. &E TT)S] mg. A 1
. 20. xy] supra_scr. ^ C 8.
v.ccl inziSri] ensl S' D. 21. TCOI>] 6 TCOV D. W] 'ku seq.
ras. B. 9f] S' D.
MA0HMATIKHS STNTASE&S B'. 95
rijg EA r^irj^drov <5rlv psc, Gwdystai,
xalYI
vitb rrjv 8i7t^r\v ri\g E r&v ccvr&v Ay Ad'
&6T XCCl J] dlTt&fl rfjg E 7tQl(pQiag fJLOLO&V {IBV
6rai Af A fyyitircc, &Q&V ds far][iQi,v&v fiL'' OTtfo
$1, dft^CCi. 5
XKTCC ra CCVTK d dod"^6rai, xccli]EH rov o^t-
JtQL(pQi,cc diet TO xal tov Ti}$ VTtb ri]v dLTt^v T^g
agog ^nv ^o rnv dMki]v ri]s AB hoyov ddo{ivov
[p. 76, 3] x T rov rrjg vitb tr\v dnt^v rijs
Z jtQog r^v VTtb TTJV diitkriv r^ H deSoptvov xal 10
CCVTOV xal % rov x^ VTtb rrjv duit^v r^g HErtfv vitb rfjv din^v rij? EB, 6}6r xal rijg EBlivr]S xarccAirt6&ai, xccl rb rr^g EH ^yf&og.
<pccvobv d',
ort?xav
[ir}rb %i[i()i,vbv
6r][iZov vrtod'G)iLd'a rb H, r&v ahhcov de n rov dia 15
r&v ^(pdi&v xvxAov r^rj^idrov ,xccrcc ra ccvra
XCCTQtt rCOV E XML EH 7tQl<pQElK)V dod"lj-
taofxrid-fiiwav T f)[iZv dia rov rrjg
xccvovtov r&v d7foAa^avo^vov rov
7tOi(p0iG)v vq) xd<5Tov r^itj^arog rov dta [ifacov 20
r&v c?dtW xvxl.ov xal rov fayiifoivov ,rovrfanv
r&v oftotov rri H jtoi,(p0La^ xal
3. ftfV] om. D. 4. 07tQ t$i dsi&i] om. D. 6. n&sdo&evtog tov l|<^funro( rov nolov SiSorca r\ (ji8Tcc^v rov kr}-
(jiBQLVOv v.a.1 rov >lo|ou tni rov ogifrvrog nsgirfigsiK rag. B.
9. ,xiqv _ 11. &_] mg . C 2. 10. Z@] Z D. Z 11.
rfj$ (alt.)] om. B. 10. rfjs] om. A. dedopevov v.al ccvrov]om. C 2
. 11. $yi] om. C 2. t% (alt.)] om. A. HE] corr.
ex NE C 2. 12. EB(alt.)] BED. 13. xara^wrfG^at] mut.
in v.arKUTtiG^a.1 D. xat] om. D. 15. aHoov] -v add. D 3.
18. nQotnriQ-tpiv&v] -i- mut. in f C 2, TtQOSKrtQ-si^vfov D.
TS] yg D. 20. vcp'~] VTCO corr. ex vn' D 3. to-D] om. B,
add. C 2. 22. TTJ] rng C. TCfOLfpeQficc] 7tfgicpQia)v at D,
ccl del. D 3.
96 KAATAIOT nTOAJEMAIOT
rog [lev avro&ev rov ra vitb rcbv avr&v
yivotisva r^itj^ara rov dia
a7t%ovra rov avrov roonixov
Grjfisiov, rag avrag xal iitl
5 ra avra [isoy rov
iioislv rag rov QQi&vrognod ra rcov vvft&yii
l'0a sKarsQa sxaregois r&v
rovrsGrw ra l'6ov
W
10 rov xal ra VTCO r&v focw itao-
aMtjhcov yiVQ\itvu, rovreduv ra faov a7te%ovra rov
avrov faruasQivov 6vnistov9 rag rs rov 6o%ovrog XSQI-
(peaeiag l'6ag sxarsQco&sv rov iGrnasQivov Ttouelv xai r&v
wxfHjflfyaMf svaMa% i'6a ra [leyed"*} r&v avo^oCov. sav
15 yao iitl rijg sxjcsi^isvrjg KarayQacpr^g VTtod'&iLsd'a xal rb K%a&' o re^ivsi rb BE4 rov boi&vrog
b I'Gog xal ytaQdAkqAog red dia rov Hxal 6vvavaitAr)QG)6a)iisv ra HA xai KM
r[itf[iara ivukKofc, ual i'6a drjkov6r
20 did rs rov K xal rov fiogsCov itokov rb NK$reraorrjiioQiov, i'6ai psv faovrai ^ [lev Arri &r dia rb exarsoav txare'oa rav AHxal MR b[ioiai
slvat,, xaratei,(pd"tJ6rai, ds xal ^OLTtrj ^ E& homy r\
E& fay, ysvtfGovrcci ds xai dvo r
ft&>] om. D. 2. yivofifva] ysvofisvcc D. 7. Andel. rd D 3
. 15. xca] supra scr. A. 16. BEom. D. 17. xca'J om. D. yeaqpop-aW] corr. ex ygcccpopsvov
20. Ante SLOC ins. V.OLI comp. C 2. tb NK1~\ corr. ex r
KB A, corr. ex rb KB B 2;rbv KB C, mg. TOV; v mg. add. C*.
21. tWt] corr. ex i'cc, B 8. ph (pr.)] om.
D^. A\ A D.
C. 22.ti[i\
xai i] Halrna. S-AKTEQU] corr. 62
D. 23. T$] corr. ex rfjs D 3. 24. fffij]
corr. e:
i'crjg D 3. y.at] om. D.
MA0HMATIKHS 2TNTABE&S B'. 97
rcov EH xal EK% at dvo per ntevgal rcclg dvetlv
focu, % plv E rf] E8, n $ H rfj KB, <W ds
XCirQCC TG)V TtQOg roig XCil & y&Vl&V, G)0T Xttl
ryv EH pdfci rfj KE
. H&g titikoyKSreov, xiGiv xccl note xccl
6 ijAios yiverai, tcara nogvcpriv.
ds 6riv rovrcov dsdo^isvcov rb Gvveiti-
)ri<3i xal itore xctl Ttotidxis 6 tfhog XCCTCC
jv yiverai. (pavsgov yaQ ovrog avT6&V, onvnb TOVS ittelov ci7t%ovrccs rov faiftiQW0& 10
r&v r^s oA^g cbrotfra'tffcos rov &SQIVOVsiov poiQcbv wy vcc x eyyiGrK ovd' o^cog
yivexai xccra xogvyijv, rolg ds vno rovg avxb
rb todovrov dcpsdTGJrccs ajta% iv ccvrfi ty ftsgwri
yCverat, KCCI, on, rolg VTCQ rovg sAdtiGovag 15
OIQG)V djt%ovTccg dig yCvrcti, Kara
riv' KCil TO JtOT d 7tQ6%lQOV TtQltlfjTOV KKVO-
VLOV r^g Ao%(D6G)g 'x&6t,g. o6a,g yag av 6
{ivog TtaQdMrjhog K7i%ri rov l6rnneQwo
Ivrbg dri^ovon rov &QLVOV rgoTtinov, rag roGavrag 20
L0vfyxovrg ig ra dvrQcc ft(>^ rcbv tiffodicov rag
3taQccxi,[ivccg civrcctg %. rov rera^rrnLogLOv poiQctg v
1. EH] E- e corr. C. 2. EB] E- e corr. C 3, mg. f
H0] corr. ex HE D 3.
_3.Post r&v del. rotg D 3
. @] e
corr. D 8. Hal B] corr. ex o D 3
. 5. #'] om. AD. xfai D.
6. ylvercu] yive C. 7. im D. 8. TLCL] corr. ex riciv D 3.
9. ya^] del. C a. 10. TOV] rov? A. 12. yC\ supra scr.
AD 3. 13. TOLS] -i- supra scr. D 3
. 14. TO] ins. C 2D 3. &tp-
EGT&GW D. 15.$f}1iov~\ D, 8r]T(.ov6ri ABC. nat] D, xara
xoovqprjv xat ABC. mdoGovccs D. 16.o^t's] corr. ex di6 D 3
.
17. TO] supra scr. AD 3. 18. av] D, sdv ABC. 19. wap-
rjio?] pr. A e corr. A. 21. csliScov D.
Ptolemaeus, ed. Heiberg. 7
98 KAATAIOT HTOAEMAIOT
rots ito&Tois pistil T&V Gefadicov lo^i>, o6as dnfycov
6 tffaoS dfp' XKTOOV T&V far][lQiVG)V 6rj[lLG)V tig
XQOS TO &SQIVOV TQOTtixbv KccTa xoQvcpfiv rolg vit*
Xtvov TOV sxKSipsvov JtaodMrjAov
5 &'. II&s dab T&V exxeipsv&v 01 Adyot r&v
povcov 3t()bs fag l6rj[iQi>vtt$ xai rgomxarats [i6'r}[Ji<(lQittt'S Gxiag A,a[ifldvovTcii,.
"On d xai 01 nQOKsCpevoi Adyot r&v Gm&v
rovs yvaiiovas KitkovGteQov ^a^ftdvovrat,
10 ajtat, rijg T [ira%v r&v TQOJtw&v 7ieQi<pQia xai
rijs [ira%i> TOV OQ%OVTOS xal r&v noAcw, om&g av
tQOV TO E, XCCi V7tOXl[lVOV TOV KCLTO,
15 TOV A diij%d'G) rjAEP did[iTQOS) 17 xobs
v T& TOV ^^^QLVOV fTtiTteda)
drjhovoTt, yivo^ivYi TV] KOLV^ Topy TOV
xal TOV [ifGrjupQivov. xal tti o^rj rj
Ccl XVTQOV k6yOV %l 7COO
20 TJJV TOV fjAlOV 6(palOCCV) CD6T ddlCCCpOQtV TO E XVTQOV
Tijs TOV yvcbpovos xoQvcpijS) voi6&& yva)[iG)V plv 6
d FKZN v&icc, ly $v Iv TCCLS
1. GsUdtwv] corr. ex otMdmv D. ajr^cov] corr. ex &n-
i%ov C 2. 2. 6 ijiiog] in ras. A, seq. ras. 2 litt. Grjfisfov C.
4. EMSLpwov] supra scr. D 4. 5.
']om. AC. 7. ntcrui-
PQIKIS D. Happdvovrag BC. 8. of] Sia T&V D. TCQO-
KfipEvoi] -(ifv- supra scr. A, 7tQOKi[iV(ov 01 D. 12. yivoixo D.15. AET] A- in ras. B 2
,corr. ex JET C 2
. 16. FKZN]-N corr. ex H A. 20. adiacpOQtw] fii] dLccytQfiv D. PostE eras. N A. 21. yvm^ajv] corr. ex yvapor C 2
. 22. raig}TKIS ri' D.
MA0HMATIKH2 STNTASE&2 B'. 99
rov
ra axaa r&v Gxi&v, xal diri%&G)6av dia rov
Eij
rs farjpEQivri xal ai rgoitixal iiEGrjufiaival dxrtvss.
E^rco ds i6r][iQi,vr] [isv r\ BE4Z, &EQivri dsr\ HEK,
%t,[iQi,vr) dsfj AEMN, cotfrs xal TT\V psr FK &SQIVTIV
yweti&ai, Gxidv, rqv 5
ds FZrfjv ds FNvijv. ETtsl roivvv
fj
[IEV F4 JCSQKpEQEia^
(Mfi iv\v i'Grjv e^YiQrat, 6 10
K
ovrov 6rlv Ag, OL&V 6 ABF [i6r][i(lQi,vbs r%, xaroa
ds rcbv 4 xal 4M r&v avrcbv xy va x, (pavEQOv, 15
ore xal AotJTT? [IEV f\F@ rtQi(pQEitt r^rj^drov Ititai
ifi y ft, oArj dsr]FM r&v avr&v v& VK x. coGrE xal
r&v vitb avrccs y&vi&v, olcov piv EiGiv ai d QQ&al
r$, roiovr&vf) [IEV vnb KEF ycwi'cc 6rlv t/3 ^ ^,
fi_dsVTtb ZEF r&v ccvr&v Is", 1}
d^ vnb NET 6/iOio? 20
v-91 va X, otcov ds ai dvo oa&al rj, roiovr&v7] [isv
vjtb KEF Y&VIK xd 7^ x, $ ds vnb ZEF r&v
ccvr&v o^3, % ds vnb NEF dpoi&s QI& ft/3 jZ.xal
1. diri^mcav} -%- in ras. A. 2. rgoitiKcxL] tgoTCMCti g' C.
4. AEMN] D, A- in ras. A, corr. ex 4EMN B 2C 2. 5.
yiyv6&ui D. 10. f^ttu] D, flrjpTTjrat ABC. 11. poqios A.12. V710Y.8Ultvov] 7lQOKl(lvOV D. 14. fGtC D. 15. TKtV d]
x& N&J C, N e corr. C 2;r&v J D. ity] corr. ex xa C 2
.
17. v& va x] co^.ex ~&v ox B 2
. 18. vd] BC, vn C 2 D.
VJTO avrag] vn' ocvrds corr. ex -UTTO rag A 1. 19. ymvtct
Icrtv] om. D, rV supra scr. D 3. 20. to' (pr.)] ^ 7)
D. JVEr]corr. ex JVT D 3
. 21. ^'] 5' D. at] supra scr. D 3. 22. x]
seq. ras. 1 litt. D.
7*
100 KAATAIOT HTOAEMAIOT
T&V yQcccponsv&v CCQK xvxA&v TtSQi TO, KEF xal
ZEF xal NET TQCy&vu OQ&o'ycovia i\ psv nl
vf}S FK evfreiag rtSQiysQeia poiQ&v i^tiv xd t K
xalr\
7tl Tils FE, faiitovGa ds EI TO fiiuxvxfoov,
5 T&V avTcbv gve ft/3 [i, v\d litl rijg FZ [IOLQ&V o/3
xcclr\
7tl tys FE o^ioios t&v KVT&V ^, r\ds iitl
rfls FN [lOiQ&v ^tO- ft)3 flxal
fjiitl tils FE r&v
st$ TO ^IKVK^IQV % i %. KHSTS xal
sv&eiobv i\FE GwayETa^ otW [iv r\
10 FK etiTiv xs id fty, roiOVT&v Qit, Irj ~vu, oiav ds-^
FZ ndkiv o A/3 5, TOIOVTWV $ d o/g, ol&v ds ^ FNjitg Zg, TOIOVTCQV | LS ^/3. xccl oi&v CCQCC
6 FE yv(6[iG)v ^, TOLOVT&V xccl ^ [isv FKGxia 6vvcc%d"rj6Tcci, tj3 v, fj
de FZ faripSQivii
15 M> Ag, f\ds FN %si,iiSQi,vrj $y % syyiGTcc.
cpavegov ds avTO&sv, OTL ncti dvdrtccfov}xav dvo
povoi, hoyoi do&coGiv OTCOIOIOVV dnb T&V sxx{,[i8VG)v
TOV FE yv&iiovos ngbs TCC$ Gxidg, TO T TOV
k'^CCQlLK didoTCCi XCCi fj flSTCi^V TCOV TQOTtM&V,20 7Cldri7tQ KCcl dvo do&l6O)V QTtOl&VOVV JtQOS T& E
didoTcu xccl ^ howfi did TO l'6cc$ sivai Tag
TOV
2. xat NET r^yoova] om. D, g NET Jj mg. D 3. 4. Ss]
om. D. 5. QVS] seq. ras. 1 litt. A. rfjs] yrjs D. 6. i^(pr.)jadd. A 1
. ^] -r\ e corr. A, corr. ex QX C 3D 3. Si] d' D.
7. gift] griy D, -9- supra scr. D 3. rj]
om. D. 8. |] seq.ras. 1 litt. A. 10. vu] v& C. 11. iF?] corr. ex vy D 3
.
12. tg] corr. ex x? D 3. xat] seq. ras. 3 litt. A. &QCC]
supra scr. A. 15. <jy x] supra scr. D 3, <o
y x D. eyytara]-yiGTct eras, propter figuram insertam et ia mg. add. B 2
. 18.
FEJ supra scr. D 3. 20. ta E] rb e~y D. 22. 04] @A C,
J xat D.
MA0HMATIKHS STNTAgESS B'. 101
6ig avTccg KXQifiovg f'vsxev txslva psvxa& bv vTtsdei^a^v TQOTCOV, 01 ds T&V
GKiGbv Jtobg Tovg 'yvoD^iovccg koyoi, ov%
bpotcog did TO T&V plv farjjisQW&v rbv %Q6vov doQitfrov
xatf CCVTOV SIVCCL^ r&v ds j^Si^ieQiv&v T& t&v 5
axga
XCCT& itaQukkrikov ldiG)[idrG)v.
Tbv avxbv dr\ tgoxov rovtoig xal 7tl r&v aMcov
Accflovrss rd 6&o6%SQij T&V BXKSL^BVCOV
tdpTG) pices &Qas fay[iQi,vijs tog avrdgxsi, 10
rag vjtQO%ds rcbv syxAfascov TtaQcivt.rJGavTsg 3toir}6o-
lis&ct TTJV x&6iv avrcov %$\v xafroAov itQO xr^g r&v
xara pfyos ^nL^v^aLv6vrov ryv dg^v dnb TOV i)7t
CCVTOV rbv (6rj(jLQivbv rtaQaMtfAov jro^tfcfyifi/ot, bg
TO JtQog [i6r}[i{lQiav psQog TOV 15
%i Tag fipBoccs xccl Tag VVXTCCS Jtddas faces
1CKVTC3V T&V iv Ty Gcpccioa TtaQaMtfA&v TGJ
llQLVG) XVXA.G) TOT [IOVOV Sfytt VTtO TOV
diaiQoviiVG)V) >S TK vitQ yY\v KVT&V T^itj^iaTcc opoid 20
T dMrjAois slvai xal face Tot$ vjtb yfjv xatf SXCCGTOV^
TOV Toiovrov pi} GviificcivovTos Jtl ^rjdf^iccg T&V
dMa povov plv 7td^.LV TOV farjitfoivov
dfycc T VTtb TOV OQ^OVTOS dtatoov^vov xccl
1. &dieTdKTa>s BC, corr. B. Mg. rovro TO -9-fo)^ Sice TO
%OQIG to ypa< 6 n/ D. 5. ^ft^fptrcov] ^BI^SQIV&V TQO-v D, TQonmv del. D 3
; rgoTtwajv Halma. 7. 5'] om. AD.8. a mg. D. 12. xa-ihttoi;] -4- in ras. A. 14. og] corr.
ex cos C 2. 15. TO] corr. ex rd D. 17. Ss] d' D. 18. ty\
rf\i corr. ex xr\ A.
102 KAATAIOT nTOAEMAIOT
rag xar' avrov rj^ieoag rats vv%lv faag rtoiovvros
at'cffi-yGiv, end Kal avrbg r&v [teyfar&v etirl
r&v 6s koiit&v eig avitia diaiQovyitv&v Kal Kara rb
ri\g fftiereoas oiKov^ievrjs eyxAijia rCbv [lev vonoregcnv5 avrov rd re vTteg yr\v r^itj^iara r&v vrtb yijv
xal rds rj[iQas rcbv vvurCbv ($Qa%vreQas
rCbv ds f$oQSi,orQG)v avdnakiv rd re VXSQxal rag fftiEQas nohv%QOViK>rQag.'ds xal afupfaxios ovrog 6 jtaQdMyhos rov
10 rjMov dig Kara xogvytyv rots vit avrbv yivoptvovKara rd rov farjiiSQLwv KOI rov Ao|ov KVK&OV r{MJ-
entire rors povov rovg yvd)[iovas iv ralg [i6ov-
dtixiovg yivtG&ui, rov ds i]lLov rb psvv diaitoQvo[ievov rd$ r&v yvo^dvcov
15 GKidg dnoKMveiv agog ii6rnipQiav, rb ds vonov agog
rag aQKrovg. KaC itirw Ivrav&a, otcov 6 yv&iicov
f, roiovr&v exarsga ijre fteQivr} KOI ^ %ei[ieQi,vrj 6xid
e xa&oAov GKidg rdg ev ralg
20 yivoyisvag Kal &g [tydevl |toAdycj diacpEQovtiag did
rb pri Ttdvr&s ev avraig ralg ^etiri^i^Qicas rds t ^n~
pSQiag Kal rdg rgoitdg aKQificbg d7toreAet6&at,.
rolg de vjtb rov faijueQivbv Kara KOQvtpriv [lev
yivovrai, r<bv dGreg&V) o^ot xar avrov rov
2. aim'] -si in ras. 1 litt. A 1. 4. VOTSLOTSQCOV, -EL- e
corr., D. 6. vvnrwv] bis C, sed corr. 7. dt] corr. ex rs D 3.
9. %GUV D. ovrog] ovrtog C, civ-cog D. Trapa/UTj/lotft B.
10. rots] corr. ex TTJS D4. 11. rd] ins. B a
, supra scr. C 2.
Supra TfiTJ^arK add. xotva D 4. 15. ngog - - 16. xca]
mg. A 1. 16. ivTav&cc] -a postea add. D. 17. %ai 17 %W-
Qivri] om. BC, post GY.IO, add. C 2. 20. a|to/ldya)] -o- e corr. B 2
,
corr. ex o> C 3. 21. lGr}(iQiccs] -a- e corr. A.' 23. <sr][iQi-
vov\ I- ins. A 1.
MA0HMATIKHS STNTAgES B'. 103
itoiovvrai, rag TtegKpoQdg, Jtdvrg de KOI avarslkovreg
xal dvvovTs (paivovrai rcbv rrjg Gcpatoag Jtoh&v iit
avrov rov OQi&vrog ovrcov xal ^irjdsva xvxhov noiovv-
r&v iitjrs rcbv TtaQaMtfAcDV asl (pavfobv T)ael dyavrj
H^re r&v [leGiHipQiv&v x6AovQov. ofatJGeig de sivcct, 5
per vito rbv farj[iQivbv evSfysG&ttC <pK6iv as itdvv
dta to rbv t/Atov ^rs rots xara KOQvyrivTtSi ret,
KV to &QOS fvxQdTov yivoiro^ \Lv\r iv rats VQOitccls 10
rov xccra xogvcpriv, &s p?d rbv
itoielv rtvg $ dtiiv ecu
OVK KV %Ol,[lV 3t7tl,6[lV(QS ^tVrov dvgo rots ano rijs xa& faces otxov-
xal ftxaGi'av n&M.ov av rig-
forogtav fiytj- 15
Gaito ra fayopwa itfgl avr&v. ra [ilv ovv I'dia rov
vitb rbv l<5ruiQivQV 3taQaMijA.ov 6vv^6vn titlv
ravra av fy.
7tQl d rcov AoiTt&V) d(p (bv xal rag oxtj0i,g
rivlg ol'ovrai, xart,Arjq)d'ai,, JIQO^^O^V ixslva xoiv6- 20
iva pri xa& ZxaGrov ravroAoyapfv, on, r rcav
xd0rov xard xogvcpyv yivvvrai r&v
o<5oi rrv fav 7ti(ELav dc6rxa6iv rov
1. noiovvrca] -vrcti ins. in spatio uacuo 2 litt. D 4. rag]
i/]
'
rag D. iteQicpOQag] corr. ex nsQicpfQEiag D s. 3.
corr. ex Y,v*1.mv C 2,HVHJ.COV D. 4. fityrf] p^de D. cpavfQo* D.
&yavfi\ &- supra scr. D 3. 5. x&v
mut. in TjLtfffrjft^ti;
3 B 2. 10. [lyre D. 13. ov%] o- in
ras. A. n7iiG^ev(og\ ns- corr. ex itsx- C 3. 14. [ISXQL] (t-
inras. D. 15. fyriGKiro] ^yrjffaro C 2. 16. rov] raov D. 17.
, -g del. C 2. 22. Ixaarov] Ixaffrrjff D, fxafftot D 3
.
104 KAATAIOT HTOAEMAIOT
tti rOV did TG)V 7t6A.G)V CCVrOV XVXJiOV, Y^V xdl CCVZOg
6 vitoxsi'iisvog ytaod^rj^og acpsGTrjxs, xccl on cpavsgbg
[iv del xvxhog yivsTcct, 6 jrdAcj per r& flogst(p jrdAo>
rov farjusQivov, diaGrruiart, de rd) rov Jtohov %ccQ[icirt,
xal oi BinteQL^a^av6^voi vitb tovtov
asl d' acpavrjs xvx&os 6 3t6A,G>
diccdrtfiiccTi, d TG> avr& ygacpo-
xal OL SVTOS rovrov dttsoss del
f$'. devrsoos yivBtai jrapa/U^Aog, xa& ov
10 f)iiQa 6rlv faacov toypsfivfttf i/3 d'. o^rog
rov t&fti*Qtvov potQccs 8 ^'. xai yodcprca did TaitQO-
f}dvr]$ rrjs v^ov. l6n d xai ovros r&v dyL<pi(5xC&v
rov r\Mov Tt&kiv dig rots vn avrbv ywopwov xara
xoavyfiv xal rovg yvcbpovas v ratg [i6ovQav>j<36i,
15 Ttoiovvros dtixiovg, orav d7td%ri rijg &Qi,vijs roonrlg
z<p xdroct rd iiorj [loi'oag o^1
/.',&6re rdg [ilv ovfr
ravrccg avrov dia7toovo^vov rdg r&v yvo^ovovGxidg ditoKMvBiv ig rd vorict, rdg d Aomdg 6cc, elg
rd POQBICC. XKL itixiv ivtav&a, olcw 6 yvto^icov |,
20 roiovr&v fj [ilv l<5rniQivri 6xid d y' /3' ? i\
xd y', f]$ %i[iai,vri AjS.
1. Sid'] d seq. ras. 1 Hit. B. 2. K^GTJ]V.V D. 3.
nolco (pr.)] wo^oot, i in ras., A; xeVr^o) D. 4. dictGt^uxi] -i
corr. ex -rj C. 5. V7CQi^oc^^ccv6(isvoi D. 6. $'] f ins. B,
seq. ras. parua C. noloi] om. D, i supra scr. D 4. 8. TOVTOV]
corr. ex rov D 3 et mg. D. &<pavsis] cc- ins. D 3. 10.
lanv D. d'] ins. D 3. OVTOS 11. d'] nag. B,
add. B 3. 11. fKHpag] comp. ABCD, ut semper.
. D 3.Ta- supra scr. D 3. 12. f'ort] -i corr. ex
rjC 3
.
corr. ex OVTCOS C 3, ccvros D. a[icpi6Kicov] -ft- in ras. A. 13.
wr'j VTTO D. 16. ^'] F^^. m] om. D. 18. v6ria\vmrBLu D
;similia saepius. <?a] G- renouat. A, G- e corr. B 2D 3
.
20. rotovTcov] rotov- in ras. A. t(3'] Z^'BC. 21. xa y']
xy a D.
MA0HMATIKH2 STNTAEE&S B'. 105
y'
. ratios ds iGxiv TtaodMrjAos, xa& bv av ywoiro
i\ psyfarr] rj^ioa &Q&V i&HpifUf&V iflL'. ovros de
ayt%(, rov farjpSQivov pot'oas rj x xal yodg)rai diet
rov Avakirov xohitov. <5riv ds xal ovros r&v dpcpi-
rov i\Mov dig rots vit avrbv yivo^Evov Kara
xal rovg yv&iiovas iv rats
Jtoiovvros, orctv rijs &Qivr[<s
ra [tEgy [taigas ^ ?<Q0rs ras [lev
ravras avrov diaTtOQZvoyLtvov ras rcbv
aitouMveiv itgbs [iSGrjuPQiav, ras de Aoinas 6%fi 10
agxrovs. nai i6tiv svrav&a, oicov 6 yvcs^icov |,
roiovrov
i$L' y', nd'. rraQros ds l&nv jra^aAA^Ao^, KU& ov av
ys'voiro ^ [ifyfarrj fjusQa CVQ&V &h}(&Qiv&v ifii' d'. 15
ovros d' an8%i rov farjiteoivov poiaas i${l xal yod-
ysrai dia rov 'Adovhinxov xoAnov. 6n d xal ov-
ros t&v a[icpi,<5xG)v rov ijAtot) ndfav dig rots vitb
avrbv *yivo[ivov xara xoovcpyv xal rovs yv&iiovas V
rats ii6ovaavtf6s6i,v atixiovs noiovvroS) orav a7t%Yi 20
(p xdrQa ra
1. Si IG-CIV} BG-CI D. 2. ds] d' D. 3. cuis%i\ corr. ex
]C 3. 4. Supra Avatirov ras. B. OVTOS] corr. ex
ovrcog C 3, civ-cog D. 5. rots'] corr. ex rccig D 3
. 6. [ifGov-
gavr^GfGi D. 8. Q^rj] -r\ e corr. D. 11. ngos] TCQOS rag D.
12. ^/.'y'] >]/_' y' A; similiter saepe. 13. tt'] A, i s' $' B,
Ts p C, i D. 14. 8] d' B, om. D. IGTL D comp. B. av]supra scr. A. 15. fajpepiyibr] om. D. d'] in ras. D, seq.ras. 1 litt. 16. <T] ^a| A, in ras. D. 17. 'Adovli-cixov]alt. i corr. ex o D. tcuv D, comp. B. ovrog] post pr. o
ras. 1 litt. A, corr. ex ovrcog C 8, avzog D. 18. VTC' D. 19.
yivoptvoig D. 20. noiovvrog] -og corr. ex -cog C. 21. ra]om. BC.
106 KAATAIOT UTOAEMAIOT
r, &6r tag plv Qi y' ravrag avrov dtattoomopevovrag rcbv yv&pdv&v Gxiag aitoxfa'vMv agog
rag ds hoijtag 6pd rg itobg rag ayxrovg. xai
wrav&tt, oi&v o yv&n&v |, rouovrovi\ psv
5 6xt,a ly y', i\ds frfQivrj /3, fj
^ ^eifiBQiv^ ftd g'.
7tttQKkA.rjA.OS) KCi& OV CCV yVOl,TO
rov farjpQWOV ^IOLQCCS tg ^J xal
ys v^Gov. fan $ Xtti avrbs r&v
10 rov fjMov dig rotg vit avrbv yLVO[ivov xara
xttl rovg yv&iiovag v ralg [i6ovQttvrJ66i,v
noiovvrog, orav aite^ri rijg &Qiviis rgonris (p' xccrQKra nfyq ^loioccg fit, Kn5r rag [iv 9 rccvrag avrov dicc-
7tOQvo[iVOv rccg r&v yvG)[i6vG)v Gxiag a7tOKkCviv Jtobg
15 [i6rm,poiaV) rag d Aoijtag ^o itobg rag agxrovg. uai
6nv fvrav&a) ol&v 6 yvcb[iG)v |, roiovr&v ^ P&v
va.
$'. sxrog Itirlv TtaQaMrjkog, xatf ov av ylvoiro
20 ^ ^iyi6rrj r^LBQa coocbv farjiifaiv&v Iy d'. anz%(, (f
ovrog rov fav}pQtvov [lotaag x id xal ygdyfrai, dia
NaTtdrcov. 6n $ xal avrbg r&v &pqpi0xnv rov
1. r*] (boc est %) fo A, lp C, t|3 BD, corr. in TQIXOV B 3.
y'J^ut.in F B 3
. 3. r#] r A, i C, 1/3 BD, mut. in r B 3.
5. ju,^] post ras. B, ^ D. 6. icxi D, comp. B. 7. r]fi8Q D.
OQ&V C. 8'] ds D. 8. ypaqpftat] 79- renouat. B 3. 9.
MeQorjs tfjs] -s t- renouat. D 3. V7j<yov] vrj- renouat. B 3
. HGUV D,comp. B. 10. Si's] dt>6 BC. Post yivoptvov 1 litt. del. D 3
.
13. xdg] reels C. 15. xat Icriv] bis D, corr. D 3. 18. va]
v vcc D, ^v aXico fii^Mcd itQOGKSiTcci TOLS vcc xai TO y mg. D 3.
19. ^Tt BD.'
20. 6000V C. ty] -y ins. D 3. <T] 8s D.
21. 5ta] ^ D, ut saepius. 8ict Nandrmv] corr. ex 8t' ccvoc-
Tcdrcov B 8,SLccccvundrwv C. 22. fffrtv D.
MA0HMATIKHS 2TNTAEE&S B'. 107
rjMov rots xar' avrbv dig yivopsvov xara xoavytyv
xal rovg yv&povag iv ralg ^rj^o^aig dtixiovg
Ttoiovvrog, orav aTtfyrj rrjg faoivrjg raoTtrjg <p xd-
rfaa ra n>Qr] [lOioag A,a, K>6rs rag pew |/3 ravrag
ccvrov dia7toQvo[ivov rag r&v yv&iiov&v Gxiag aito- 5
xMvsw TCQog ii6r][i($()iaV) rag d% Aomag 6cjrj agog rag
agxrovg. xai i^nv svrav&a., oicov 6 yvcbjiov |, roiov-
rcov17 pv faripEQivri 6xta xft g', ^ $ ftsQwii y L' #'
9 n
7taQdM.rjA.og, xa&' ov av ytvwtQ 10
(bgcbv farftiSQiv&v ~iyll. KTtiyti $ovrog rov ItirjiiSQivov [toioag wy va, xal yQaysrai duo,
Ttocorog ds 6nv ovrog 7taQdAA.yA.og r&v
ersQOGxi&v' ovdsTtore yap roig V7tb avrbv
iv ratg ^e^ri^QCaig at r&v yvco^iovcov Gxial 15
Ttobg ii6r][ipaiav KTtoKUvovGw, aW iv \L\V avrfl
rri ftzQivfi rooTtfi xara xoav<pr]v avrotg b rjA.iog
xal 01 yv(b[iovg atixioi, ftfooovvrai,' ro6ovrov
anfyovGLv rov IGVHLSQIVOV, o6ov xal rb &Qivov roo-
Ttixbv 6r][iLov' rov dl aA,A.ov Ttdvra %oovov cci rcbv 20
yvc)[i6v(x)v 6xi,al Ttobg rag aoxrovg (X7toxMvov6iv. xal
oicov b v&Gov ^ roiovrG)v i ev
1. roi<s\ om. D. uvxov] avr&v A. 2. jiSffTjftfJpi'cag] peoov-qavr\Gt6iv D. 7. ot'cov] o- corr. ex t A. 6 yvebfteoj/] corr. ex
z&v yvco(i6v(ov D 3. TOGovrcov D. 9. vrj ?'] corr. ex r[, J D 3
.
10. IGTLV C, comp. B. nccQciU^og] n- corr. ex v A. ys-
tTo] yhot C. 11. d'~\ SB D. 12. ovrog] corr. ex ovrcos C 3.
13. Za3i'v7]g D. ovros] ovrcos C, ovrog 6 D. 14. vno]'
CD. 15. ffxtat] -K- in ras. A, pr. i e corr. D. 16.
<7T^f3(Hay] -G- e corr. D. CCKOKKIVOVGIV C. 19. ant%ovGi D.
22. tanv evrctv&a D. 23. 7) (alt.) p. 108, 1. fort] om. D.
108 KAATAIOT HTOAEMAIOT
i<5ti. xal Jtdvrsg ds 01 rovrov
p>%Qi tov rr)v rftisrsQa
ovros stsQoGxioi, rvy%dvov6i,v ovrsg' ovdsnore yapxax avrovs OL yvcbpoves dv ratg p0ri[i(lQtais ovre
ywovtai ovrs rocs Gxias itoiovtiiv TtQog [i6r]ii-
aMa itdvrore TCQOS CCQKTOVS, dia rb [tr^de tbv
rtors Kara Ko^vfp^v avrots yiyvsGd'ai.
a& bv av yevoiro
7yl_' d'. Kitiyjti d7
10 ovrog rov farnisgivov yboiQag v^ t/3 xal yQatpsrai dia
IlToA.[iccidos trijs iv qflatdi,) xaAovpevrjs ds'
i^nv evTav&a, OLCOV 6 yvcojKov |, roiovrcovfj
yi'', fj ds farjpSQivJ] Ag/.' y\ ^
od g'.
15 -91
'. SVCCTOS fan 3taQccM.rjA.oS) xa& bv av
rj [isyfarrj ^BQa WQ&V farjiisQLv&v id. ane^st, d9
OVTOS tov i6r][iQi,vov fioioas A KJ5 teal yQacpsxai dia
nils Kates %G)oas rffc Atyvitrov. xaC i&nv
OICQV 6 yvG)[ia)v |, roiovr&v ^ psv frsQivrj <5xi
20 ^ ^ faYHLSQivi} A t/3', j]ds xsipsQivr] ny t/3'.
bv av
id d'. uitfyu d*
1. K6%i6g] &- supra scr. A 4. 5. TTOLOVGI B. 6. TCCCVTOTS]
seq. ras. 1 litt. D. apxTovg] -x- supra scr. A 4, rccs &QKTOVS D.
jitrfD. 7. UVTOIS MOTE xara KOQvcpriv D.
CD. 8. SGTL D, comp. B. 9. d'] 8i D. 10. (JLOLQCCS]
Ss]om. D. 11. sv] sv rj] D. j}paldri C.
mg. A 1. 'EQUSIOV] 'Eg- in ras. 4 litt. A 1
. 13.
14. oiJ] e corr. D 3. 15. WVUTOS C. isnv C. 16.
Ss D. 17. I] in ras. A. did] ds did C. 19. /_']xs D.
20. ifi' (pr.)] i B' BC. ^7] corr. ex Ty D 3.
ij3' (alt.)] I $'BC. 21. ^rt D, comp. B. 22. <T] ^' D.
MA0HMATIKHS ZTNTAEE&S B'. 109
ros rov farjiisQivov H,OIQK$ Ay Trj KCCL
6
,TOLOvr&v fj per frsoivri 6ma t, j]
ds i6t]^iOivrj
i<5xi 5rce0aAA7?Aog, xa&' bv av ysvoiro 5
rj \Lyi<5xr\ fi^eycc cbQ&v fariiLEQivcbv id/.'. aitE%ei d'
OVTOS rov iGifHLSQwov [loigas Ag xccl ypKcpercct, dia(
P6dov. xcct IGTW sinccv^a^ o'i&v 6 yvthpov |,
de %Bi^8Qivri ^yy y'. 10
/3'. d&dexccTos 0rtv TCa^d^iq^og ,jca^' oi/ av
-^ [isyfavn fniQa COQ&V farjiisgwcbv id /_' d'.
d' ovro? roi) ItirHieQwov jioiQag At/ Ac #at
ta ZJ{ivQvr}s. uai i6xiv wrccvd'cc, oi&v 6
|, rotovrcjv ^ iilv ftsQivri GKIK Ts rS, rjds i6r\- 15
y, a %Ei^QLvri Qi_ y i .
TQSMSxcudexccTos fan ^ccc^ctAA^Aog, ^a^1
'
6v av
v\ psyiGxri fmsga WQ&V i6rj{iQi,VG)V Is.
ovros rov farjueowov [IOIQCIS ^ v$ xal
. KO.I i<5xiv evrccvd'cc^ oicov 6 yv&yiwv 20
[iev
2.^f'tfTjg] -0- e corr. A. 3. z] ins. D 3
. /_'] om. D. 4.
t|3']t'
j3'AB 3
,I ^' BC; similiter saepius. 5. ta'] at B.
saviv C. 6. df
] ds D. 9. f) dt i' y'] bis A, sed
corr. fly] ft y D, ^ add. D 3. y'] om. C. 11.
t|3'] |3tB.
^(jTi D, comp. B. 14. ZIIVQVTJS] -s e corr. D. ioxiv\
IX 15. r*] 4 A, ^ B, 15 B 3, rs C, l_8" C 2
,/
ij D.
16.p, %m,Qt,vri\ supra scr. D 3
. 17. ty'] yt B. T^KT-
otat^'xarog^ 19. tf] dg D. ?s] I ts D. 22. 5'] in
ras. A. px] corr. ex ^x B 3
, px C.
110 KAATAIOT HTOAEMAIOT
id'. r06ao6xaidxar6s dn TtaodMrjAoS) xa& bv
av ysvoiro % iisyfarrj fj[iQa &Q&V far][iQi,VG)V Ts d'.
d* ovrog rov farftiEQivov poi^as ~\iyd xal yad-
dia MaGGaMag. nau <3nv fvrav&a, OLCOV 6
5, roiovr&vi] pv ftsQwrj 6xia %.{_' j/, ^ ds
v/_' y' ifl\ rids ^BI^BQLV^ Q^id.
bv av
ovrog TOV far][iQivov [loiQCis ]Te a xal
10 dlK ll00V JI6vtQV. GTW dl fVTCiV&tt, OIG)V 6
I, roiovT&vfj ply &Qivri 6mb v/y d
r
, ^ d LG^-
rcov avr&v |, rjd$ %i,[jiQivfj QV i$ '.
xxcu,dxaT;6s i6nv nccQccMyAos ,xa& bv av
V} [ifyfarr] ^Iga fagcav L6i
Y^iQivS)v t L' d'.
15 ait%i ds o^tos rov far][iQLvov poiQas ^ va xal
ygd(prai, dia rcbv nrj'y&v rov "I6roov jcora^iov. <5nv
dl Ivrav&a, OLCOV 6 yv&ii&v 1, roiovr&vf) [iv
6xia xsi', $ Se forjiifOLvfi %yL' y' ifi', n d
20 i% . 7traxaidxar6s 6riv 7taodMrJ.og natf bv av
ywoirodf ovrog rov farjiifaivov poiaas ^YJ A/3 xal yod(prai,
1. id'] 81 B. t66UQi<jY.uiSmciTos CD. 3. (IOIQCCS] om.
AC. ^] corr. ex I B 8C a. 4. Matftfa/Uas] pr. G in ras. A,
dice ^v^avriov mg. A 4, Mccccdfas BC, pr. a corr. ex IK D 3
. 5.
x] x C, x|3 D. 6. pp] Qii S' EC. 7. IF'] EL B. IGTL D,
comp. B. 9. a] 1 C. 10. j&s'ffov] -v supra scr. C 2, [itsov
TOV D. I'ffrt A, comp. B. 12. t/3'] corr. ex 18 C 2.
13. 15'] gt B. Ixxa^^atrog] AB, E^xat^f'xaTOg B 3 CD.
SGTIV] comp. B, Ss SGTI D. 14. tGTfpSQW&v] om. D. 15.
8t] 8' C. xal y^aqpfrat] bis D. 16. TOV "/CTT^OV] "IGTQOV
rov D. 18. |yj ||5 D. 19. poor] mut. in ^>odB3
. s'] mut.in ^5" C 2
. 20. *n ^ B. iffrt D, comp. B. 22. 8f] 8' BC.
MA0HMATIKH2 2TNTASE&S B'. HI
dia rCbv Ixftofaav Boav6&vov$. i'tiriv ds eweav&a,
OIG)V 6 yVO)[lK)V ,rOiOVrOV
T] [lV &QIW?I 0XLCC
,xcc&' ov av
ywoiro fj pfyfarr] r^SQcc ngcbv farjiisgivav Tg 6'. 5
d' ovro$ rov far][i()ivov [loigas v d xccl yQK-ia ^6rjs rifc Maicbndos Mpvqs. ftinv $ v-
OICQV 6
10'
ov av
fj psyfarri YI^QK COQ&V faruiEQiv&v Ig/.'. an-
d ovros rov faripZQivov ponces VK[! g' xal ygd-dia r&v voTi&Tccrav vys BQTTCCVICCS. Z<5nv dl
,otov 6 yvaiicov 1, roiovr&v
i\ ^lv ftzQivii 15
Ace'
i' r d
av yevoiro
ovros TOV tGrftLSQivov [loioccs vfi v xccl yQayercii dia, 20
r&v rov 'Ptjvov txfiok&v. fariv d vrav&a, OLOV 6
roiovr&v i ilv ftfaivr Gxia k r $
1. 6s] d* D. svtctvd'K] -K e coir. C 2. 3. %ei(iQivrii A.
Q7t D.' Mg. 79. y B 3. 4. IT?'] Tjt B. IGXI D, comp. B.
nagdJi\ D. 6. 8'] 84 D. v 8] C, ~vS ABD. 7. MaionSos C.
_^] 8' D 9. r*] fo in ras. A, r BC, r D. 10. ^ y']
tfTjy D, -r] e corr. C 2, supra y' add. o B 3 euan. (mg. r B 3
)et
eo C 2. 11.
i-fr'] -9-t B. 8vvccKaiSeKctT6g~] pr. -a- suprascr. D 3
. IG-CI D, comp.^ 13. 8s ]j^_C. s' xat] g% D
(h. e. Mat'). 17.(jxfl-] GH^ post eras, crx-d
1
y D. Supra y'add. r B 3
. 18. tcyrtv C, comp. B. 19. 8'] 84 D. 21.
fdTt A, comp. B. 22. Supra y' add. d B 3.
112 KAATAIOT HTOAEMAIOT
xa'. Eixotirbg TfocjTog EGxiv Ttaod^rj^og ,xa& bv
av ydvoixo q \Ltyi6xv\ fftLEoa &Q&V farjiifoivcbv it,.
aitB%t, 8s ovrog rov idri^EQivov [lotaag vd A xai ygd-
<pxai dice, r&v rov Tavdidog fxfioA&v. ftiriv d v-
5 rav&a, OLCDV o yv&^iov f ,roiovtnv
?? plv6xia A.d i' y t/3
r
, f}$ faripSQLvii jr/3/.' t/3', ^ ds-
/' JB>'
6or] L -
xfl'. SiKOGrbs dsvrsQog fan 7tciQccA.A,r]A.og, xct&' ov
av ysvoiro fj psyiGrr] r\^BQa caocov fayiiSQiv&v i^ d'.
10 aitiyti d' ovrog rov farjiieqivov (lotgag vs xcci YQK-
(percci dia BQiyawtiov rqg [iyK&rjg Bosrraviag. stiri
ds svrciv&a) OL&V 6 yvco^icov |, roiovrcovi] pv ftsgivri
6xia fa d', ^ $fa'iW>EQi>v'fi
X r^, T]df %iiiQivfi rdL'.
ny'. ixo6rbg ratrog 6rlv ttaQcckkrj&og, xcc& ov av
15 yeVotro f] {ifyfarrj fftLZQcc (boobv for)[iQLva)v tj/.'. ait-
d' ovrog rov far][iQivov {loioag vc; xal
[i6r]g rijg ii/
ydAr]g [email protected] v&KQv roiovr&v
20 xd'. Eixotirbg rtraorog 6nv jr(>aA^Aog, na& ov
1. sttiOGTOs itQ&z6s &>ttv] TtQ&TOS *v.l efaoGtos D. 3. ds]'
C. T] A, K BCD. 6. y'] corr. ex t D. t^'(alt-)]om. C.
8. flnoGTOS SevrsQOs] devTsgos xal efaoGTOg D. 10. ^']
^ D. 11. BQiraviccs D, t corr. in a D 3. &mv D. 13.
d'] ins. A 1 ante ras. 1 litt. Tte] corr. ex ny D. p^j r A,
IS C, f BD, corr. B 3. /.'] s
rD. 14. r^trog xat f^offrd? D.
SGTI D, comp. B. 15. a.7tE%si] 8t,%si, C. 16. ^'] fo' D.
17. BQETTCCVLOCS] rfjS BQsrrccviag A, rfj$ del. A 1
; BQfrccvviccg D.
*'] ^ D. _ 18. if] -^ e corr. D 3. r*] -^ ins. A 1
, y BC,corr. B 3
;r o D, o del. 19. y'] om. D. jff*e B extr. co-
lumna. -rAf] r^eD. 20. TSTCCQTOS v.ai ewoGtog D. $GTL D,
comp. BC.
MA0HMATIKHS STNTAgEQS B'. 113
av yevoiro r\ {Lsyfarr] qpSQcc agcbv
aTtiy^i ds ovrog rov farjpfoivov poiQag vt, xccl
dia. Karovgaxrovtov rijg B$rraviag. l6xi ds evrav&cc,
ot&v 6 yv&iicov 1, roiovrcovfj [lev ftfaivfj Gxia A-fr y ',
^ ds farjusQivfj 9/5 y' t/3', ^ df isiptQivri TOft if} '. 5
its'. stxoGtbg Ttepitros ttirlv nccQccMrjAog, Haft' bv av
ydvoiro fj peyfaTr] quGQcc ctigcbv i^r^L^QLvCbv Irj. aTtijjti
ds ovrog rov iGrftLSQivov {loiaccs wj w& yQKtpetat, di,a
voti&v Tr}$ [iMQag BasTTccviccg. 6nv ds evrav^cc^
6 yv&pcw 1, roiovrcovfj [ilv fteaivr} 6xicc ji r, 10
$1ds fariinsQivfi 9?, ^ df %iiioi,vrj vtO-
ifi
'
.
Kg'. SixoGrbg exrog 6tlv TtccQaMrjAos, KK& bv av
yivoito r\ \jLtyi6tri rj[iSQa COQ&V forjpsQivav njL'- ax-
ds ovrog rov fayiieQivov poiQag v&L' xctl yQaysrat,
a rfbv iifa&v rrjg P,IKQK$ B^rraviag. 15
OVK r6di&a d vravfta r rov rrdrov r&v
i r r
rovg ytaoa^^^ovg xal rrjv r&v ^aQ^idrcsv diayoaav
o^rjg poiQag (fwdy&f&cu, xal dia rb
lv 7tl r&v t'ri, ftoot,orocov Jtoo<3ijxiv 20
dib xal rovg rcov Gxi&v agog rovg
yv&povag Myovg &g iitl oupwaitinwov rox&v itQi,66bv
2. 8e~\ 3' C. 3. KCCTOVQCCHTOVIOV] rov GCCKTOVIOV D. BQST->Cug\ -rcc- in ras. A, BqetrccvvLas D. Saxw D. 4. y'] s D,
supra y' scr. g B 3. 5. rof5] roq D. t/3'] j- D, r supra
scr. B 3. 6. 7[{jL7tTo$ Y.oc.1 sfaocrog D. sort D, comp. B.
nocga.M.r\lo<s\ pr. I e corr. C. 9. Bgsravvias D. 10.ft]
ft ft D. r^J -R AD, in ras. B 3, p C, supra scr. quaedam
uan. C 2. 12. sxrog xal F^xoCTOg D. ari D, comp. B.
14. 8] S' C. 15. j^ax^ag C. BQsravviKs D. 16. fV-
Tfu^fO' D. rfr|Ta^TOv D. 17. re] corr. ex da' D. yCvtcfrKi C.
21. f^e^ya^fff'O'at D. 22. &cpoqLG^iv(ov CD, corr. D 3.
Ftolemaeua, ed. Heiberg. 8
114 KAATAIOT nTOAEMAIOT
x'. xccl onov [ilv roivvv % {ifyfarr] fftiEQcc GOQOJV
&, Xivog 6 naod^rj^og dnfysi rov
noioccg 1-a xccl yodyfrcct dice rfbv POQSI&V
rijg iiixoag Bofrrccviccg.
5 xr}''. onov der\ [isyforr] f][iQcc (tiQ&v itixiv farj-
'i KtVOS 6 JtCCQCchhykoS KTcfytl XOV 107]-
xccl azrai, dia r&v
defj \ji,yi6rv\ ^socc COQCQV stitiv
10 iiSQiv&v Jc, Metros 6 TtaoecMrjhos artfysi rov
xal YQacpsrcci, dta &ov^g r^g
K' . OTtov df ^ \LByi6xvi r^ieoa faocbv i<5xiv
Kivog 6 ytaQccMrjAog uitiyti rov
.' xccl yodspsrai, dia Exv&ix&v e&vcbv
15 Aa'. ojtov dsrj psyfarr] ypsQcc caoav itinv farj-
xfl, sxeZvog 6 ^^aAA^Ao? d7ts%i, TOV farj-
y, Xtvog 6 xccQccMrjhog ditfysi rov i6r}[ioi,vov
20 iiotoccg gg.
Ay', onov d% y [L&yfarrj fniQcc ao&v 6nv
xd, Xtvog 6 jcccQdM.ijhog dn%i rov
poiQag Jg rj ji. Tto&rog d 6rtv ovrog rfbv
xccra yag povriv rqv &Qi,vriv raonqv ^ dvvovrog
25 fast rov qMov at 6xi,al r&v yvcopovcov 7tl ndvrcc ra
4. BQtravvlas D. 7.fi] -ft
e corr. B 3. 10.
corr. ex IGTI^QLV&V C 2. 11. ^y] t?$-L- D. ovZrjs tfjs
VIJGOV] corr. ex CKvowav eovtov ayvwGTcov D, cfr. lin. 14. 12.
isnv tGj][LEQiv&v] om. D. 14. Sv.vQ'iK&v] Syi.vQ'r^&v C, corr.
ex GMOIY.(QV D 3. s&v&v] corr. ex eovoov D 3
. ctyvcoGtav]
corr. ex ccyvrnGxtoG D 3. 16. x|3] ttnoGidvo D. 19. xy] stv.o6i-
D. 23.?] ft] ? D. */j ^
J
D. 25. TO] om. B, add. C 2.-
MA0HMATIKHS STNTAEEaS B'. 115
TOV baftovrog [lEor] rag ifao<5vv0i,g itoiovvrcu. xai
ffSriv vrav&a b [LEV &EQivbg rgortixbg jrapaAA^Aog del
<pavo6g, b ds ^Et^iSQtvbg rooitixbg del dcpav^g^ did TO
diMpoTsoovg evakkat, EfpditTEG&ai, rov boi^ovTog. yive-
TCU ds xal 6 Ao|6g xal di,cc psti&v rcbv ^cpdiwv xvxAog 5
6 ccvrbg rco 6^tjoi/rt, orccv avrov TO IKQWOV
si tie rig a/Utts ftsMQiag f'vsxsv xal itey! r&v en
eyxlfasov sitifyroir] nvk rcbv bAo6%Q6-
TQO)V 6Vll7tTCQ[ldTa)V, BVQOL V, OTtOV TO f^CCO^CC TOV 10
POQIOV 7t6fov flOlQ&V StiTW |g fyyiGTCC, Xi ^dvvovtiag o'Aog Tag etp xaTQa Tqg ^EQTOV dia {I,6G)V T&V t,GtdCc3V XVX&OV pOlQttg 18'
TJJV yLsyCdTriv fipfyav xal T^V T&V Gxi&v 7tl ndvra,
TK pfyrj TOV bgC^ovrog 7tgtayco'yriv 6%dov prjviaiav 15
b'Grat, ya^ xal TavTa vxarav6r}Ta dia TOV
xavoviov r^g Ao|c6^C3g* o6ag yao av
VQG)[iv TOV farjjjisQivov jioiQag TOV itaadMrjAov dn-
%ovra rov dno^a^dvovra Myov svexfv 9' xdroa
TOV TQOTtLXOV 6r][llOV [lOLOag t,/
yiv6^lVOV $ TOT r\%0l 20
dfl (pavfobv 7)dfl dytavri, {iTa TOV aito^a^avo^vov
TinjpaTog TOV did {ifa&v TCOV tydicov xvx&ov, ratg
roGavTaig poioaig drjAovort, faifyEi T&V TOV TfTaorrj-
liooiov r^'Yi^drov 9 TO ^ao^a TOV POOELOV
1. ^97]] /*- in ras. A. 3. TO] om. D. 4. svcddi- D.
6. tcrHLSQWov] om. C, supra scr. B 3. 7. avccrsUrj] B, ava-
rsUH D, bvctx&ri A, fa&liii C. 8. IS mg. D 3. 9. lyx^t-
Gfcov] corr. ex ov Y.IIGSQ> D 3. 10. W'] B, om. ACD. 12.
dvvovaas] -o- in ras. A 1. 14. tj\v (pr.)] rrjv re D. 16. yi'yvf-
6ai D. 17. &v\ D, sdv ABC. 19. $<p'] T&V tcp' A, corr. A 1.
20. ytyvoftfvov D. TOTS'] om. D. 21.r/']
ins. C 2,
f^ D.
23. JLetyet] Jl- e corr. C 2. 24. Tfirjfidrmv'] -T\- in ras. A,
-v supra scr. D 3. jfogclov] -t- ins. D 3
.
8*
116 KAATAIOT UTOAEMAIOT
Aa'. xal oitov plv roivvv rb ^ao^ia rov jrdAov
dvvovtiag
[loioag A*
0%sdbv itl [irjvag fyyidra dvo rtjv re
5 JHIQCCV xal rovg yvafiovas 3tQi,6xiovs
Ag'. oitov dl rb Capita rov itohov poig&v i<5tiv
oy y\ *xl av rig VQOI pr} dvvovGccs rag Ifp
rijg &Qiviig r^OTt^g {loioccg jZs* &6r rtjv r
fj[iQav xccl rovg yvco^iovag Xfoidxtovg inl
10 fyyiGra 7taoarivi,v.
),' . onov de rb f^ao^ia rov rtohov IIOIQ&V i(5tw
orj y\ Xl av rig VQOI pri dvvovdag rag (p xdrQcc
rijg avrijg rooitrig {lotoag |* &6r
r^v re [i<
yi6rr]v rj[iQav xal rr^v r&v Gxicbv
15 aTtorffotGd'ai,.
Ay'. OTCOV $ rb Z^ao^a rov noAov HOIQ&V <5rw
Jtd, Xl av rig vooi \L^ dvvovtiag rag <p xdrgarijg ftfowfig roonrlg poioag of* KH5r Tffvra^rjviaiav
itdhv 6%dbv rqv ^yie'r^v fipfaav yivEG&ai, xal rovg
20 yvapovag rbv faov %oovov TtfoiGxiovg.
A-01
'. OTCOV $ rag oAov rov rfraorrj^iooiov poioag
9 6 fioQEiog Ttohog aito rov 6aiovrog f^Qrai^ Xt rb
plv ($oQi6rQov rov i(Sr^iQivov rj[it,xvxA,iov rov dia
lisGov r&v ^G)diov ohov ovdeitore vjtb
25 rb df vori(brQov 6Aov ovdfaorf vitfo
1. te"\ add. D 3. 2. IGTI D. 5. ytyvfff^at D. 6. Is']
add. D 3. 11. ilQ add. D 3
. 12. oFq] -TJ renouat. C<y' Jxft] corr. ex ys-nsi D. 13. 3>6ri\ cb? D. 16. Zij']
add. D 3. 19. G%s8bv nccUv D. 21. rds] zccvrag D. olov]
corr. ex 61?; D 3,deinde ins. td? D 2
. rT<xQrr}iioQiOv] tert. t
supra scr. A 1. 24. ytVsrat] ytyv
tat D. 25. y^v] yfjv
D.
MA0HMATIKHS STNTAEE&S B'. H7
fjusoav sxdtfTov eTovg ytyvstiftccf) [itav de vvxTa,
xaT8oav eyyitircc Qaiirjviai'av, Tovg $ yv&povag ndv-
TOTS TtsotfXLOvg Tvy%dvew. i'dia ds teriv xal Tijg
TOiavTrjg eyxMds&g TO re TOV fiogsiov noAov xaTa
xogvcpfiv yCyved&ai xccl rbv forfl&Qivbv rtjv re rov 5
asl yavsQov xal rr\v rov ad a<pavov$ xai STL rr\v rov
S01V KTtO^a^KVSLV f)7tQ y^g [IBV TCOLOVVTCC
TO POQSIOTSQOV SCCVTOV ndv ffltttyafytoV) vitb
TO VOTKDT8QOV.
Usgl T&V iitl Trjs syxexAiiievys 6<paiQccs tov 10
xai TOV
$rj T&V xa&oAov itSQi Tag
avsl'rj dt|at, rt&g av
IxdGTrjv EynlLGw xai oC Gwavacpsgoiisvot, TOV 15
XQOVOI, Talg TOV dia pfa&v TCOV Z&
xvxhov nsQiysQstaig, a<p &v xal Ta aMa ndvTa
xaTa ptQog axoAovd'&g ^iv nffrodzvfrfideicti, xaTa-
XgrjGoiisd'a [isvToi Talg T&V Z&di&v 6vo[ia6iai,g xal
jr' avT&v TCDV TOV Ao|oi) xvxAov d&dsxaTrjiiOQicav xal 20
ag T&V ao%c!)v avT&v drtb T&V TQOTtix&v xal farjiiSQi-
v&v Grjiisiwv Aa[i/3avoii8VG)V) TO [lev dnb Tijg tagivrjg
1. ytVttfohu CD. 2. ^yytcrra] eiTiGrct D, r\roi D 3.
\ alt. v ins. D 3. 3. sen, D, comp. B. 4.
om. D. 5. yiyvscftcii] A, yhssO'cii BCD. 6. ccyuvovs] &-
ins. D 3. 9. voTeiooTtQov C, corr. C 2
; voteioregov D, VOTLOTS-
QOV D 3. 10.
'] I BC, om. AD. lyxtx^f'g B. cyai-cg] GtpaC- e corr. D. 12. 6vvKvcc(pOQ&v~\ -o- e corr. C. 13.
ing. A. 14. civ HapfidvoivTo] ccvcdctpjidvoiVTo D. 17. rcc
Ua] A, raUcc BCD. 18. r]piv axoXov-O-cog D. 20. T&V]TOVTCOV D. xai] om. D.
118 KAATAIOT UTOAEMAIOT
is to, sitopevK rijjs r&v oAov
Koibv xaAovi/rsg, to de dsv-
rfoov TavQOv, xal iitl t&v %rjg coGavrog xara rijv
TtaQadsdoiiEvqv v^nlv ra&v r&v i$ tydi&v.
5 dsfeopsv de TCQ&ZQV, Qti a[ faov axfyovtitti, rov
avrov iGripsQivov GYHLBIOV 7t8Qi<pQeicci, rov dtu
XG>V tydfav xvxhov rats i'ticus asl rov
xvx&ov ytQi<pSQSicu$ dwccvatpegovrai,.
i'titG) yaQ iisGyppaivbs {lev xvxkos o
10 %ovro$ d^ v^iiKvx^iov rb BE/d^ rov ds far][iQivov rb
AEP xal rov Ao|oi> xvxAov
dvo ruijuara r6 re ZH xal
rb K) a)6r zxdrfaov pwr&v Z xal GripEC&v rb xccrti
15 rv faivv fariQiav V7to-
avrov
6ag ras ZH xal K dia rcbv
K xal H 6rniLG)V avacpQ0d'ai,.
20 A^yo, on xal at fxarfya avrcov 6vvava(poo^vai, rov
i(5r^LQivov 3tQi(pBQiai, rovr&nv ai ZE xal E,i'Gat, efaiv.
yao avrl r&v rov faqpfoivov TtoAcov ra A
2. KQLOV] comp. B, ut semper in signis. 4. i$] A, 6m-6ey.cc BCD. 5. Ifjfifjiu a mg. B, a Hfjmicc mg. C. dst^ofisv
SB] om. B. <?] drj D. tinszovocci] -at in ras. A."
6.
avrov ai](jLQi,vov] faqiieQivov rov ccvtov D. 7. tai$] on rctig D.8. 7tQi<pFQica C. 12. ZJf] corr. ex ZE D. 14. wC\
om. D. 18. xat] om. D. 19. v.u.i\ om. D. avacpEQS--i/a- supra scr. C 8
. 20. at] supra scr. D 3. ovvavava-
svai, D. 21. xal @E] E0 D. 23. iffrco] mut. inA 4
. avri] del. A 4. r&v] om. B, supra scr. C 8
.
rov] om. D. nolov B.
MA0HMATIKHS STNTASE&S B'. H9
xccl M Grjiieta,, xal yeygdyftodav dt' CCVT&V
xvxk&v T^^iccTa to re AEM xccl A teal en r6 re
AK xal ZM xccl MH. eitei ovv toy e(Svlv % ZHTi] K, xccl 01 diet T&V K xccl H yocc(p6[ivot,
aH^Aot l'6ov aiCBiovdiv <p' exdreoa TOV
G>6re xal T^V [i^v AK rij MH yive6&Ki fav\v, rfv de
EK rri EH, faoxtevoct aoa yiv&tui TO plv AK@V& MHZ, TO de AEK T& MEH. xal
'
$ ^Iv vxb
KAE aocc y&via L'6rj efalv T% vnb HME, r\de VTCO
KA o'Ai? T% vnb HMZ oty' &dTe xccl Howr} ^ vnb 10
EA Aowrf/ Tfi vnb EMZ fay e'tirai. nal (Id6i$ aocc
y E (Ideei, TTJ EZ fay itiriv' oneo edet, dei%cu.
ytdfov de defeoyiev, OTI ui avvavacpegoiievai, TOV
tGYHieQivoi) TteQiytQEiai Tcctg focus xcci i'Gov anexovGcuc;
TOV KVTOV TOOTtMOV 6rHLiQV TOV ditt {leCf&V TG)V fC3- 15
dfov Kvnkov GvvKiKpoTeocci, 6vvcc[i(poTeQai,s CCVT&V Talg
lit 6od"f}s Tils Gyatocts avacpooccis fam d6iv.
yap 6 ABF^J [ie<5r]ii{lQi,vbs nul tcovri[ii,-
TO Te BE^J TOV OQL^OVTOS xal TO AEF TOV
,Kctl yeyodtpfrcoGav dvo l<5ai Te nccl faov 20
TOV %ei^egivov Grjiietov TOV Ao|oi) xvxlov
1. xat^pr.)] om. D. di' UVT&V] corr. ex diu r&v D. 2.
to TE (pr.)] om. D. xt (pr.)] AK e corr. D 3. xal tti
3. ZM xca] MZ D. 4. dice r&v] corr. ex 81* ccvr&v D.
%at(alt-)] om - D- 6 - ^H MEND, del. D 3. 7. iao-
Ttlsvga} corr. ex loonfovgov D 3. AK~\ -& e corr. D 3
. 8.
AEK] EAKT>. MEH] -H in ras. A. 9. yom'a CCQCC D.10. (Ufl] om. D. 11. EMZ] AC 2
,MEZ BC, corr. ex
HMZ D 3. 13. Ifiwa $ mg. B, JT lr\^a mg. C. Ss] Sij D.
16. Gvva^cpotBQcei] ccl ovvupcpotSQUi D.
rats] supra scr. ^-a-y B 3. 17. avarpogcci D. facet] LGJ\ D,
supra scr. $ B 3. 18. ABTJ] ABF D. 19. rov (pr.)
AET\ mg. B 3C 3. TO (alt.)] om. D. 20. facet] supra scr. D.
120 KAATAIOT IITOAEMAIOT
XQiq)Qi,ai, ijr ZH rov Z vrtoxi[ivov
xalYIH rov vnoxsiiisvov eaQivov
xal to ftev H Grjtisfov xoivbv rrjg avaroA.ijs avrcbv
Lvai xal rov 6o%ovrog dia, rb vitb rov avrov
5 aAA^Aov xvKkov rc5 farnneQivK*
TtSQiAaiifSavsGd'ai, rag ZH Kal
H TteQiysQSiaS) GvvavcKpsQS-
cf&ai, de d^ovon rqv [lev Erri H, rty de EZ ri] ZH.
10 tpavsgbv ovv yivercu avro&sv,
on xccl olri v\EZ fay <srlv
rats rt' OQ&ijs rijg Gyaioasr&v ZH xccl &H avayoQaig. eav yaa v
vonov rov Gr][iQivov jrdAov rb K15 dt' ccvrov xal rov H yLyi<3rov xvxhov rrccorri^6oi,ov
rb KHA faodwccpovv r& iri OQdijs rr\$ Gcpaioag 6pt-
r H rijs
ZHi\
dl AZ ^ Gvvccva-
xal 6vva[i(porQccg
20 rag &AZ GvvaiHporfycug rats EZ faag r slvai xai
vjfb [nag xal rijg avrijs Xoi,%(j&ai rr^g &Z'
xal yfyovtv
fvbg povov25 xara [iaog Gvvavayoaag
dia rovrcov, on,, xav g>'
rag
,7too6an;od-
4. vnb rov] vn B. 6. vat] om. D. 8. 0E] E@T>. 9.
- e corr. D. 13. xat] om. D. H] corr. ex N A.
vno&ffievoi] v- e corr. D. 16. tcoSwa^ovv] -v add. B 3C 8.
*rjs] om. D. 17. TJ (alt.)] ins. D 3. 18. rjj] corr. ex ro D 3
.
19. ZH] H Z D. wars] corr. ex re B 3,rs C. 20. Ante
rds ras. 1 litt. C. <9EZ] 0- e corr. D 3. 21. onsQT D. 23. ^' Ini D.
MAGHMATIKHS STNTASE&S B'.
%o[iv xal rag r&v Aomcbv rgi&v
121
rovr&v ovv ovrcog %6vrov vf
P6dov itaQakkrikog ,OTtov
f\
fanv far][iQi,VG)v id L'I b ds
Ag, xal 6rco
nafav 6
Ttohog
[ilv o^toiog
rov 5
6
to BEA,dl to AEP, rov de
rcsv tydicav TO ZH0ovrcog %ov, &6T to H vito- 10
Xt6d'ai, rb WQivov GVHLSIOV. xal
kqyd'WTOs rov oai'ov nohov
rov farjufoivov xara rb K 6r^-
yieiov yeyQKy&a) di? avrov xal
rrjs xara rb A roping rov r 15
dia {LBGcw rCbv ^cpdC&v xvxkov xal rov bgi^ovrog
psyfarov xvxkov rsragrruioQiov rb KAM. rtooxffad'G)
$ ryg HA 7tQi(pQiag do-O-ft^g tr[V 6vvava(pQOiivr)v
rov far][iaivoV) rovr6nv rr\v EH^ VQelv xal
Jto&rov ^ HA rb rov KQLOV d&dfxaryiiooiov. 20
7ti roivvv Ttafav iv xaraygatpri ^yfar&v xvxAcov
stg dvo rag EF xal FK yfyoa^^vai, itilvij
rs EAxal
fjKM Tu,vQv<5ai aAkij&ag xara rb A, 6 rifc vnb
rr\g KA Jtobg rqv into rqv diitki\v ri\g
re rov ri$ VTIQ rfv ontv 25
4. ftf'v] om D. f][ieQa] j\- corr. ex v A. 5. (3o(uog A.
D, e)QTi]Tca ABC. 6. teT] -s e corr. C 2. 7. iv
'om. D. 9. picmv] -co- e corr. A.Sic* rov D 3
. 15. re] TB dt D. 16. uvnlcov D. 19. avty]bis D, corr. D 3
. 22. xcu] om. D. i rs 23. 1 at E4 D.25. ^T Pz/ D.
14. di' avrov] corr. exuvnlcov D. 19
ij rs 23. 17] at
122 KAATAIOT nTOAEMAIOT
rijs KA Ttgbs ryv VTCO r^v dijthijv rijs AM xal rov
rijs vnb rrjv dirtAijv rijs ME ngbs rr\v VTtb rqv. 74, 9]. AA'
rj plv rijs K/l 8nt^o/3 xal
f)vn avryv sv&sla r[ir][idrG)v o A/3
5 ^ de rils F4 poiQ&v Qrj xal q vnb avr^v sv&eia
(jidfcov c,J d v$) xal vtakiv % plv dt^AiJ rijg KA p
Q&V QV% pa xcdfj
VTib avrrjv sv&stcc rprj^dtojv QI Aa
f]ds 6inkvi rijs AM iioig&v uy tO1 v%" xal
i\vnb
sv&eta rp'rjpdrcov xd ie v^' lav aga axb rov
10 o A/3 d itgbs ta c d vs Aoyov g>Aco^v rbv r&v
(>tj Aa Is TCQOS ta xd Ie v, KarakeKp&riGBrai 6 rijs
i)7tb rr\v 8nt)^\v rijs ME ngbs rfjv VTCQ r^v diTt^v
rijs EF ^6yos 6 r&v Ty o 7- ngbs ra QX. nai itiriv
fjvitb rrjv diitlijv rijs EF rprjpdrcov QK' v\ aga VTtb
15 ryv din^v rijs ME r&tv avr&v stirw Irjo . tiers
xalr\ y&v dtJtAi} rijs ME iteQUpegeias [ILOIQ&V h'tirai,
, avrr\ dsf]ME r&v avrGbv
t] Ay. AA7
i\ HM jtsQKpsQSia rfj HA sn' og&ijs rijs cftpai-
GvvavacpeQsrai) r&v TtQoaxodsdsi'yiievcov [p. 84, 11]
20 <Srl [lOLQ&v x v' xal Aoiicr} aga ^ EH
4. 3] mut. in y" B 3. 5. 8ft ds SinJifj D. vno] vn D.
6. rg] v?" e D. 7. ^a] p$' D et, (3in ras., B 3
. M]vn D et corr. ex vno C 2
. 8. vno] vn D et e corr. C 2. 9.
ir^<W A._ J^ 8 (pr.)] y" in ras. B 3. 11. Xo] ta' D,
corr. D 3. *8 Is v\ renouat. B 3
. Is (alt.)] MJ' D, corr. D 3.
6 rf)g vno'] renouat B 3. 12. ME] ME loyog D. 13.
EP] E- renouat. B 8,ut in seqq. complura. Ir\
o s] corr. ex
t fl ffO- Ir\ Is D 3. 15. o i] corr. ex Zs D 3
. 16. totcci] Ictiv D;deinde del. Izvs~jJip. 17. tg] add. B 3
,om. C. Xij] ^ B.
18. 6^73] e corr. D 3. HM] corr. ex M C 2
. 19. cvvavcc-
vacpSQSTcci D. nQoanoSeSsiynsvtov] post -a- ras. 2 litt. A.
20. loriv D. 21.iJ3]
t- in ras. B 3, x|3 C, ifi supra scr. C'.
MA0HMATIKHS STNTABE&S B'. 123
xal GvvanodsdfLXTai,) on xal TO psv t&v'
dodsxccTrjuoQiov rots avTols %QOvoiS GvvavcccpSQercu,
id1
t/3, xaTQov ds TO TS Tijs HaQfrevov xal T&V Xrjh&v
rotg fafaovtiw els TYJV dwrAiJv T% lit' dg^s Tijs
avayopav %QOVOIS AS m^' oney edsi dti^cci,.
itdhv v\HA itEQiyeQSia 7tQi,s%eTG) T&V dvo dco-
aTrftioQiov TOV TS KQIOV xccl TOV Tavgov ^Loi'^ccg |*
dy TCL {jitOKEipeva T&V akkov HSVOVT&V T&V CCVT&V
$1 per diTtfa] T^g KA (loiQ&v yCv&tui Q^ v&^Lt/3
xal
fjvitb avrfv ev&stcc TIIYJIIKTGJV ()tj3 wy vg, ^ $* diit^ 10
TVJS AM pOiQ&v fta & wj xalrj
V7t CCVT^V ev&eZa
tpYilid't&v pf} a prj. sav CCQCI ncttiv aito TOV xtibv
o A/3 d Jtgbs Ta QJ d v$ hoyov atp^o^ev TOV tS>v
gift ivy vZ rtQO$ TK ftj3a jiu?, XKTcdi<pd"tj0Tcu 6 Trjg
vxb Tijv di,7tA.r}v Tils ME rtgbs TYJV vitb TVJV dinKr^v 15
os b t&v A/3 Ag d ngbs tec, QX. XCCL
iv\v diTthijv Trjs EF TjirjiiaTcw QX' r^ O.QK
v Tils ME T&V CCVT&V tetiv Aft Ag
xu.1i} psv dunki] Tils ME TtSQitpegsLas poig&v i<5nv
Ace A/3/
yyi,6Tcc, avrri derjME T&V CCVT&V Is p. 20
arjME <ttrj xaTa TK KVTCC TtQOKjtedetx&r] [p. 84, 13]
vt, p8' xal Aoiitri ago, v\HE poiQCbv fativ
vv\. 6 CCQCC Kgibs xal 6 TCCVQOS avccysgovTai 6vv-
sv OVOIS cc v G)V 6 Kib
1. cvvavccrtoSedfwTcci D. 2. cwavatp^Qerai] post pr. aras. 1 litt. A. 3. xat] xal TO D, r6 ins. B 3
. 4. -nfc(alt.)]om. D. 5. oiiSQ s^ft delicti] om. D. 6. vcov] om. D. 9.
yivsroci, fioLQatv D. ^TJ] QVT\ D. 10. vno] VTI D. 11. JIK]
-u renouat. C 8. ^] ABD, o A 4B 3 et in ras. C 8
. 21. f)]
xal i] D. 22. HE potQ&v SGTLV] EH D. 23. cvvccfiapoTsgoi,
Jv] 6vva(icpots(>ois D. 24. cvvavacpSQOpsvos] D, corr. ex GVV-
ois AC, Gwccvarpsgo^svois B.
124 KAATAIOT IITOAEMAIOT
%a6voic; i& ifi- xal povov ccacc TO
Tavoov dodsxaryiioQiov GvvavcupeQSTKi, %Q6voi x/5 jitsv
dia Ta avra de xdfav xal to (iv TOVr
Tdorj%6ov
d&dsxatrjpdQiov GvvavV%d"ri6Tai Tolg foots %o6vots
5 x(i jiHf,xdToov ds r6 T rov AZOVTOS xal TO TOV
Tots fairtovGiv Eig Trjv diit^v TJJS
avcupoQccv %QOVOI,S Af /3.
ds xcclvj ftv yLEyiGTri rj^isocc, fag&v itixiv farj-
id L\ fjds eA.a%faTr) &
/.', dijAov, OTL ncti TO
10 [ilv alto KKQKLVQV [iXQi> TOV TO^OTOV i
fj[ii,xv%A.iov 6vv-
avVxd"*J6Tat, TOV far]iiQi,vov %g6voi<s 6it> A, TO d%
cforo AlyoKfQG) pfygi 4idv[i(QV %QOVOLS QpP A. >B xcct
XCCTQOV {lV T&V XaTQG)d'V TOV fCiOWOV 0rj^lLOV
TTKQTrHLOQiG)V 6VVCCVVX^t]6TCCl, %()6vOl<S OK If, XttT-
15 QOV $ TG)V XCCTQG)d'V TOV [JiT01tG)Ql,VOV
V0t,$ ~QTJ jl. Xal kOLTtOV [lV CCQCC TO T T&V
HCCi TO TOV Afy6KQG3 dcotifXCCTTJllOQlOV XKTOOV 6VV-
avV%&Yi6Ta,i %QOVOIS x& it, Tots tefaovGiv ei Tovg
TOV TfTaoTrjiioaiov %o6vovs 'oa tf, Aotjrov d TO T TOV
20 Kaoxivov xal TO TOV TO^OTOV XKTaov %a6vois A Is
Tots teinQvGi ndkiv fig TOVS xal TOVTOV TOV TTaoTr]-
q)CCVQOV) OTL TOV CCVTOV CCV TOOJCOV TOVTOIQ
3. 6s] Srj D. 'TdQwoov] A, comp. B, v8qt%66v C, V$QO-
%6ov D. 4. 6vvctv%ftrlGtai B, Gwccva^r^cttca D, corr. D 3.
Ante rots del. o D. 5. gxarfpov] -o- in ras. 2 litt. A. 6.
rr?s(pr.)] CD, rot? AB. 8. 6s"] corr. ex Srj D 3. 9. 6s*]
6' D.10. TOV] om. D. 14. 6vvccvavt%fti]6tTcct, A, supra scr. vs A 4
.
If] corr. exir^
D. 15. -QOV ds r&v Ixar^-] mg. A 1. 17. cvv-
ctvavfx&riGtTKi, AC, corr. C 8,vs supra scr. A 4
. 19. rov (pr.)]
om. BD. 20. rb rov] BD, rov TO A, TOV C. 21. teinovGivCD. TOV] om. D. 23. uvrov] bis D, corr. D 3
. TOVTOIS
TQOTtOV D.
MA0HMATIKH2 2TNTAEE&S B'. 125
xal Tag T&V B^KTTOVOV T^ri^KTov TOV dt,a
T&V <pdiG)v xvxhov GwavctTohcig.
(f av v%or]6T6TQOv xal ti&odi,XG)T()ov avTccg
*a xal ovT&g.
6TG) yap itQ&TOv [isGriiiflQivbs xvxkog 6 ABF4 5
xal OQ^ovTog [lev fipLKVKhov TO BE4, farjpfQwov
ds TO AEF, TOV d dia fisdcov T&V fydicov TO ZEHTrig E Toping KKTK TO SUQI-
vbv 6r](iiov vitoxi,[ivr]g. xal
Jt aVTOV TfJQ 10
ETOV dia TOV
TG)
TOjfiT,
xal
Tog TOV A itokov TOV 16^8- 15
CCVTOV TTccQTrj^ioQia p,eyi6TG)v
TO A&M xccl TO AKN xal E'TI, TO AE.
<paVQOV TOIVVV KVTO&SV 0TiV,
OTi TO ETOV dia fifVov TCOV Jwdtcov ml pv oQ&fig Tijg
ty EM 7tQl(pQia TOV l<3rHLSQI,VOV 6VVKVa(pQTCCI,) 20
7ti $ TYIS yxxki,[ivr]g Tr\ fay TTJ NM, litBidr^nsQ
f) fJLV K TOV TCCCQCi^^OV 7tQHpQLa, 6VVO.V(X,-
<pQT(U TO E T[JLrl[lCl, 6[IOLCC 0Tl T% NM TOV l6V\-
[JiQLVOV) CiC d' O^IOICCL 7tQl,(pQlCCl, TG)V 7tCCQaA,A,rjA.G)V
Iv faoig jcavTcc^ij %Qovoi,g avacpsoovTcu. xal r EN 25
2. cvvccvKCpOQcig D. 3. noi ptQ'oMwtQOV\ mg. A 1. 5.
mg. BC. 7. ^EF] corr. ex. AEF D 3. 10. ccno-
C. 14.-xvjtlov D. 17. to (pr.)] r6 rs D. 20.
EM] ENM D. iteQicpfQslas D. 21. eyKhpevris A, corr. A 1.
NM] MN D. 22. K&] OK D, 0K D 3. avvuvava-
D. 23. icriv D, comp. B. 24. 8'] dt D. TTKQ-corr. ex 7tuQcd1ii]l.oLs D 3
.
126 KAATAIOT I3TOAEMAIOT
<5rlvfj
7tl
rov E rpijfiaros uvuyoQa rife id
0<pcu'oa$, dedsixrai Tf, on xal 3ca<9-oAov, eav
nv<s ovr&s 3tai(pai,cci, [isyfatcov xvxhcov cog rj
5 rb EN rpriiitt nsQis&i, TJJV V7tQo%Yiv r&v siti rs
teal rr\g 'yKK^ifjivrjs GcpaiQccg avcctpogibv
rov dia ILSG&V r&v t,G)di(av nvxkov
3tQltpQSl,G)V i}Tt6 T tOV E XCci XOV yQCC(pO[lVOV dlCC
rov K10 rovrov
p6vcQV rov r
rov far}[iai,vov ^utxv^Atcov, xctl
dia rov Z voriov 7t6Aov rov
fariiLSQWOv yyQd(pd'G) dvo re-
15 rccQrynooicc n&yfarcov Kvnk&v
ro r ZH xal rb ZKA,ds rb pev H 6rj-
rb xotvbv rov di,a rov
xxi<5&G)
v xccl r&v rov xal
20 *yQccq)0[ivov Jtccoa^tj^ov xal rov opt'fovrog, rb de Krb XOLVOV rov yoa(po[i6vov dt: rrls dox^S Aoyov VXV
1. ^/larrcov D. 2. GcpcciQcts] GtpuLQK$ uvucpogd D. ccva-
om. D. TTJ
] ini D. 3. on xal xa-^d/lov] xcct xa-91-
6/lov on D. SKV] corr. ex &va D 3. 4. TtSQicp^QEiai, ovrcog D.
me ^ AC, A&M supra scr. A 4, i] A@M xat post tog ins.
mg. C 2, obs ?j ^1M in ras. 7 litt. B 3
, wg 17 A&M xal ^ D.
yfKN, ro] xal ^ ^^JNT" ro mg. B 3. 6. xat] xal int. D. 8.
E xat] corr. ex EX C 3. 9. oTrcp ZSei ^r|at] om. D. Deinde
? ^ xaraypaqDT? D (fig. in eadem pag. est). 11. ^6r\^-
D 4, ^ D, f D 3
. TOO*] om. D. 12. TO] rcov roi) D.
D 4, ^ D, ^ D 3
. 14. for^etvotT) D 4,
f?\ D. 16.
TO rf] ra D. xal TO] om. D. 17. ft] di? D. 18. ^a] 6? t-
a D. 20. xal tov o^ovrog] om. D. TO 8s K~] rag. A 1.
MA0HMATIKHL 2TNTAEE&S B'. 127
i&v 'Iftdvov tjxal aMov Tivbg TCOV TOV
T^^LCCTCOV dfdopwov. etg dvotfi)
ndKiv [isyforcov xvxAcov
3tQicpQiag rag Z xal E ysyguppivai fidlvij
TS
ZKA xal17EKH TtpvovGat, aUtflag Kara TO K, xaC
6 xris vitb TJJV diTChfjv rr\s H itgbs TT\V vitb r^v 5
rrjs ZH Adyo? 6 Gwrjupsvog sx re rov rfjg VTtb
TYJV dinAyr ryg E agog tv\v vnb TJJV dtjrAijv rijg EAxal sx TOV rils VTtb rr\v 8iitKr\v rijg KA TCQOS TYJV
tr\v dnt^v Trig KZ [p. 74, 9]. AA' iv TtaGaig
ijTS dt?rA^ T^g H TtSQiyegsias fj avri\ 10
ttiriv yaQ r\ psTa^v TCOV TQOTtLX&v xal dia
TOVTO xal koiitri % dmMj T^g HZ. xal bpotcog mlr&v avT&v TOV dia \ni6&v r&v Jcodtcoi/ rpy^atfov ij
TS
rijg AK 7tQiq)Qiag dutkij xaTa naGag Tag dyxAfafig
i&ilvv\ avT^i xal didoTat, dia TOV Tijg Ao%(b6G)g xavo- 15
Wov, xal koiJtr} dta TOVTO itakivj] diithi] Tijg KZ'
&6TS xal TOV Tijg VTCO TYJV dtjrAijv Tijg E 7tgbg Tyv
vitb tr[v diTttfjv Tijg EA xaTateiittf&ai Aoyov TOV
CCVTOV v TtaGaig Tatg iyxkfatfw litl T&V avT&v TOV
TTaQTr){lOQlOV T{ir]lldTG)V.20
lav drj TOVTOV ovT&g fyovT&v Tqv Tr^g KA rtQi-
y>Qtag diafpogav dia 8dxa T^^iaTov TOV aito Tijg
farjiiQiag fag xgbg TO %i\iQt,vbv TQomxbv
TTaQTr)[lOQLOV 7taQaV^0CO^LV Tijg pfyQl TCOV
JtQt(p()t,G)V diaiQ0COg aVTCCQXOVg XaTCC 25
Tijg
1. rov'] om. D. 3. nctl] om. D. ij rf] at D. 4. nctl
om. D. ccUrjlcus C. 6. ZH] HZ D. 6] om. CD.8. KA] AK D. 15. dido-cat] -o- corr. ex -i- in scr. C.
17. -Ttlr\v 18. diTtirjv] mg. C 2(alt. -itlfjv etiam in textu C).
19. h] 8> D. 26. H] corr. ex &E D.
128 KAATAIOT HTOAEMAIOT
f^opsv TtKVtote ^OIQ&V [it, [ifi ~p nut rrjv vno
ccvt^v Ev&slccv TIWIIIKTWV pr] Aa vs, rv\v ds tr\<sHZ
A/3 it> % xai rr\v VTCO ccvtqv sv&stccv
[id vy. ctidavr&s de xcd tTtl [ilv TTJ
5 dsxcc[ioi,Qiccv ctTt%ov6rig rov eccgivov Gijpstov o>g ngbsrb %em,SQivov tQOTtinbv 7t8Qi,cpQSiKS tv\v [iv rvls KA
\ y ~i$ ual rv\v VTCQ avr^v
v\xe A#, tqv ds rrjg KZ dtjc^
QOCC vS [id xctl ryv vitb avrrjv sv&slccv
10 QL& ft/3 id. ml ds rri<s
7tQi,<pQLccs iv\v [iv Tijs KAxai TJJV VTtb avrfv v&tavds Tr}s KZ diTt^v HOIQ&V ()|d vd nccl
ccvrqv sv&slav r^irj^idrcov git] v ftf. itl d rijs A
15 ponces art%ov6ris 7tQi,<pQ{ccs iv\v [iV rr}s AKpOlQG)V Wy l& VTJ KKl TrjV i)7l
Twv xd L v$, rrjv d rijs KZxal rqv VTtb avryv v&lav r^r^Krc3v QI,
Aa T. litl
d rrjg fl iioigas <x7t%ov6rjg jtQi,(pQias tfjv [iV trjs
20 AK diit^v pOiQcbv A ^ ^ xal tfjv vitb avrr^v v&iccv
1. (ioiQ&v] sic ACD. vno] vn D. 3. vno] vn' D. 5.
rag I ft D. cog] corr. ex COGTO D 8. 6. rv\v\
corr. ex rrjs D 3. KA] AK D. 1. TJ y] rjy AD, corr. D 3
.
ff\v\ fn(i. B. vn6~] vn' D. 9. vno] vn3D. 10. enl]
corr. ex sn C. K (JLOIQCCS] slnoGtrjc ft D, ei'-noGi p D 3. 11.
xr\v] -v ins. D 3. KA]_AK D. 12. *ca] ins. C 2
. vno]vn 3
D. tg] corr. ex /Is D 3. 13. vno] vn' D. 14. TJMI;-
fiara D. 15. AK] KA D. 16. vjj] j]BC. ^7 xat]
NH SV
_D. vn6] 81 vn D. 17. Is] id' D. _ QVS] QKS D.
ft |3] pp D, fia ABC. 18. vno] vn' D. ia] A, o suprascr. A 1
,US C. Ts] i D. 20. AK] KA D. dtTr^v] -v
ins. D 3. i
jj] Jiij D. ^ (alt.)] om. C. vno] vn' D.
MA0HMATIKHS STNTA3E&S B'. 129
ce IK jity, rr\v $ ri\g KZva v(l xal rr]v i)itb avri]v sv&stccv
1
. eitl d rf$ v
vi)v [lev rijs AK 8nt'kv\v [IOIQ&V Ag sjiZg
xal rr\v vitb
&VTTJV sv&Elctv Turjuccrov Af T A#, r^v ds tys KZ 5
Qpy vd td KKL xv\v vitb avrrjv sv&stav
s ftd. sid ds rijs f iioigas fateffyfaift
v pw rtjg AK diTthrjv poiQcbv ]IK o1/tj
Kal rrjv VTtb ccvrriv sv&iccv r^irj^ccrajv pfl a pij, rr\v
$1 r^s KZ dnt^v [loigcbv ghrj v& pfi xai rr\v f)itb 10
ccvrfjv v&tav T^rj^idrov pt/3 wy vg. iitl df rijg o
Qi(pQtas rr^v [iv rijs AKji %$ xcci rv\v vitb avTrjv SV&SIKV
g 7^, n)v dl rijs
xal rrjv vitb avrr^v v&iav r^iiccrcov 'giv& ftf. 15
AK diit^v [lOiQ&v jZ? vS A/3 Kal rr}v V7tb avtijv
ft ;i, tyv $ rijg KZl rfjv vitb ccvrrjv i)&lav
d Tsr. 20
xal 8ia ta itgoKSL^evcx, ,eav aitb rot) rtjg t>^6 ri}v
b$ rrjv i)7tb tr\v diithijv rrjs HZAdyov, rovt6Tiv rov t&v
^LTJAce v agog ra Q& pd vy,
fxatirov r&v Kara
2. vno] vTt D. QLS] QI& D. 4. xr^v (pr.)] -v renouat.
B 3,corr. ex -a D 3
. AK] KA D. te] -g renouat. D 3. vno]
vn D. 6. vno] vn D. _7. F] e corr. D. 9. VTTO] -yjr' D.
10. xfjs] trfv D.^/Irj] >l7]
C. vno] vn' D. 11. r^rjficc-
roov] -j]- corr. ex v in scr. A. 13. vno] vn' D. 15. VTTO]
vn D._ i^] corr. ex ve D. 17. ytX] ^^1 D. vno] vn' D.
18. /^(ali)] jl seq. ras. 1 litt. C, om. D. 19. vno] vn D.
20. <H 8] QI$ ABCD, similiter saepius. 22. HZ] ZH D.
Ptolemaeua, ed. Heiberg. 9
130 KAATAIOT HTOAEMAIOT
rijg VTtb ri]v diithijv rijg AK Jtgbg rv\v vnb rr^v
rijg KZ Adycoi/, xarakeup&riGsrat, r^iiv xal 6 rfjg vnb
rijv diTtAijv rijg E Jt^bg rr)v vnb rty diithijv rijg EAAdyog Kara xdiSag rag fyxMtisig 6 avrbg r& rcbv | iicl
agog ra & A^ ?fal de rijg x itgbg ra Irj vg, iitl $\
rrjg ~K Jtgbg ra MJ a, snl ds rqg ft Ttgbg ra Ag Ay, enl
ds rijg v ngbg ra [id t/3, iit\ de ri\g | ngbg ra v ftd,
iiti ds rrjg o xgbg ra vs ft, iitl de rijg it agog ra
10 vrj vs.
tpavegbv de avr6&V) ori, xal xa& Ka6rriv rcbv
iBvriv fyovreg ri)v diitM]v rijg
, fat&tiifctff rotiovrcov farlv poig&V) otfoig V
rr)v Aa%farr]v r^^Qav fj t^/Ltf^tv^, xal
15 rfv VTtb avr^v v&iav rov re Adyov ravryg rbv ngbg
rv\v vjtb ri)v diTthijv rijg EA, f^o^isv xal avrr^v dsdo-
xal xv\v diithijv rijg EA 7tQi<pQiag, rjg rv\v
)rovrsdnv avri]v rqv EA, 7iQi%ov6av r^v
[p. 126; 5] vjtQO%i]v acpekovrsg aitb rcov
20 in OQ&ijg rijg dyatgag rijg xxi[i8vrig rov di&
7tQi,(pQLag avacpOQ&v rv\v xara rb V
rijg avrijg 7tQi(pQiag avatpogav
1. T7)s(pr.)] rbv rijs D. 3. Ttgog EA] om. D. 4. ra]r&i corr. ex rot C. 5. div,u poiQas] dsKccpoiQias B. Iqpafitv]
I- e corr. C 2. 6. #] corr. ex o D 3
. Ay] corr. ex \r\ D 2.
itgbs ra] om. C, ngos D. 6s (alt.)] 9 ins. D 2, 9 D
3. 10.
vs vi]' D. 13. tart D, comp. B. 15. vno\ vn D. 16. -bito]
-6 e corr. D. vnb rr\v] om. C. 17. Trepiqpf^fto; D. ^g]corr. ex slg C 2D 3
. 22. Hie des. fol. 42r col. 1 in A uacante
plus quani dimidia parte, in qua KVCOi\ secrecygacpt] ; fig. initio
columnae 2 est.
MA0HMATIKHS STNTASE&S B'. 131
ya.Q vnodsiy^arog svsxsv ndkiv
rov dia 'Podov TtaQaMrjAov, XK& ov % psv dtn^ij rijg
E 7tQi(pQiag ILOIQ&V stinv A A, 17& ^it avrr]v
v&ta r^^idrcov A?? Ad syyiGru. STtsl ovv 6 avrbg
Ao'yog 6rlv r&v f ngbg ra Ay Ad xai r&v [isv 0- Ay 5
ra f 17, r&v dl Irj i/f ytgbg ta i$ ta, t&v dlwrjaT<X
1/rj o, r&v ds Ag Ay nfpog r& xy x&, x&v ds
pd i/3 TCQog rot, xrj sci, t&v ds v ^d jrpog ra A/3 AJ, TWV
df vsji JCQOS ra Af v/3, TV df v^ v rtgbg ra AJ v/3,
yivsrat, xai fj JIGV vnb xr^v dfjrAiJv rijs EA 7tQi(p- 10
r&v df'xa poiQcbv viceQO%Ktv r&v
r^^drcov^ i\d fmfafia rijg vit
avr^v 3tQi(pQiaS) rovrfarw avrrj i\ EA^ ILOIQ&V Inl
filv rrjs TtQ&rrjs dsxa^ioiQias /3 v^, sitl ds rrj$ dsvrs^ag
v, iti ds rrjs rgfarjg r] A?/, litl ds rijg rsragrris 7a tj, 15
7tl ds rrjg Jts[ntry<s 1/y ^t/3,situ ds rr^g sxr^ Ts
^ts", itl
ds rrjg spdoprjs i>t, fcd, sill ds r^ff 6yd6rj$ ITJ xd, xal eid
rrjs tvdrrjs ds d^Aovdrt avr&v rcbvl/tj /If. &6rs
7tidrj [p. 84, 15] xal tri OQ^S rijg 6<pKiQK<s 17 pev
fi
r
%(>t rijg TtQ&ryg dsxafioigtag jtsQL<pQSi,a 6vvava- 20
(psgsrai, %QOVoig -9* t, rjds p>%Qt> rrjg dsvrs^ag Irj x,
17df p%Qi rijg rQir^g xv, fj
ds IIS%QI* rijg rsragryg
1. fVexfv ndUv] XKQLV D. 3. EG] 9E D. A] seq.
ras. 1 litt. D. <?'] <?e' D. 5. #] corr. ex o D 3. 7. o]
in ras. A 1
;b B, ut semper fere. xy] -y in ras. C 8
,x^ B.
it^] x^ D. 9. jig It] bis D. vjj] v- e corr. C. 11.
(jiOLQ&v] post p ins. t D 3. VTCEQOI&V] VTISQOZ B, -j]v add. B 2
.
15. Fv] ~iv D.TJ] corr. ex r) D 3
. ^] i- euan. B. 16.
?XT7jg] ? AC. 17. Y.8 (pr.)] xrj^ A; x$ D, r\ supra scr. D 3; XT?
BC. 18. ds] om. D. 20. dfxftot(>mt(i D. 7CSQicpQicc<> D.
_ 21. Z, T)] convex T^ AD 3. dfvr^ag] ^ D, {3
D 3. 22.
v, f)~\corr. ex v?j C.
132 KAATAIOT IITOAEMAIOT
A A, f)ds PE%QI, rife Tti^Ttr^ [i^xy, $ de ^E%QI rijg
vt, ftd, ^ df ft(> rife
T^g oydd^g o#, 5
rots oAov roi) TetaQtyiioQiov XQOVOIS 9 ? (pccvegov,
5 ort, ^v oupsh&iisv atp' SKaGrys rcbv EKKBI^VQV iit
rils 6(pciiQccs ctvKcpOQGbv xr\v ofaeiccv
s xattx trjv EA neQi<pQwv vneQO%i],
xal rag w r& vnoxst^Evc) x^art r&v ccvr&v avcc-
10 EKapoiQias TteQicpegsia rots AoiJTotg ^povotg
t/3, ^ d ft^pt r^? TSTccQTqs MS
Ay jitg, ^ de ^^t rij
rijg Endows v vd, ^ d ft^t T% oydd^g f
15 ^ df ^^^ rtjg Evatrjg, tovtEtitivrj
oAov roi)
f'x rijg fi[ju<f{a$ rov ^sysd-ovs tfj$ q
QOVOIS oa Is. xal ccvrcbv KQK r&v dexa-
Vfj {LEV XQ&TV} 6VVKVEVE%%"lfl6Ertti %Q6vOi<3 ff fcd,
^ d dEvtEQa S UK, i]df rptTT^ g A, ^ df
20 ^ df TtEyMtri Ay, ^ ^ ^^ ^ ^/5, ^ df
^ ds oydorj & fc^ 9 ^ df Evdtri I Ad.
1. Post^ del. rjD 3
._ 2. gxrijg] TTTTJS D. ^] -5
euan. A. |rj] corr. ex 77D 3
. 3. e] ins. D. 5. cup'] &nb
Tfjs cp' D. synsLfisvmv D. JJT'] snL D. 7. vTrs^o^?)?]corr. ex vnego^v D 3
. 9. (TvvavavfVf^rjaeTat D.17 f*^]
corr. ex jyiiv D 3. 11. dfvr^as] p"'
AC. 13. jxg] |tiyD.
16.(3 linnet mg. C. 17. cvvccvacpfQo^svoLS D. ^ovotg]
corr. ex ^ovos A 3. %at] xat r&v D. ^sxafiot^cov D. 18.
tfvvava^ibfaetca, supra scr. f, D. 19. fa] af D, ^,' D 3.
20. gxrrj] s' B.
MA0HMATIKHS STNTASESS B'. 133
<bv aitodeSsiyiisvcdv avro&sv 6ovrai> Jtdfav dice ra
tivvaitodedsiyyisvai xal ai r&v konccov
Kara, TO axoAov&ov avayogaC. rov
TQQTCOV
G)v ftp' xcc6vr]v
ye rqv nag' waGr
ravrag xavovix&g 7tQO$ r^v 7tl ra
iev CCTCO rov vn avrbv rbv l<5v\-
, cp&dvovrfs d ^%Qi rov Ttoiovvros COQ&V it,
v, xal r^v naQavt.rjGiv avr&v 10
7toiov[ivoi dia TO pr] a^Moyov yCvsG&ai
r&v fira^v rov fifMOQfov jcaoa ra b^ia^a dia-
TtQOTa^avTfg ovv ra rov uvxhov AS dfxa-
3taQad"tJ6oiiv IxaGrr] Kara TO e^ijs rovg re rijg
avacpOQ&s rov xMpaTos %QOVOV$ nal TYJV iiti- 15
v avr&v rbv TQOTIOV rovrov.
-at corr. ex a) D 3. 5. qp' xa-
supra scr. D 3. Ante avKcpOQag del. xa-O1
'
waGfriv D 3.
6. oWug] ovs D. 8. vn'] corr. ex In D 3. fcripSQivov]
$, D. 11. inLKQQiG) itoiovpevoL] r](iLCQQi,a67ioiov[ievoi D, a mut.in co D 2
. ysvtG&ui C. 13. nqoGTa^ccvtsg D, corr. D 3.
In extr. col. del. navoviov T&V nata SS^K^OLQLKV avucpo-o&v D 8
.
134 KAATAIOT nTOAEMAIOT
o=L
IS-
I$= J "J-J3
tfo
x
a CQ.
a IP a.
;!,;
I
23 | ras. .8?
s p- U> CD -N J
Qr Q,
a ?*
^Q,
cfecfefc
cp
1
o
14
MA0HMATIKHS 2TNTASE&S B'. 135
*t
m***
18-3 2 2
%-sg-'
u> a m"* - X
>Oee
ttt
rs
to to
<Ln
1e
i1
Or~
I
><a_*u> "53*
:J. ^V> fc QQ O
$= R-
1
IKO OQ
fl g
39la
fl'43&
.- afi
- 1g. j
09. pq 4^^^? .
S^Vf8
SI-g-
illO g S3
Q 11
h
II--3 OJOJ oo
-,,.*;- g o
136 KAATAIOT IITOAEMAIOT
s>
O-J. or-or=-3, ibi o-"
AJ5CQ
ea.
ed.
ssr
IP ^. Ji
^J5*-*
'I
x's
o a '
3-Sl.
s s s
i I-25 * ^
-2
^>
S "J
II i
iI
MA0HMATIKHS STNTAEE&S B'.
4*-*^$".a,
137
s- a
u>^j a. ^
a. ^ 5*
* 2 2
UJ 005
ig-
JT 005 005
o :Sfl
a co. a.8
.
CO. J^^54
005CQ.O
% Q^ Q..2 Q ^3 sr.Q ^ a a>H a.
<o IP&*"> sti -g tJ
r^coggrt ' > O&
. S
g .^ .rn-fc-S...Aa'^"i Q *
*-|.: -1-r^r jt*. U.
8 1:
S-^05 O $4 ~ti
jH
g .
a-J<>
-s ggt!
9 Sn
* 5^=-2 =5
138 KAATAIOT IITOAEMAIOT
1
"!""
-i? 3.
$.81:
3.^-
1 o
<sa.u> ^*.
tie
ii
vofc
poto
^j
-8
r*i
a?-*
s s
\aa'
** oa.CQ.oa. Qa.oa.Qa.
MA0HMATIKHS STNTAEE&S B'. 139
<fcX
1 1
rii
a fa8
QQ.QQ.3s g
X *"* X "i
g1
- X "J
t
ca. * in?> X
10 8
X "i
^^ ^Oi
r- O
f
2 ^^
140 KAATAIOT IITOAEMAIOT
PQ
- 58.
*2- a
9 1
g-2
*2<2
I
MA0HMATIKH2 ZTNTAEE&S B'. 141
if- a
^2*2*2 S 5-S
w
I
^5-s.?*
>i SH
05 2 . % .g- O 80
o.S
ft ^ g g
a* ($!~3 C6 I 1
^ 2 u>
,
8 n' <N^-: .so
ft
142 KAATAIOT HTOAEMAIOT
-&'. Iley! r&v xccra [ISQOS rats avacpogals
"On tie r&v avacpOQix&v %poVoov rbv
rgoitov f\iiiv xr&ei,[iVG)v evArjjtra ra hoiita jtdvra
5 yevrftferat, r&v els tovro rb [isgos Gvvreivdvrcov, KOI
ovre yQaiipix&v dei^ecov agog exatfra avr&v dsyGdiisftcc
ovrs xccvovoygaqjiccs TtegiGGils ,di avr&v r&v {)7to-
tfv yap 1% do&*fai}S fiptQas fy VVXTO$
10 fa[i{lccvTai, rb /Ltf/f-O'og fyiftprfolmow r&v XQOV&V rov
otxsi'ov xMnaroS) sitl plv rijs tfiiEQccs r&v anb trj$
polices l*>%Qi> tils dtaftcr^ov^g wg sis v&
ccnb rrls diapergovGrjs tbv r\kiQv en ccvr^v
15 iiotgav ttibv yaQ 6vva%d'VTa)v %QOVG)V rb plv nevre-
Aaflovrfs o^v, odcov eGrlv fagcov farj-
rb {)7toxt[ivov $i,K6rr][icC) rb de d&dexarov
f|oftv, o<?cov %QOVG)V 6rlv
rov avrov diccGrrfpccros-
20 evQitixerat, $ xal 7tQO%ei,Q6rQOv rb co
Acciipavo[Lvrjs ex rov Tt^oxeL^evov r&v avatpoo&v xavo-
viov rrjs VTtego'xfis r&v 7tccaaxi[iva)v
fjlifyccs [ilv rri rjfaaxfi fiot^a, vvxrbs $ ryev re r<p vnb rbv l^^egivbv TtaQcdAriAq) xal iv
1. -91
'] om. AD, mg. BC. 2. anolovd-ovvTcov D. 3. &vcc-
Kov XQOVOV D, sed corr. 7. vno8ei%&'riGoiiivcov D. 9. r[\
D. 10. &9tpf2&&r D, roov supra scr. D 3. 12.
ABC, [toig (^ D. 15. [loiQav] ABC, om. D. 16. lap-D. 17. 8] om. C. 18. AajSovrf?] om. D. 20. Postadd. Y,ctiQiy.6v B
3. 21. 7iQoJ,K(ji^ccvo^vr]s D. 22.
A, corr. A*. 23. [IOIQCC] AD, comp. B, ^VQKI C.
24. rov} -6- in ras. maiore A 1. rw (alt.)] bis D.
MA0HMATIKHS STNTAEE&S B'. 143
rov vyfoxi^vov x^arog' rfjg ydo vai6xo[ivr]g v
ox'fjg to $' Aanfidvovrfg xal ml [isv rov f$OQiov ^1-xvxfa'ov ryg l6vr]Vy^vrf g poioag ov^g 7tQ06nd'vrgavrb rotg rr^g farjiiSQivrjs piag cogag is %a6voig, itl
ds rov voriov ayxugovvrss &ftb t&v avr&v Te %qovG)v 5
rb jrAtjO-og rcdv XQOVCOV TVJS
$ rag plv dfdo^vccg xa,iQMa$ &gcx.g ccvcc-
ig foqpQi#ct$ xoMcvtAaGidGccvrfs rag plyfill rovg rqg fniQag fafivrjg rov olxsiov xM- 10
parog cbQicciovg %govovg, rag df vvxrQivag iitl rovg rijg
vvxrog' r&v yao 6vvcc^vrcov rb is' kafiovrsg
hoar foijiitQiv&v* avdnafav ds rag
ag cogag dva^v6o^v stg xaigixag
avrdg inl rbv is xal ^BgC^ovreg eig rovg vito- 15
xi[ivovg rov oixsiov dia^r^arog foaiaiovg %Q6vo.vg.
do&tvrog r^ilv %QOVOV xal cooag bitoiatidTenors
xo&rov [ilv IT\V dvareMovtiav rors poigavrov dia pte&v r&v Jcodtov xvxAov ^rj^o^ifd'a itoM.a-
itka<5id<3avrg rb Tt^^og r&v &Q&V fmfyag plv r&v 20
aito dvarohijg tyfao, vvxrbg $ rcbv dnb dv6og 3tl
rovg oixiovg faataiovg %g6vovg' rbv ydo
g'] fXTOv D. JLapfidvTfs A, corr. A 1
; \cc^dvov\ D. 3.
j? C; ffofvrjy^f'vTjs D, post etc- ras. 2 litt. 5. Te~\
D. XQOVCOV] -<ov e corr. D 3. 8. didonsvas D.
fv C. 9. noKTiCi'jtlaGia.GCiV'i D. Post \t,iv del.
ovv D 3. 11. mgiuiovg\ -i- ins. A 1
, seq. ras. 5 litt. D. 12.
if'] iff ABC, TttvrsHccidfxaTov D. 13. ifep&ra&Mr] corr. exD 3
. StSfo^ivag D, dsdopsvccs D 3. 14.
6idovTeg D. 15. TOV If] r&v dsKcmsvre D. 16. eapcaovg C.
17. oiaaS^nors D. 18. (loigav'] corr. ex wguv D. 20. nlf]-
-og renouat. B 3. x&v (pr.)] r&v Se&mpbrca* D.
144 KAATAIOT HTOAEMAIOT
dlEXf$a&OV[lEV f\llQag {lV CiltO TrJQ fjkLCCXijS
vvxrbg de artb ri\g diapergovGrjs &g ig tec
jt6[iva r&v cjdicov Kara rag rov VTCOKEL^VOV K^L-
parog avatpogag, xal ig r^v d9
av xarccvrtftir]
5 6 aQi&iioSi KiVYiv (ptftioiisv TOTS rv\v [Lotgav
sav ds trjv iiEGovgavovGav v7tQ yi
rag naiQixag &Qag itavrors rag ano rr\g
reg sitl rovg oiKtCovg wgiaiovg %Q6vovg rov
10 aQi&pbv tKfiakovpsv ajtb rr\g ^Uag% poiQag stg ra
srtopsva Kara rag cV OQ^g rijg Gyaigag avayoQag,xal slg $v av K7t6rj iiolgav 6
rors vitEQ yY\g iiEGovQavtftiEi,.
byioi&g $ ccjtb {lev ri\g
15 pEtiovQavovtiav VTCSQ yijg A,r]il>6[iE&a GxstyaiiEvoi rbv rrj
avarskhovtiri itaQansinsvov rr}g
v r& rov olnsCov uMfiaro
an avrov itdvrors rovg rov rfra^rrj^oQiov %Qovovg Q
rfjv TtaQaKEiyLZVYiv r& aQi&iiG) [loigav x rr\g smtivv-
20 aycoyrig rov it' o^^ijg ri}g Gtpatgag eskidiov rors vitsg
peGovQavovGav SVQ^O^BV. avaitafav 81 aito ryg
yijv iiEtiovQavovGyg rrjv avardMovtiav itakiv Ay-
a 6xipd[iEvoi, rbv rr\ [lEGovQccvovGrj poiya
tfg eTtiGvvay&'yrig aQi^^bv iv r& ri]g
25 Gaiag GEfadiG)' rtQ06&vrg a avr& Ttdvrors
1. TJJUxTjg A. 3. TOV] supra scr. B 2. 4. %at] om. D.
6. Ante yf]s ras. 1 litt. A. 8. do&ficris] do&L6ris WQCCS D.
9. G)QUXLOV$~] corr. ex xmqiafovg C 2. 11. Tag] rfjs B. &vcc-
cpoQKs] mg. A 1. 12. &v] D, sdv ABC. 16. fatccrelwoffj} C.
17. ohsiov] pr. t e corr. C. V.KVOVI D. 18. arc'] seq.ras. 1 litt. A, aito D. 22. ncchv'] om. D. 23. [IOLQK]
ACD 3, p B, ^ot'pt D. 24. Iv] om. C.
MA0HMATIKHS STNTABE&S B'. 145
ccvrovs 9 %$6vovs tiutixstyoiisd'cc x rijs
rov vjtoxf,[ievov xMparoS) Ttoict fiotQcc TCCCQCC-
xsttcci, ro5 aptttywp? xaxivrjv rors Kvar&hovGccv evQij-
<}0[lV.
(pavQbv $ xat, on rots pw vitb rbv avrbv peti- 5
otxovtiw 6 ijfaos ra$ faces faitft6Qt*$t
rijs [isGrjiipoias ty fov neGovvxtiov, rots
VTCO rbv avrbv [i6r][i(lQi,vbv rotiovrois farjiisgivots
oticus &v [loiocus 6 [istirHiflQivbg rov
nag exccrsoois dicccpsor]. 10
i. Ilspi r&v vrtb rov dia [isGcov r&vxal rov ps6r]iif$Qi,vov yivo[ievG)v
AOITCOV dl ovros sts tnv vnoxsc^svrjv ftsogtccv rov
rbv itegl r&v y&vi&v TtoiriGaG&cti koyov, Af'yco ds rcbv 15
rbv dice petfcov rwv ,G)diG)v xvxhov yLvo^ievov^
on, ooftriv yovCav vnb psyfarcov xvxhcov
#9t^jr0#af, orccv x6A,G) rr\ nowy ropy rcbv
xccl diatirtjuan rv%6vn yQcccpsvros xvxhov %
vrj avrov itSQiysQeia vjtb rcbv rqv ycwiav 20
3tQi%6vrG)v rprjpdrcov rrccQrr][i6oi,ov rov
2. vrtOKSititvov ] corr. ex eitinsiiiEvov D 3. ju-orpa] B;
fiA CD, ut solent. ,5. (JHXVSQOV jttfV] supra scr. D 3
. 7.
rots] COIT. ex TOV$ D 3. 8. (lEGri^Qivov^ jx D. 9. oWtg]
ccts corr. ex olg D 3. ftoi^at?] om. D. 10. nag'] fiot^at?
nag' D. diacpsQzi, B. 11. t'] om. AD, mg. BC. r&v (pr.)]
corr. ex tov B, corr. ex rov D 3. 12. xvx^ov] om. D. pBGrip-
PQWOV] jiD. 14. oVrras C. 15. r&v (alt.)] rov B. 16.
yLyvofisvcov D. 18. Xf'yojttEv] -v supra scr. A 1. 19. ypa-
ysvrog] corr. ex ygcccpovres D 3.
Ptolemaeus, ed. Heiberg. 10
146 KAATAIOT DTOAEMAIOT
xvxAov itoi^ xa&oAov ts, ort, ov ccv %?] Aoyov fj cbro-
voiivr} 7COiop0t,a Ttobg rov yoaywra xvxAov,
ov lQtjxa[iv rgoftoV) tovrov %i rbv Aoyov rj
7tQi%0[ivr} y&via VTCO rys xM<5a)$ r&v
5 agog tag t66a()a$ OQ&ds- &6*>) 7it,dri
oticw ccv
xaifj {>7tOTivov6a avrqv ycovia, oicov
ri [ILCC oQ&rj g.
t&v dfj agog rbv AO|OJ/ xvuhov
10 cci iiafoGtci %QrJ6i,[jioi, Jtybg tv\
Xivat ffaiv ca t vitb rijg To/&ijg avrov xal rov
psfSruifiQivov 3tQi%6[ivai, xal at vitb rijs ropfe avrov
xccl rov oo^ovros MX&' mdtirrjv &6t,v xal dpoi&s ai
VTtb Tys TO/iijg avrov xal rov dia r&v nokav rov
15 6(){ovro$ ygacpoiiwov ^yfarov nvxhov
rats roLCivrcag y&vicus xccl r&v a
rovrov rov xvxAov ytotfpOLG)v VTCo r
xal rov %6Aov rov 6oiovroS) rovrztirw rov
xara xoavcpyv 6rniiov. f'xatira yao r&v xxi^ivov20 drtodi%d*vra agog rs rr\v ftf&Qiav avrr^v Cxavcordrrjv
%d)Qav xal Ttobg rd stfol rdg 3taaaA,A.d,t,s rr^Q
rb ittelGrov
3too%G)Qtv dvva-
avv ri}$ zxeCv&v TtQodiKAtjfa&s.
25 7Cl d xal r66aQG)v ovGcbv ycovicbv r&v
1. noiEL B. 6V] corr. ex o D 3. &no^K(i^Kvofisvri\ pr. o
corr. ex s A 3. 3. fyei] corr. ex fysw D 3
. 4. vno\ om. D.5. &GX' D. IneiSvi'] corr. ex snidij A 3
. 6. vQiOKr)i;ai]corr. ex fv07J<>xr]Tca A. 9. #77] de supra scr. D. 11. rov- 13. *al (pr.)] supra scr. D 3
. 12. cu] om. C. 17. vno]v in extr. lin. A, no add. A4
. 18. xat] KVTOV KKL corr. ex
Y.KL D. 22. GvdttsTca C.
MA0HMATIKHS ZTNTASE&S B'. 147
vitb Tils r&v dvo xvxh&v roiifjSi rovrttirw
dlCC [l6*G)V T&V fydlGOV Xal VOS T&V dV^Tt^eXO-
avrcj, rt$l piac* rijg Kara rr\v ftiGiv 6[iotas for
Aoyov 7tot,i6&a(, ^fAAo^ti/, TtQodiOQiersov, on xa&ohov
rfbv dvo ycovi&v rcbv jcegl ir\v ito[i8vr}v tr\ xoivrj topi] 5
TG)V XVXA,G)V 7tQl<pQl,aV TOV Sia ^i(3G)V TG)V
x^v an? CCQXTCOV vitaxov6roV) &6TS ra ^v^xal ras xrjfaxorrjTas tag ajtodfi^ri^o^vas dvai
y&vicbv. a7tA.ov6TQas
fOV {l6r]ll(lQl,vbv XVXA.OV &G)QOV[lVG)V 10
rov Ao|oi) ycovi&v anb TOVTCOV a^6^id'a xal
)on, ra i'Gov drtfyovra rov avrov
rov dia [i6G)v rcov
ycwias I'tias j
t6rnLQwov yikv 15
ART) rov d
rCbv tySi&v rj
d rov i^-rb Z 6rj[ilov, xal
l,6G)V l'0K)V 7tQL<p- 20
Qici)V r^js rs BH xal B
(p xdrQa rov B faring i-
dia rov Z TtoAov xal
V XVXA&V 7tQl(pQiai
xvxhov ras
dia
vov 0r}[iiov
^@
3. Post pi&s ins. C 2.
6. 7tQt,(pQt,Kv^ mut. in
corr. D 3. 7. T] ra ^
9. K7iA.ov6rQccg] -ov- e corr. D. 11. a X^fifta mg.mg. B. 12. fcrjjuf^ii/oij] comp. D, ut saepius.
Jiicp&tG(bv A. 21. B] T?fc 6) D. 22. E] supra scr. D 3.
24. Ante xvxZcov del. TCOV D 3. nQi(pQicu] -i in ras. C.
10*
5. ya>vi&v r&v] supra scr. D 3-
C 2; 7tQl(pQ8t.CC V.U.C D?
D. 8. rds (alt.)] om. D-
. C, paragr-20. ano-
148 KAATAIOT nTOAEMAIOT
% re ZKH xal r] Z&A. A^eo, on, fay terlv y vxb
KHB yewLK rfj VTCO Z@E. KKI 6nv avro&ev yccve-
faoyaviov yaa yivsrai, TO BHK rafafovaov r&
7tidrj7tQ xal rag roig xfavQas rats rQitilv
5 itkevQtti$ i'6ag l^i sxaGTyv sxaGtrj) rrjv plv HB rfjjB
,
rfv ds HK ri] A [I, 15], ryv deBKry BA [p. 118, 5]-
dsdsixtai, yap ndvra ravra iv rolg [ntQo6&v' xal
ycovi'a aga v\btto KHB y&via ry vnb B@A, rovr-
10 rtdhv dsixrBov, on r&v rb i'^ov aite%6vrG)v
rov did [i6'G)v rcbv ^wdiwv xvxhov rov avrov rgo-
at TCobg rov
yco-
viai 6vva[i(p6rQai, dvalv OQ-
15 &ai$ fcai, sltiiv.
rov dia
ABT rov B
20 xal ctTtokrifp&EiGcbv iy xdrQa avrov rtQi,cpQi,(bv i'G&v
ri\g r B^d xal rijg BE 'yfyodcp&cdo'av did r&v z/
Kttl E GrjiiEiov Kul rov Z itohov rov ItirnLEQivov [i6-
7tQL(pQi,ai, fjT Zz/ xal
fjZE.
1.j\ re] KL D. xai
rf\ om. D.L'GYI\
i'- in ras. A. 2.
Supra Z&E scr. E&A D 3. 3. Icoyoviov A, corr. A 1
. ytyve-XCCL D. 5. endcr?]] om. C. rf?] corr. ex rfjg D 3
. 6. tj)
(utrumque)] corr. ex rrjs D 3. A~] A D. 7. TCCVTCC ndvra D.
8. KHB] corr. ex KBH D 3. B@A] corr. ex B@A B 2 C 2
.
9. Z(9E] -E e corr. D 3. ont-Q i-'dei $*%ai] om. D. 10.
pucc mg. B, ^ Ifi^a mg. C. Post L'GOV ras. 8 litt. B.
13. (isGrj{iQi,v6v] comp. D, ut saepius. 14. cvvctficpoTSTEQca A,corr. A 3
. 18. fj] corr. ex v A. 21. trig TS rfjs] t&vB4 D. 22. xat ("pr.)J om. D.. 23. $ rs ^] ZJ D.
MA0HMATIKHS 2TNTASESS B'. 149
onrj
rs vitb Zz/5 ycovia xccl ^ vyt ZETdvGiv OQ&CCLS facet, i6w. 6ri ds KOI
rovro d^ov avro&sv. 7cd yao rcc A xal E GYHLEIK
faov Kit8%i, rov avrov rgoitwov Gypst'ov, fay stirl xccl
fjz/Z 7tQi(pQia rfi ZE" xccl yovia agcc rj
vitb Z/IE 5
ycovia TV} vnb ZEBi'tirj
fariv. dM.ar\vnb ZEB KOI
ZEF dvelv oQ&als facet, efaiv xal % vnb Z4B apa
rijs -bnb ZEF dvtilv ogftccts fo<u efaiV OTCBQ
rovrov rtQorf&fGOQqptvcov &rco
6 AETd, rov df dia pfacov rcov ^codicov
xvxfaov rb AET rov AILGIOV V7tOXi[JiVOV rOV
QLVOV roonixoV) xal ifoAa) rw A,
dia6rij[iccri $ rr\ rov rerga- 15
ycdvov TchsvQK/
y'y()d(p&K) rb
BE4 rjiiixvxfaov. 7td roivvv
6 AETA yL6rnifigivb<s did re
r&v rov AEF Tto^ov xal
dice rcov rov BE z/ yfyytaCfftt) 20
rrctQrr}[ioQiov 6rlvfyE4 7tQi(pQioc [Theodos. I, 9]
*
KQCC 6rlvr\
vTib dAE ycovicc. 6^0'^ d did ra
deiyiLtva, [p. 147? 11] xal f}
vnb rov fteQivov rgo-
Ttixov 6ir]iiiov yivo^idvY]' oTtSQ edei dft^ca.
1. ZJS] corr. ex 4ZB D 3. j) (alt.)] om. D. 2. elaw
D. 3. xat] om. D. 4. sGrtv D. %<u] om. C. 5.
ZA D. ZJB] JZB B. 6. for] x<| mg. D 3. xat']
?j VTCO D 3. 7. dvciv~] -I- in ras. C. daiv facet D.
Z4B] -4- e corr. C 2,ZAB B. 8. dvatv] S- in ras. C.
OTCEQ tdfi dfi^ai] om. D. 10. (isv xvxAog] om. D. 13.
rov] om. D. 14. TCO] corr. ex TO C 2. A] corr. ex nym-ccp D 3
.
19. nolcov] -v ins. D 3. 23. nqoa.nodf8Eiy^vu D. rj]
add. D 3.
24. CTjftftov] om. D. OTIEQ edei Ssi^ca] supra scr. D 3.
150 KAATAIOT UTOAEMAIOT
15
0TK> n&r)iiflQt,vb$ per xvxhos b ARTA,farj[iQt,vov ds finixvxfaov TO AET, xod ysyQdtp&G) TOV
diK {LSGov Tfbv a)diG)v TO AZT fipMvxkiov ovtog,
TO A GrjiifZov slvKi TO
TS TK> A xccl diaQTr^aaTi
TOV TSTQaycbvov Ttksvga ye-
TO BZE4 fjiiixvxkiov.
dice TK O.VTK dy, titsl 6 ARTAdid TS T&V TOV AET Keel dt,a
10 T&V TOV BEA nohcov yiyQCMTui,
<5TlvijT A Z KOLl
I TO lV ZTO ^i^iQiVO
[p. 81, 50]
fjZ
ds vttb 4AZ yoviK TOLOVT&V gl/y me, oi&v 6Tlv
ilia OQ&ri 9. dice d TCC HQodedeiyiiEVK [p. 1487 10]
KKL i] VltO TOV EttQWOV far][IEQLVOV 6y[lEiOV
covicc T&V AOLTC&V ig *&S ^vo OQ&ag20 [loiQ&v Jg #.
6 AETA xccl
TOV df dlCC [l(5G)V
Z 6r][liOV VTfO-
TCEQlCpEQElKV
ZEwy ~VK
TG)V
6TO)
16YI{lQLVOV {LV ri^LiKVK^LOV TO
TG)V ^G)diO)V TO -BZZ/, CO(3T TO
TO yiSTQ7tG)Qlv6v, T^V df
1. ^ffTco] corr. ex l<jm> in scr. C. 4. catfrt] corr. exSre C 2
. Gripsfov] corr. ex GJI^LCOV C 2. 5. ra] corr. ex
TO C 2. A] corr. ex itQwrw D 3
. KKI] om. D. 6. Try] ds
ry D. 9. dice, (alt.)] Sid re D. 11. SGTLV] CCQK ZGTIV B. 13.
TQOTCIY.OV] -ixo- in ras. A. 14. syyiGtcc] alt. y corr. ex i in
scr. C. 16. i] vcc] om. D. 20. %f (H add. D. 21.
piv\ om. D. 22. del comp. ins. D 3. 23. BZJ] corr. ex
BJZ D 3. ootTTf] to? D.
MA0HMATIKHS 2TNTABE&2 B'. 151
irov vg TOV rijg naa&Evov xal TO Bde
TO) rov
TO H&EK iiyiixvx.kiov ,xal 5
Tqv VTCO KB y&-
VQiV.TOLVVV 6 ABF4 [l0-
did T Tcbv TOV
AEF xccl dice T&V TOV HEK 10
xd6Trj yiVETcu T&V BH xal B xal EH. dia dl ri]v xccTayQcccprjv 6 rijg vitb TYJV
Trjs BA TCQOS TJJV vitb rv\v dijc^ijv Trjg AHGwfptTKl X T TOV T^S VTtO T^V diTt^V Ti]S B Z 15
r\v vjcb Tr\v di7cKi]V Tijs Z xctl TOV Tijg VTCO
v rij? 0E yfQog T^V VTCO T^V ^ntl^v Tijs EHTV\V
[p. 747 9]. AA
5
^ ftfv diTtArj rijg BA dia TK
poiQ&v fanv xy x xali\ VTCO ccvTqv v&tcc
xd Z?, 17d dmhij rijg AH [LOIQ&V ovz ft 20
xalr\ VTCO avTyv v&la T^YI^KTOV QL^ Aa, xal
?] plv diTcki] Trjs ZB {loiacbv | xali] VTCO
1. TIUQVOV C. %at ro] TO $e D. 2. !!KQ-a.
ftevov] naQvov D. 5. H0EK~] corr. ex &HEK D 3. 9. rov
AET xat] supra scr. D 3. 10. SLO. %5>v\ om. D. HEK]
mut. in H0EK D 3. 12. xa! E xai] jB D. 13. ds] corr.
ex Tf D 3. 14. Ante rrjs (pr -)
eras, rfjg vnb rr\v Sm^riv A.
15. GvvfjTtTUi] 6 Gvvruiptvog D. 16. @Z] Z6> D. 19. x]om. BC. vn6~] vn' D. 20. tg] corr. ex ^,g' D 3
. QVS~] -v-
corr. ex 77in scr. D. 21. vito] vn D. fu^fta] v- e corr. A.
^a] ^o"i? D. 22. rrjs] r- in ras. A. ZB] BZ D. |]ioriv | D. -yjro] vn
3
D.
152 KAATAIOT UTOAEMAIOT
v&icc Tiirjpdrcov , fjds dmhij rrjs Z
xcclrj
vrtb avrrjv sv&eta r^irj^idrcov lyy ve wy. eav CCQK
7td2.iv anb rov r&v xd 7g agog ra QI ha Aoyov agp&co-
pw xbv r&v | JtQOg ra ^y ve wy, xccratei,q)d"ij0'ccct, 6
5 rvjs vjtb rv\v diTthfjv tij$ E 7tQO$ rr^v tino r^v dntK^v
TJJS EH Aopos 6 T&V pfl vrj fyyiGTa 7tQO$ to, QK. XCCL
etitivfj
VTtb r^v dirtAijv rye; EH r^irj^drov QK' xal
f\VTtb TJJV diTC^v KQK rrj$ E rcbv avt&v i(5tiv
[ifi vrj.
K>6re xcclr\ psv dt,7thi\ rijg E [toiQ&v stirw
[ij} syyiGTct,
10 ccvrfj dsfj
E r&v avr&v xa. xal oA^ [isv CCQCC fj
&EK avrtj rs xalj]
VTtb KB yovicc IIOIQ&V EGTIV
dia ds ra TtQoajtodsdsLy^vcc [p. 147, 11] xal17
vnb rrjs KQ%fjs rov ZKOQTIIOV yivo^isvrj y&via. x&v
facov <STCCL JIOIQCOV QLK^ EMttga [p. 148, 10] drj
re
15 vnb rils ccQX^S t v TCCVQOV xccl rijs (XQ%ijs
t&V
itl rijs avrijs xarccyQcccpijs q ZB XQt,(pQi,cc
VJtOKfa&G) dvO d&dfXCCTrjUOQl&V) K>0t TO B20 elvKi ryv KQ%YIV rov Asovtos xal r&v avtcbv
riv jiv diit^v v^g BA ILOIQ&V slvcaficc
xal
vnb avr^v v&tav r^^drcoAH poiQ&v pA-9
1 xal rr\v vnb
*d, xal itdfav rrjv pw SmKrp rijg ZB
1. 8ntKfi~] -i- corr. ex rj D. _ Z6)] corr. ex 30 A. 2.
vito] vn' I). xy] om. D. 4. xy] om. D. 6. fyytcrra] syy-in ras. A4
,e corr. C 2
. 7. ft om. D. 8. SGTL D. 9. @JE]corr. ex M D. 10. rj E] e corr. C 2
. 11. @EX] -Kin ras. B 2 C 2
;corr. ex E, KA D 3
. ienv] om. B. 12. ngo-
D. 15. r&v] -&v in ras. A. 16. vo\ A, ^ BCD.sdei dtt&L] om. D. 19. dwccTruiOQicov D, corr. D 3
.
21. dinlfiv] -v ins. C 3. 22. rr\v (pr.)] corr. ex xa>v D 3
. vno\vn' D. 23. vno] vn' D. 24. ZB] EZ D.
MA0HMATIKHS STNTASE&S B'. 153
lioiQcov OK xal rr^v vitb avri]v v&tav rfirjfjidr&v
^y ve xy, rr)v d di3tA.ijv rijg Z UOIQCOV xal r^v
vjtb avri}v v&iav rprjiidrcQv |. av aocc ita'kiv dnb
rov r&vji/3 ft itobg ra gift xd Adyov d(pJ.G)[iv rbv
r&v ~gy r ivy xobg ra 1, xaraA.i,(p&ri6rai, 6 rijg vitb 5
rijg E agog ryv vitb rfjv dnt^v rrjg EH6 r&v x vy rtobg ra ox' fj
aoa vnb r^v diithijv
rrjg E yCveroii rcav avr&v xs vy. &<5rs xalv\ [iv
^t^A-fJ ri]g E ^LOIQ&V h'&rai x ZyyiGra, avri] $f)
E riibv avrcbv ipL'> ofy [iv aoa rjEK avrtj rs 10
xalrjvnb KB y&vta poiQibv 6nv gPL', di& ravra
$ xalfj plv VTcb rijg do%ijg rov To%6rov 7tOL%o^i8vr]
r&v i'ticov oj$l_\ fxarsoa $rj
r vitb rijg do%ijg
didviacav xal rijg do%ijg rovr
Tdoo%6ov rcov Aot-
ig rag dvo ogftag IIOIQ&V of/.', xal dedixrai, 15
ra 3tooxi^va rijg pw avrijg 6o[ivrjg
xal ml r&v b'n [iixgoiifofGrzocov rov Ao^ov
aTtaQxovGrjg d' &g Jtobg avrriv ri}v rijg
xal rijg xa& exatirov r&v dwdfxa-
20
1. vno\ vn D. 2. QY v ] eras - propter fig. D, posteaadd. eadem manu. xy] om. D. 4. TOV\ rov re D, TS e
corr. D 3. 5. xy] om. D. 6. <9E] corr. ex EH D 3
. Deindeadd. Aoyos D. Ttgog EH] supra scr. D 3
. 7. Adyog]om. D. 17] corr. ex ty' D 3
. ^x- r[\BC 2D 3
, ^ ACT).
9.6Tiv_D.
10. //] ins. D 3. Mrf] s ofy D. 11. ^f]
corr. ex gift D 3.
/_']in ras. B, ^i D. TKVTO] TU avtd B,
rctvTcc CD. 12. Ss] D, ^' ABC. TOV] TO D. ns^is^o-pevr) ycovid] corr. ex 7feQi%o[ivrjs yavi'as D 3
. 13. /_'] ins. I)3?
i Icrrtv D. 14. a^^^g] om. BC. 15. [IOIQ&V] om. D./_']
4i Iffriv D, i tcTiv D 3. 18. d
3
]Si BC. 19. rcov] supra
scr. AD 3.
154 KAATAIOT HTOAEMAIOT
ia'. Ilol rcbv vitb rov avrov Ao|oi> xvxkov xal
rov oQi^ovrog yivoptvov y&vi&v.
'E(p%ijg $ dsfeonEv, rt&g av ^a^dvoL^ev itl rov
vov xMparog xal rag xobg rov bot&vta rov dia
r&v t,G>diG)v xvxhov pivo^e'vag y&vtag cbrAovtfrc-
Qav xal avrag s%ov6ag rqv [i&odov r&v koiitcbv. on
fiV ovv ai Ttobg rov ^i0r]^^QLvbv yivopsvai ai avrat
fttiiv ratg xobg rov lit* oa&fig rijg
(pavsgov VXv $ rov xal rag lit
10 Gyaigag kaiLpdvsG&at, deixrsov it&Kiv Ttacbrov, on ra
i'6ov vLTtiyovxct, 6rj[ita rov did [iGa)v r&v
xvxhov rov avrov I0rj^ioivov tir][iiov rag
7tgbg rov avrov boi&vra yco-
viag i'Gag dhhrihaig TCOIZI.
15 fGrco ydo ii6r]ii/3oivbg xv-
6 ABF^J xal l6rj^iQi,vov
Yiiiixvx^iov rb AET, oQi-
t,ovrog d rb BE4, xal y-/
yod<pd'G) rov Ao|oi> xvxkov dvo
20 r^itj^iara r6 re ZU xal rb
KAM ovrayg fyovra, &6re exd-
rQov [iv r&v Z xal K Grj^i&v vitoxBlG&ai rb [iro-
jt&Qivbv toypAQLVOV, rqv d Zfl" 7tot,cp0Lav rfj KA
1. IK'} om. D, mg. A 4 C 2,
at, mg. B. 3. 9s] Sri D- v
Zcc{jificivoi[iv] corr. ex avcdccfjipdvoifisv D 3. 4. diSopEvov] SL-
corr. ex n- in scr. D. 7. ywo^eu] -at supra scr. A 1,corr.
ex yevopsvai D. at] supra scr. D 3. 8. efaiv] -v del. C 2D 3
.
9. TOV] supra scr. D 3. syy.SY.kiiLevY] A. 10. A7)fifia a
mg. B, a IfippK mg. C. 12. ar^LfCov] supra scr. D 3. yivo-
liivag] ^yxfx^-tftfVag D. 22. otat] om. D. 6r}piov C. (isro-
no)Qiv6v] -x- corr. ex ft D. 23. ZH] ri]v ZH D: KA]corr. ex KJ B 3 C 2
.
MA0HMATIKHS STNTAEE&S B'. 155
faqv. kiy&, on xalfj
vitb EH y&via far] 6riv rfj
VTtb 4AK. xa stiriv avrd&sv dqhov' ttioy&viov yaQytuhv yivsrcci rb EZH rQiittevQOv r& EKA, itd dia
ra itQodedeiyiLSVK xccl rag rgsls itfavQ&g rats VQrtl
faces %ei, xa6rr]v xa6rr]^ rv\v pew ZH tfj 5
, trjv ds HE Tr}s topils rov optfovrog r EA,ds EZ rijs avccyoQ&s ry EK [p. 118, 5]. fay &QCC
xcil ^ [isv vTtb EHZ y&vCa rtf vitb EAK,ds
rji>7tb EH AoM-fj rfi VTtb 4AK l6r\ S&TIV
idei drgat. 10
da, on xccl r&v
V\tOV
Toov avarohwri H.STK tfjs
rov tregov dvnxfis dvtilv
far] fatCv. sav yap 15
bgC&vtK plv xv-
rbv ABT4, rov ds
&v r&v ^cpdCov rbv
AETZ, rfyvovrccg aMr]kovs xarci ra A xccl F Gr}-
ftfta, 6vraiKporQcci plv ijrs vxb ZA4 xal % vitb 20
4AE dvtilv doftals l<5ai yivovrcci. far] 6*i] VTCO ZA4
1. ioxLv] -v del. C 2D 3. 3. ro5]]corr. ex x&v A, corr. ex
TO D 3. dice] corr. ex 8r\ in scr. D. 4. nQocdsdsiyiisvci D,
-a- del. D 3. -ratg] D, om. ABC. 5. lxa<ytr^] corr. ex
l-AK6xr]v D 3. 6. HE] corr. ex NE B 2 C 2
. E A] -A e corr. C 2.
7. rf|] corr. ex rfj$ D. 8. iavfv] -v del. C 3. EAK] corr.
ex ERA D 3. 9. EH} EH- e corr. C 2
. 4AK] corr. exJKA D 3
. far] 10. d%cci] om. D. 9. i<rtt A. _ 10. s'Ssi]
-- in ras. A. 11. dt] S' A. JUjfifia p mg. B, ^ l^ppa C.
14. dvTiKfjs] -v- e corr. D. 15. i'arj IGXIV} ABC, foai
IIGIV D et supra scr. C 2. yap] AC 2D 3
,om. BCD.
^
17.
TOV (alt.)] renouat. C 2. 18. fifdcov] -v ins. C 2
. 19. ripvov-IK<S] r- in ras. A. xa] corr. ex TO C 2
. wat] orn. D. 21.
EA4 D, -A- renouat. D 3.
156 . KAATAIOT HTOAEMAIOT
rf] vnb Z-Tz/' coGrs xccl 6vva[i(porQces rrjv r vitb
xcel rfjv VTCO 4AE dvo oofrdg noiEiv OTCEQ s'dsi
r rovrcov ovras E^ovrcov,
[p. 154, 10] xal rcbv faov ditEftovr&v rov
5 cevrov i6r}[iai,vov Gruisiov at Tfobg rbv cevrbv QQi^ovra
&Ecoaov[iEvai, y&vCcu, facet,, rb xcel r&v rb faov ceit%6v-
rcov rov cevrov roonwov Grjiistov %j\v rov roov dvce-
rofaxrjv xal r^v rov srEgov dvnxr^v 6vvce[icporoa$
dvtilv OQ&CCIS faceg stvai. &6rE xcel dice rovro, sav
10 rcc$ KJtb Koiov ^%oi rcbv Xrjhcbv yivo^iEvces dvarohxas
', (SwcertodEdEiyiiEvcei Etiovrai, xal at rov
)v fiiiiXvxA.iov dvcerohixcel xccl En a[ rcbv dvo ^i-dvnxcei. ov ds rooitov dEixvvrcu, dice fiaa-
rj<5d[jiEvoi xdhiv VTCodsfy^Lceros EVEKEV
15 ro3 avro3 jrapaAA^Aca ,rovr6nv xce&' ov 6
%ilQrcei rov
Agi
ai {LEV ovv vrtb rcbv ,
w GriiLEi&v rov did
20 <7tov rcbv ^Ktdicav xvxhov
rbv oQi&vrce yivo^iEvca
vicei 7tQO%Ei'aa)s dvvcevrca
EKV y&Q
jiEV xvxAov rbv ABF4, rov ds v%o-
25 xEi^iEvov OQi^ovros rb dvarokixbv f)[nxv%A,iOv rb AE^J
2. ortfQ idsi dsi^KL] supra scr. D 3. 3. STficv[jipi]6STca'~\ -i-
in ras. A, rt CV^IJGSTCCL D. rs] supra scr. D 4. 6. TO (pr.)]
T D, del. D 3,om. B. T&V} corr. ex rov C 3
. 10. T&V\ om. D.
Xrik&v} Xj\- supra scr. A 1. 11. Gwanod^Ssiy^svcii] G- corr.
ex o A, GWKTioStdtiptvKi C. Deinde add. 8s D, mut. in 8y D 3.
12. *a~\ comp. ins. D 3. 15. voinieziv] -v del. C 2D 3
. 16.
A. In fig. a polo ducta est EK in AC.
MA0HMATIKHS STNTASE&S B'. 157
xccl rov lilv farffUftvov reTKQTrjpoQiov rb EZ, rov
6s diet pea cov T&V tydicov dvo TO rs EB xccl EFovrcog tyovrcC) K>6r rb E 6r]^itov nobg fwv tb EB
OElG&at, yLSTOTtOQlVOV , TtQOg df TO EFxal rb ^lv B yivtti&ai yti^BQi
rb ds F &Qiv6v, Gwdysrai,, on, rr\g plv z/Z
ysosias V7toxi,[ivr]c; poiQ&v i/d, xarQccg d r&v BZxccl ZF T&V fo&v wy vcc fyyiGra, xccl
f) \L\V
rb E x6hos 6rlv rov ABF ^rj^Qivov^ xccl ri\v
vxb 4EF ycwCccv r^v yivQ\LivY\v vxb rrjs
KQLOV roiovrcov dvai A #, ol'cov <5rlv i\ [itcc
vnb 4EB r^v yivQ^ivr^v vitb ril
Tcbv ccvrcov o vcc.
LVCC df xcclfj
T&Vr
cpodos cpccvsocc
7tl
plv 10
rov
j 9,
T&V
Aoi- 15
TCCl,
rog
vCccv vjtb rijg
TCCVQOV xccl rov
vov 20
[lV
xvxkog b ABF4, rov d' vitoxEipwov bg^ovrog rb ccvcc-
rofaxbv yuixvxfaov rb BE4, xccl yzyQKy&G) rov dice
2. ET] TO ET D. 6. TO 8s\ Ss TO D. T] supra scr.
C 2,E B. oTt]
f
o B. 7. BZ] corr. ex EZ Cl _ 8. xi.'(PrO]
om. D. -Aui f) [isv Tz/] bis C, corr. C 2. 9. I &] corr. ex kfr
C 2D 3. CO(7TF D. lO.JrW C. JlECJl^QLVOV
11. Z/ E T]
supra scr. D 3. 12. I #] corr. ex ^ D 3
. 13. 8t] 8s df-vrs-
QCIV D, rr\v add. D 3. 15.
17] om. D. ZotTrwv] koin&v r) D.
19. Ante y.aviav ras. 1 litt. A. 20. vno] vno re D. 22.
h D. 23. <T] 3s D. TO] om. D.
158 KAATAIOT DTOAEMAIOT
r&v ^(pdicsv rb AET i^Lixvx^iov^ cadre rb E 6r[-
rrjv KQ^V elvai rov Tccvoov. xccl eitel ev rovrc*
i& xUpart, rijs da%ijs rov Tccvoov KvarsMovGrjs petiov-
QccvovGiv vnb yv\v aC rov KCCQXIVOV poiQat, 1% jiZer
5 dedsfyaiiev [p. 144, 6] 7^^, itcbg ra roiavra %
di& r&v
yverat, ^
G) drj 3t6kG) re? E xccl dt,cc6rij[iccri, rr/ rov rsroa-
ytovov Tttevoa psyiGrov xvxhov r[ii}[icc rb HZ, not
10 3tQo6avci7t7tA,rjQG)6d'G) ro rs EFH rrccorr]n6Qi,ov xal
rb EA. yivsrai de xccltf
re z/TZ xccl $ ZH&xar
f
acc rfrccarrjiiOQiov did rb rbv BE b^Ct,ovra did
r&v TtoAcov ivcu rov rs ZJTz/ [i6rj[ji{$Qivov xccl rov
ZH& neyfarov xvxAov. ndfav fael cc[ plv rov KCCQ-
15 xivov 1% ]LCC [LOiQcu uitiyjQvGw rov fay[iQLVOV itobg
rds ccaxrovg till rov did r&v noAcov ccvrov iieyfarov
xvxAov iioioas xfi jL' xr&i,rcci, [p. 81, 32] ydo t\\jiiv
xccl rccvrcc' b df t&HUQivhg uTtiyti rov Z nohov rov
QQitpvros Bill rijs ccvrrig Xai(paLccs rrjs ZJTz/ ^oCgas
20 ACT, GwdyErcii xcclfjZF itQt,(pEQt,cc {loiacbv vvj p.
rovr&v dri dofrwrcov yivzrai hontov did rrjv xara-
iv [p. 767 3] 6 rr}s VTtb ri\v ntkv\v rrjs F4 Jtobg
vjtb rr\v dt^Aijv ri\<s z/Z Aoyog b 6vvr][jL[JiEvos ex re
2. Ante *at ras. 6 litt. D. 4. pec] corr. ex ^A? B 3. 7.
B. 9. vtlevQ&, a renouat., C a. HZ] ZH D.
10. TO] TOL A, sed i eras.; corr. ex TOO D 3. 11. Post EJ0
ras. paruaxn C. Ss] 8ri D. 13. (jiSGrj^eGrj^QLvov C. 14.
snel at] corr. ex Int D 3. 15. ccni^ovGi BCD. 16.
om. D. 17. xfl]- in ras. B 2
. ^xT&fctrai] -r- alt. in ras. A 1.
20. ZT] TZ D. 21. 5rj 9o*tvcmv\ AD, S^co^vrcov BC.22. -cfjs (alt.)] corr. ex xrjv C 2
, TTJV B, om. D. 23. re]
om. D.
MA0HMATIKHS STNTAgESS B'. 159
rov rrjg vitb ir\v nt'kv\v rijg FE icgos rr^v vnb rrjv
d(,itki]v rils EH xal rov rijg vjtb rr^v diitA,i}v Tys
H Ttobs rfv vnb rv\v dntki]v rij$ Z. aMa did rd
7tQoxei^va rj [iev diithii rijg Fz/ yiOiQcbv i&nv |/3 t
xal % VTIQ ccvrriv sv&sta r[irj[iKTG)v |/3 xd, 17de
rrls z/Z [loiQ&v ^Jt xcclr\
vnb avrqv svd'ela
rcov ^x, xccl itdkivr\ [isv diitAij ty\g PE {IOLQ&V QVS x
xalfj
VTtb avrr^v sv&slcc r^r^idrov QI^ td, ^
rijg EH poiQcov ^Jt Kal r\vxb avri\v ev&elcc
Tav ^3c. sav aQtt ccTtb xov Myov rcov |/3 xd JCQOS TK 10
QX ayeA&iisv rbv r&v git, id xgbs ra
Gstcci, fftitv 6 rrls vjtb tr[v di,7tA.ijv rijg
v%b rr\v ntKv\v tij$ Z Aoyog 6 r&v |y v(l itgbg ra
^x. xcii i$rivf] i)Jto rr^v 8ntk;
v\v rijg Z r^^idrcsv
QX' xalYJ
vttb rriv diit^v aga r^g H t&v ccvr&v 15
etinv %y vfl. GHSTS xal % per Sinki] vys H poiQcbv
iGxiv %d x, f\ ds H avrtj re xal % vxb HE y&vfar&v avtcbv A/3 I' oitsg sdsi, Ssl^at,.
6 d' avTog TQOTtoS) tW[iri
xa&' f'xaGrov ravro-
iyxvv&nev rbv vjto^ivri^ar^^bv rrjs 6vv- 20
,xal iitl rcbv koLTt&v dcsdsxar^o^cov re xal
cw v\yiiv v
3. Z0] Z D. 5. ^6] i>n' V^ ds] r C. 6.
vn' D. 8. vno] vit D. 9. QTt] $r) A. vno] vn' D. 10.
r&v] rov T&V D. 11. xara^gj^fffTat C. 12. @H] ABC,H D et supra scr. C 2
. 14. <9Z] Z<9 C. 15. H&\ corr.
ex II A 3. 16. lmv\ A, om. BCD. 18. onsQ ZSei defect]
om. D. 19. d'] om. BC. fvcc iWcrroy] bis D, corr. D*.
20. vTTOftvrjiaTtaLtdv -a- e corr. D.
160 KAATAIOT nTOAEMAIOT
ifi'. IlOi rcov ftobg rbv avrbv xvxkov rov
r&v Jtohcov rov ooi^ovrog yivo^VG>vXal JtQig)QiCOV.
AfiJto^vrjg drf rijg (p6dov, xa& r^v av
5 xal rag agog rbv dice rcov noAcov rov boi^ovrog
exdtirrjv lynkiGiv xai KU& ixddrrjv ftitiiv
rov diet psGcav rcbv tydiov uvxhov yavias tivvciito-
cos efpaiisv, xa6ror xai rf\g ebroAafi-
QHpQitt$ rov dice r&v 7t6&G)v rov 6oi-
10 frvros xvxhov V7i6 r rov Kara xoQvcpijv (Sr^neCov xal
rijs ytobg rbv Ao|6v uvxhov avrov ro/iijs, Bx^ri^o^e^a
xal ra ig rovro rb [iQOg 7tQoA,a[ipav6[iva xal
no&roV) on x&v faov a7t%6vrG)v rov avrov
6r][iiov rov dia pfacov r&v ^cpdi&v nvxhov
15 6rjtiiG)v fcovs XQOVOVS axohaiiflavdvr&v l<p xdrQarov iL6rj[i{loivov ,
rov psv nabs avarohds, rov d'
irfyov TCOOS dvGpdg, ai re anb rov xara xoovcpijv cV
avra nOi(pOiai r&v pEyfarcw xvxh&v faai aMrfhais
i0lv xal at nobs avra yivopwai y&viai, xa& ov
20 di6riA,d[Ji&a ro6jtov^ dvtflv ooftais i'6ai.
0rco yao ii6rjnf$Qivov r^irl^ia rb ABF, xal vrto-
xi6d'G) 7C avrov rb [iv xara xoovfp^v 6rj[iiov rb
B, b dl rov farj[iQivov 716^0$ rb P, xal /
yi
yod(pd'a)
rov dia [ifacov rcbv ^codicov xvxhov dvo
1. t|3'] mg. C, om. AD, |3t mg. B. avrov] lo%6v BC,mg. IQ^QV pro scholio C. 4. dij] Ss D. 5. r6v\ suprascr. C 8
. 7. Post nvxAov ras. A. 12. xal ra] xa, xat D.
rovroi] corr. ex rov D 3. 14. rpojrntoi;] -i- corr. ex o in
scr. D, supra pr. o ras. 1 litt. /Uyju^a a mg. B. 18. T&V}om. D. I'cai] slalv foca D. 19. f^fftV] AC, comp. B, om. D,-v del. C 2
. ctvrov D. yivopEVKi] yivopccvai, A, mg. e.
MA0HMATIKHS B'. 161
TO rs A^dE xal rb AZH ovrog sftovrcc, coo'rs ra Axal Z 6rj{isicc l'6ov rs K7te%Eiv ccnb rov avrov rgoitwov
xal faces K3toAa(jifldvi,v 3tQi,cpQias rov <Jt' avr&v
TCCCQCC^ri^OV (p' K(X.rQK
H rov ABF [i6r][i(lQ(,vov. 5
Zk- -*^>^ ysyoKwQ'GMSav ds xccl
7tQl-
dia rav z/, ZKTtb plv rov r
rov farjiieoivov 10
re F4 xal $ TZ,ebro ds rov B rov xarcc
xoovcprjv GriiLsCov ijrs EA xccl
fjBZ. AeyG), on,
rj
ply BJ rtSQHpeQEicc ry BZ fcq stitiv, i\81 vnb B4E
ynvia ^isrcc rijg VTCO BZA dvtilv QQ&aig for). 15
yag ra z/ Kal Z (Sr^iEia ['Gag rov di ccvr&v
rov ABP ^6ri^QL-
far} 6rlvrj vjtb BTd y&via r?] vnb BFZ. dvo
6rw ro rs BF4 xal rb BFZ rag dvo
rats dvtil ttfovQttZs foag %ovrcc sxaroccv sxcc- 20
rsoa, rty ^lv FA rfi FZ, xowijv ds rijv BF, Kal
v ynvi'a ryv vnb r&v i'ticov jtkfVQ&v
v V7tb BF4 rf] vitb BFZ' xccl fid6iv aoa rqv
rfi BZ l6r\v Z&i xal y&viav xv\v vnb BZF rr^
1. rd(pr.) TO (alt.)] ra A4E D. 2. xa] om. D. 3.
corr. ex ccnola^avo^vriv D 3. 8i~\ ins. D 3
.
6. 8s] 1* B. 10. rov] corr. ex TO D. 11. ij FZ] at
TZ, FJ D. 13. 7)(sec.)] om. D. 14. BJ] zJB B. negi-D. 15.
t'<J7j]mut. in IGKL D 3
. 16. %at] om. D. 18.
] -Z ins. postea D.~
17] om. D. BTZBTZ] BZT D. 20. SVGLV C.
ex T7]v A. 24. BZT] BJT DPtolemaeus, ed. Heiberg.
19. SGTIV~] om. D.
fysi D. 23. r%] rrj corr.
r$] ycovicc D.
11
162 KAATAIOT nTOAEMAIOT
vit
[p. 148, 10], on T&V faov a7ts%6vTG3v TOV CCVTOV
KOV 6r][iiov aC Jtobs rbv dta T&V yto^cov TOV farj-
pSQivov ytv6(ievai ycovtcct, 6vva^i(p6Toca dvalv ood-atg
5 facet i6w, 6vva[i(p6Taai, ccocc y T tixb F4E xalfj
iwb PZA dvelv oQ&cct$ faat, d<5iv. Idsfyfrri de xal
ilvjtb B4F rfi VTtb BZF fay xal 6wcc(i<p6tQtu
77r VTtb B4E xccl % vTtb BZA dvtilv
10 rtdfav drj dsixrsov, ort r&v avrcbv Giftisi&v rov
dia [teGcov rcbv ^coduov xvxhov i'Govg %QOVOVS
(p XKTQK tOV ^LS^r^l^QLVOV Ctl T CCTCO TOV
xoQvyrjv fit' ccvra yQctcpo^vcci [ifyforov xvukcav TCSQL-
<pQiai, fcai, aMtjtyis siGiV) KOI ai agog avtag yivv-
15 iiwai, ycoviai GvvayifpoTZQai ijr ngbs avarohas xal
f} agog dvGptts 6v6i rats vjtb TOV ^6r]^otvov nobg
TO CCVTO Grjiitiov yivoptvuis facet i6iv^ OTKV (p* xcc-
TOCiTI
VOTICOTSQK TOV XCCTCC XOOVCpV 6r][llOV TWy%(XV<fl.
20 XO&TOV d' VltOXMtidCi) K^g)OTOOC VOTLCOTfQtt, XCti <3TG3
TO ABF^J^ en CCVTOV d TO
TO F, jrdAog d TOV
1. B4r~\ seq. ras. 1 litt. B, EZT D. 3. at] euan. D,
rov] mut. uoluit in rcov C 2,
corr. ex t&v D. 5. LGKI\ corr.
ex I'euis C 2. EIGLV} ACD, comp. B, -v del. C 2D 3
. ij re]at D. %ai
i] vno} om. D. 6. ogfi-ai D. 7.l'ar]~\
corr. ext'cat D 3
. 8. ij re] at D. vno (pr.)] supra scr. C 2. %at 17
vno] om. D. dp^atg] -g ins. D 3. slew facti D. 9. onsg
%dL Sei^aL] supra scr. D 3. 10. Mjiipto ^ mg. B. 13. nsgi-
cpi^BiKi tfeai] -t t- corr. ex IV A. 14. ttfftV] comp. B, -v del. C 2.
16. i]\ om. D. 17. TO avrb ffrj^ftbi/] mut. in TOO avTw <nj-
ju-fto)A 4
. ytvojLtfcVat?] -g e corr. D. 19.7) voticorzQK] corr.
ex 'j]v on STCQK D 3. 20. d'] 8s D.
du CCVTCOV
MA0HMATIKHS ZTNTASE&2 B'. 163
TO z/5xal y^Qafpfta) dvo T^Tfj^iaTa TOV dia [i6cdv T&V
xvxhov TO T AEZ xal TO BH om&gTO E 6YjHtov xal TO H TO avTO
(p' xaTQa TOV di avTov TtaQakkrikov itQi-
cpQi,av a7te%iv 5
TOV ABFA \LBG-
H[\ ~~~~^-^ rujL&owov. xal
10
CCTIQ [lV
TOV r TO T PExccl TO FH, aitb
$ TOV <4 TO T
xal TO AH. dia Ta avTa drj TOIS ^7t^o0d-vf15
jtl Ta E, H 6rj{iZa TOV avTov itoiovvTa,
faag avTov rtQicp()tac; (p' xaTQa noisi TOV
PQIVOV, iGoitfovQov T xal faoy&viov yivsTai TO
T& TdH, &6TS xal Tr\v FE Tfi FHtipa) di} 5
ort xal 6vva.yi<p6TQKi ijTS vnb 20
FEZ xal % vnb FHB dvtil Tats vnb 4EZ, AHE
7tl yaQ i] {L\v vttb 4EZf] avTrj i<5nv TTJ vnb
4HB, % d V7tb TEA for] tetlv t^ vnb AHF, xal
1. ptcov C. 2. TO (pr.) TO (alt.)] tec AEZ D. 3. tfrj-
om. D. v7tOKi[i8vov TO amo D. 4. di' avtov] diet,
V ccvr&v D. 12. TS] corr. ex TO C 2,om. D. 14. TS] om. D.
15. SLO] 8ia 8ri D. dri\ om. D. 17. Trotrjffft D. ^iGr]^--v- in ras. C. 18. yfvsTai] om. D. 19. Post FJH
B 3. T^] T^V C. ^Gr\v\ -v
-v- corr. exju,C 2
. 21.
JEZ] corr. ex EJZ D 3. 23.
I B, ut saepius. 24. ZGXI B.
11*
supra scr. f-r (h. e.
supra scr. D. 20.
FEZ] corr. ex EFZ D 3.
JEZ] corr. ex 4H D.
164 KAATAIOT nTOAEMAIOT
vitb FEZJHB facet
aQce ijT vitb FE4 xcel % vitb FHB
facet ffalv TTJ vitb 4EZ' co6T xal 6vvce[i(p6Tocei ij TS
xalfj vitb FHB dv0l Tcets vitb 4EZ,
'
01tQ $t dfl^Ki.
avTa T[iri[iceTce T&V X-
TO T ATO B floQtoTQce
/
ytv<5&cet TOV FTO avTo xcel ovtog
TOVT0TIV
ra
10 GvvaiKporsQtti jT vnb
KEZ y&via xal % vitb
AHB dvtil Tats vnb
4EZ foal i6W. Xi
yap [ilv vitb 4EZ15 ^ aVTtj 0TIV TTj Vitb
JEK Tfi vjcb
xod olri agcc r\vnb AHB far]
T7] T V7CO jdEZ xal Tfi
20 a[i<p6T()ai, ijT vnb AHB
vitb 4EZ facet sfaiv.
'
co6T %al 6vv-
V7fo KEZ dv6l
TO {lV TOV CCVaTOhLXOV T^tj^iaTOS {l(}OVQaVOVV
TOVT0TiV TO A, VOTIG)TQOV lVCii TOV JT XCCta KOQV(pr\V
1. y ri\ at D. v.ai 7] vno\ om. D. 2.
-v- corr. exju,
C. tf] om. D. 4. AHE~\ corr. ex HE C 3.
-X D. 5. ).fj(ifia y rag. B. nv.liv\ di]
BD. 13. JHB mg. A 4. 15. fGnv]
18. AHB] corr. ex ARE B 3 C 2. tW BD.
Gvvcc[i(poTQtxis] 6- e corr. D. 20. KEZ] corr. ex KEB D 3.
22. ^rj(i(icc d mg. B, a IfjinpK mg. C. faefafrm C, corr. C 3.
drj] om. D. 24. rovrsonv'] -v del. C 8.
D. 9.
-v del. C 2,iavi B.
MA0HMATIKHS STNTAgES B'. 165
>v, TO $ TOV Ttobg dvGpas T^uarog [LSGovgavovVj
TOVT6TW TO .B, (lOQflOTfQOV TOV CCVTOV. Af/GJ, OTl
GVVCCllQpOTfQCU rjT VTCO
, FEZ xal f} VTCO AHBdvO TG)V VTCO 4EZ {lL- 5
dv<slv do&ccts.
fj [lV VTCO
far} 0TLV Tf} VTCO
4EF) GVVKlLCpOTfQCil, d
ijT VTCO 4HF xcd
fj 10
VTCO AHA dvGlv OQ&atsfaai i<5iv, Kai 6vvct[i<p6-
AEF xcclr\
VTCO AHA dvtilv bQ&a,t$
d KCil f] VTCO
KQO, ijTS
i6Cv.
VTtb A'HB' ci)6T xccl 6vvaii(poTQas rtfy rs vitb FEZ 15
xal rr\v vnb AHB 6vva{i(porQG)v rcbv VTtb 4EZ teal
g rig vn^ ^eovag ivcci,
t vnb 4EF xai rr\ VTCO dHA,tfalv dvtilv 6o&at<3 facet,' OTCBQ sdei delicti.
<T, oittQ vitoksiTtsrai^ Kara r^v o^ioiav 20
TO [iv TOV XQOS Kvatoka$ T^tj^aTos {i6-
ovoavovv 6y[itov TO A J}OQIOTQOV yivoyievov TOV
viv v .
v\ -v del. C 2.
\v\ -v ins. C 3.
C 2D. s-
2. rovrsGTiv] AC, Tovtecri BC 2 D. 5. JHB mg. A 4,sed
del. 6. slaw] -v del. C 2; comp. B, ut uulgo. dvaiv] dvo D.
8. IffttV] -v del. C 2. 10. T}]
om. D. 12. elcv -v del. C 2.
13. rj] om. D. 14. tanv] -v del. C a. 16. rr\
xat] om. D. 17. TovTeCTiv] AC, TOVTEGTI B
ova C. 18. 6vvce(ji(poT()ct$ D. 19. flair] comp. B, -v
del. C 2. 8vav] dvo D. 6g&de D. onsg Zdei SE^CCL]
om. D. 20. Ifjuiia s mg. B, y JLTJPIIU mg. C. d'] drj D.
21. TO] mut. in TOV C 2. rov] om. C. T(JLIJIIUTO$] pr. ja
supra scr. D 3. [IEGOVQCCVOVV] corr. ex ^GOVQCCVOVGIV C 2
. 22.
TO] ov TO D. Fig. e corr. A 4,
litt. in ras.
166 KAATAIOT nTOAEMAIOT
JT, TO d TOV itobg dv0^iag T^itj^aTog psGovQavovv TO
B VOTICOTQOV. AsyG}, OTi 6VVCt[l(p6TQai ijTS VTtb KEZ
xccl ^ V7tb FHB dvo TCOV VTtb JEZ shaTTOvs'g sltiiv
dv0lv oo&atg. dta
5 TCC avTa yag net-A
l /Q
xai V7tb FHB
10 TS vjcb 4EZ Kcd
Tij$ vnb A HB,TOVTS6TLV dvO TG)V
V7CO 4EZ, &KT-
Tovsg yivQvrai 6vvan<poreQcci,s tr\ TS vitb 4EK xal rf;
15 VTtb 4HF' avTCiL ds dvtilv oo&ats faai dt,a TO xal
6VVCllL(pOTQCC$ [ISV T1JV T V7CO 4EK KCil TJJV VTtb
4EF dvalv do&cclg fcag slvcu, fcyv ds xal TTJV vnb
on ds IK 7too%ioov dvvccvTai, A.cc[if$dv6d'cci, T&V
20 yivoiidvov V7tb TOV Ao|oi) xvxkov Ttobg TOV dice TOV
xaTcc xoovtpfjv 6r][iiov yLtyiGTov xvxhov ycovi&v TS
XKi JtQl,(pQl,G)V ,KK& 0V SL^KK^LSV TQOTtOV, KL TS
7tl TOV ILStirinfiQlVOV Xttl STtl TOV OQ^OVTOQ
avTO&sv av OVT&S ydvoiTo di]kov. sav yao25 iis6ri^QLvbv Kvukov TOV ABT^d ncd OOL^OVTOS
1. to (pr.)] TOV BC. 2. jj] corr. ex a in scr. C. 3.
sldTToves] -e- in ras. A 1. slaw] -v del. D 3
. 4. dvalv] dvo C.
5. ydg] om. D. 12. TOVTSGTLV] -v del. C 2,TOVTEGTL D. 15.
Sia] nod did D, corr. D 3. xat] om. D. 16. cvvcc^icpOTSQccLs D,
corr. D 3. 17. i'^v] far] D. TIJV~] i] D. 18. onQ edsi] a
D. 19. at TrTjiUxoTTjrfg ante T&V ins. mg. A 4. 20.
D. 21. ycovycoviwv D.
MA0HMATTKHS ETNTAgESS B'. 167
TO BE4, rov ds dta pfa&v rCbv fcodtW
xvxhov rb ZEH ditoGdrjitors %ov, orav psv dia rov
{i6ovoavovvros avrov 6r][iiov rov Z vocbpsv rov did
rov A xard xoovcpyv Giftisiov
yQacpoyiGvov peyiGrov xvxA.ov, 5
6 avrbg ysvijtisrcti, rco ABF4^<?^/fyn>c5 ,
xal 0rat,ij
rs
vnb 4ZE y&via avro&ev
t\\Liv dedojievrj dia rb xal rb
Z 6q[itov xal rrjv nobs rov 10
liEGrjpfiQivbv avrov yivo^ievrjv
y&viav [II ? 10] dedoG&ai, xccl
ccvrrj i]AZ itsoHpegsia diK rb %sw r^ia^^ rto6ccg
IIOIQCCS Bid rov ii6r][i(lQivov ro rs Z Gqiistov Kitii^i
rov i6ri^BQivov xal 6 farjiisoLvbs rov A xccra xoovcpyv 15
<5iflH,8iov. orav $ dice rov dvarilMovros ccvrov
rov E vocbpsv rbv dia rov A /
yoccg)6^vov
xvxkov cjg rbv AEF, avr6&v xal ovroog
n q [iv AE 7tQt,cpQia ndvror
dia rb rb A 6r][ilov noAov fivat rov 20
BE4 doi^ovroQ. OQ&YIS d oijtfrjs dfl dia rqv avri]v
alriav ri] vnb AE4 ywvCag xal ddo[ivrjs tr}g rov
/lo|oi) xvxhov Ttobs rbv dot&vra, rovr&riv rijg vnb
4EH, do&riGBrai xal 6'A^ vjVTtb AEH ycovta' OKBQ
r
di dtf^ai. 25
2. xvxZov] om. D. ZEH] corr. ex ZH D. 3.
gavovvrogD. 6. ABT4~\ ABT D. 8. JZE]AZED. 10.
%at] nutd D. fr\v\ corr. ex rov D 3. 13. avrrj r]~\ KVTTJV C,
ccvrriv TIJV D. nQupQLccv D. 15. 6] ins. D 3. 16. did]
mg. add. D 2. 19. AE navrort] in ras. A. 20. TO (alt.)]
om. C, corr. ex ?- D. 23. OQL&V D. 24. 4 EH] 4EHD. OTIEQ Zdsi ^ft|ort] om. D.
168 KAATAIOT I1TOAEMAIOT
)on rovrcov ovrog fyovr&v, av
(p'
rag ngb rov [isGrjiifigLVOV [tovag
y&viag T xal it()Lq)QLccg xai [lovcov r&v aitb ri\<s
KQ%fjS rov KCCQKLVOV ^BIQI rijg ttQ%ijg rov
5 dcodexarrjiiOQicov STtiA.oyiG&iisd'
%o[iv [p. 162, 10; 160, 13] xal rag re pera rov
Kvr&v y&viccs rs xcci rtSQicpzaeiccc; xccl k'rt, r&v
rag re TCQO rov iisGrmfiQivov ual rag pera rovf
iva ds xcti inl rovrcov
10 &B6iv h'<podo<s (pavega yevqrai,,
svsxev sx&rjdotJisd'a rr\v faop4vrfv xa&oAov dsl^iv
evbg &0)Qriiicirog vjto&fyevoi xara rqv avryvrovreanv XK& v 6 floQeiog itoAog rov ogftovrog
B^Qrai [loiQctg Ag, ri\v KQ^V rov KO.QKIVOV loyov
15 yj&Qiv [itccv &QKV t6r^iQivriv aite^LV
rov [i6rju,pQivov ,%&& yv &6t,v iv
[i6ovQctvov6t,v [iv aC r&v z/tdtfytoov potoai,
avccr&AovGiv de aC rijs naQ&vov poloca t AJ.
ai,vbg xvxAog 6 ABP4 xal OQI-
20 frvrog {iv fiiiiKVKkiov rb BE<d^ rov de dia pfaovr&v t,G)diG)v rb Zif ovrag %ov, (o6re rb [iv H
1. f'qp']litt D. 2. xJU'fffoos D. TKS] e corr. D 3
.
corr. ex itgos D 3. 4. xapxtV D, supra add. D 3
. Alyo-
KEQCQ] ros supra co add. D 3. 7. I'tt] corr. ex snC D 3
. 8.
Post kom&v add. TK$ TE ngb (hue supra est ras.) rov fifffrjfi-
@Qivbv KVT&V (o supra scr. D 3) ycoviccs rs V.CLI TttQicpSQtias v.cxl
sni r&v HoLTf&v D, del. D 3. rds T] supra scr. D. 10.
9eaiv] om. CD. 11. dfi^iv] d- corr. ex I C 2. 12. fl-ecD^i?-
juarogj -rjfi-- e corr. D. 13. rovrsori D. ^f^Qrat rov OQI-
ovros D. 14. iijQrai] -rui in ras. A 1. As] rQiuy-ovraQ D.
16. ?jV] riv St D, fy dri D 3. tv] corr.
ex^hnv D 3
. 17.
HfGovQctvovat, D. 18. ctvur&lovGi D. A] corr. ex 1%' C.
19.Srji] D, de ABC. 21. ovroos] ante r ras. 2 litt. A.
MA0HMATIKHS STNTASE&S B'. 169
6r}u,iov rr\v aQ%f}v sivai, rov Kaoxivov, TO ds Z iiti-
3 rb ds
did re rov A Kara
Kal dia rov H rye;
rov Kaoxivov yisyiGrov 5
rb AHEF, TCQO-
v rv\v AHVQtV. (pCiVQOV
on, f\ inly Z 7tQi,<pQia
v fariv w K, 17d HS 10
anb rov
6 d
at yisv r&v
Tg t/3 aitokuyifidvovGi rov
Jtobg agxrovg poious wyrov A Kara xoovcpyv 6y[iiov poiQag A^, e'Grai Kal
r\15
[ilv AZ rtQicpQi,cc jiLoiQ&v t/3 vy', fjdf ZB r&v
KQLTI&V fig rb reragrr^ioQiov uoiQCbv oj f. rovr&v
do&tvrav ywsrai ita^iv dta xr\v KarayQa(pi\v [p. 76, 3]
6 rtfc; vTtb rqv dnt^v rijs ZB nobs rqv vnb xr\v
diit^v rijs BA Aoyog b 6vvr][iiivos x rs rov rijg 20
vitb rrjv diTtkijv rijg Z@ nobs rr\v vjtb r^vrr
ts H Kal rov r^ VTCO rrjv dnt^v rrjs HErr^v vjtb rrjv oiit^v rf}s EA. a/U'
i\ ^ilv ri}S ZBitinv gvd id Kal ^ w^o avrqv evfata
25
1. 6r\iLLov] GTJ Gr}[i iov C. 2. |u,otipag(alt.)] om. D. 6.
v D. AHEF] A- renouat. C 2.
{J. i]\ supra scr. C 2.
7) jitfV] in ras. 3 litt. B 3. 11. ILQIQ&V] om. B, (JLOLQ&V
scnv D. 13. &7tokct[ipcivov6iv D. 15. As] mut. in te o B 3,
corr. ex U D 3 euan. 17. fioi^&v'] om. D. 24. ^<^] corr.
ex ~Qd B 3. p? IJTj D. vno] vn' D. 25. EA] EA SiTt/ifj D.
V7l6] V7t' D.
170 KAATAIOT IITOAEMAIOT
v v&icc xali] [ilv Trjg Z
V KttlYI
VTC
vrj) r\d Tr\g H noiQ&v QV id xccl
r\VTC
V&itt T^irj^iaTCOV Qit, ifi.KV KQtt CiTCO TOV TG)V
5 V& TtQOg Td ^JC Ad^OV d(pAG)[lV TOV T&V Qi& VTJ
TCC Qit, t/3, XKTCC^i(p^(3Tai flplV 6 T% VTtO T^V
Trig EH agog Tr}v VTtb Tr}v diTthrjv Tr]g EA Aoyog 6
) tg eyyitiTK itgbg Ta ~QK. xcci <5Tivr\ vTtb xr\v
Tr]g EA T^ir]^,dT(ov (>x*xccl
r\ vito rr\v diTckr}v
10 CCQCC Trjg EH T&V amcbv l<5Tiv Qid I?* &6Te xalr] [iv
Trig EH jfQi(pQLccg {lOiQwv <5Tiv ppd KS h'y-
avTi] dfrjHE T&V avTcbv o/3 iy. xal
ago, r\AH TWV ksntovtifbv itinv lg TO
15 <p>r]g dl noil Tr]v VTtb AH
KO.I Jt6Ac) T& H Xttl
rri TOV TfTQay&vov a y-20
TO RAM, o)GT, 7td o AHEnvxlog dud T T&V TOV E&MKeel did T&V TOV KAM itokcov
EM Kol KM TttaQTiiiioQiov yiV6&cu.
2. 07T
ex 8' D 3
7. rfjs (alt.)] om. D.
EJEf] HE D. 12. HE] EH D.
ovv did
H 8ml.fi D -
]corr -
corr. ex xcmdTjqp'ibfafTca A 3.
10. TT)S] -r}- corr. ex o in scrib. C.
14. (JLOIQ&V] om. D. 18.
ncc dtaatuart diccGTiiccTi, d D. 19.H] corr. ex Tr\ D 3.
nUvQa] TT D. 21. 6] supra scr. D 3. AHE] corr. ex AE D.
22. te] om. D. 23. KAM] -A- e corr. D. SKKTSQCCV]24 xat] om. D. TTor(pT7] 1uo(HOi> D.
B. ovv] d' ovv D.
D.
mut. in yiyveo&Ki A 1
,
MA0HMATIKHS 2TNTAgES B'. 171
xarayoayriv e'tirat, [p. 74; 9] 6 rrjg vTtb rqv
HE nobg rrjv vitb rqv dirthijv rijg EK Aoyogsx re rov rr\g vTtb rrjv dtjrAijjv rr\s H
tv\v vnb rriv dtjrAiJv rr}g A xal rov rr\ vitb
mKrp rijg AM agog tqv vjtb r^v di7ckr\v rijg 5
KM. AAJ
TI {ilv rrjg HE dinkr] ^LOLQCOV etinv
5T Kcd$1
V7t avxriv sv&etcc r^ftarov Qid I?, i]ds
EK VLOIQ&V Af Ad xalYI vnb Kvrv\v sv&stcc
Ag Aif, XKI Tt&Kivfj plv rijg @H dtjrAiJ
QVS id xali\
vjtb avtfjv sv&sla. r^irj^drov QI i($, ^ 10
LOIQ&V xd fig xal % vnb avrr\v v&Zcc
% [id* K>GT, iav anb rov koyov rov r&v
ptd Ig TtQbg ra Ag A^ acpeh&iiw rbv rcbv QI t/3 nobg
ra x ftd, Karakei<p%"Yi<5era,t, fjptv 6 rqg vnb rqv diTt^v
rqg AM itobg rr\v vTtb rqv dtjrAijv rrjg MK hoyog 6 15
jr/3la eyyiGra itQog ra ^.qg MK rfirjiidr&v Q% xal
aoa rtfg AM r&v avr&v itixiv it{I
la. &(5r nalij
[ilv diTthi] rqg AM 7tQi(pQiag yioig&v i<5xiv ytz x^,
avrq $r\AM r&v avr&v ^y id. xal komi] aga i\ 20
AK JtOi(f>Qia avrr] rs xalr\
vjtb AHK y&vCa<3rlv JLtg jiZg* afire xal r\
vitb AH ywvia
ig rag dvo oo&ag Ztirat, ^LOIQ&V ^Ay id" oitQ
6. KM] MK D. &Ud A. HE] corr. ex NE C 2,
corr. ex @ D 3. dady] seq. ras. 1 litt. A. 7. xg] x D.
vn'] vno B. 8. W] ly D; vno] vn D. 9. H]HO I). dtnlfje D. tGtiv] om. D.lO.jj^ (pr.)] ins. A 4
.
vno] vn' D. 11. VTCO] vn' D. 12. xi] -f e corr. D.
rov (alt.)] om. D. 13.iJ3]
ins. D 4. 16.
7TJ3]ar- in ras. B.
TJ]om. D. 17. 7J] om. D. 18. TWV 19. ytM] rC. D. 21.
AK] KA D. AHK] -HK e corr. A 1. 23. rap] ra C.
172 KAATAIOT I1TOAEMAIOT
6 [lV OVV TOOTtOS Tijs TG)V
xal sill T&V koiit&v 6 avTbs GvvdyzTai, r^ifis fc', i'va
xal tag aMag ycovias TS xal itQi<peQiac;, o6ov ys.
ftxbs %Qiav v rats Kara ftf'pos ixt&dtysGitV 66&ai,5 7tQO%iQCOS %G3UV l^Tfd'fi^VCCS, 7t%0'yi<jdlL&K XCtl
TCivtccs yQa^Lxcos ttQ^a^voi, [iv djtb rov dia Mfgoys
,KK& 0V ^ pGyfavq ^(l^QU CdQ&V <5TLV
iy, (p&dGccvTfs $ ^%Q^ tov yQctcpoutvov
rbv Tlovtov dia t&v xf$ohcbv BoQv6&vov$) OTCOV
10 17 lUyfavq rjiifycc aQcbv i6nv farnLSQiv&v 7?.
7tl[
xal
XG)V TOV did ^L(J(DV TG)V t,G)diG)V
T[ir][idTcov Ty dC vbs d&dexaTriiioQiov, 7il ds
15 Tcov Ttgbs dvciTohds fyxctl rtgbs dvGpds TOV
V &<5G)V Tfj did [LICCS COQttS far][lQl,V7JS.
XCtl TrjV TOVTG3V eK&B
6TOV xht[lCC T Xttl d&dfXCCTyilOOlOV 3tCCQCCTld'VTS V
[lV TOiS ItQ&TOtS H>O6l,V TYJV TtOGOTTjTCC TK)V Trjs ty20 xdTQCC TOV ^0^^l^Ql,VOV diK^TK0BG)S ^LBTK ir\V XCiT
CCVTOV &4tiiv farftiSQW&v tb^wv, iv de TOIS dVTQOi,s
T&S TtrjAMOTrjTas t&v dab TOV xaTd xoovcprjv
XXl[lVOV d&dXKTr]llOQl
i 7tQt,Cp()lG)V) V $ TOIS TQLTOLS
25 TTKQTOIS Tag TtrikiKQTriTag TWV vnb Tr}s
1. r&v\ om. D. KfOXftpfrqc D. 4. pEgos] A, supra
scr. 't\ A 1. 6. did] om. D. Mf^drjg] Mtgoc A. 7. IGTI D.
11. wdcxjiv D. 13. IL860V D. 14. tfoofoxcm D. 19.
-v del. D 3. 21. avrov] corr. ex avr&v C 2
. 23. <5eo-
D.
MA0HMATIKH2 ETNTASESS B'. 173
vo[irg Kara TOV Lcooi6^evov lv TOOTCOV
ymviCbv, iv plv Toig Tofaoig rag t&v nobg
TOV pstfqp/fytyot? &6(OV) v de rots tTUQtoi$ rag
rcov JtQOs dv6^dg. &g xal iv &(>%% pivxvi disGrsM-
ft^, psiivriad-ai, dft, on, r&v dvo r&v -6^6 TOV sito- 5
pevov r^^iccros fov dta [isti&v rGbv
v yavi&v rv\v ait' KQXTCOV TOV CCVTOV
asi 7taQEiA,rj<pa[Jiv TO^OVTWV iy xdc6Tr]s
7trjA.ix6Tr]Tcc xagKTi&lvTSiS) O'LCOV Itirlv f] [iicc
Xttl 0TiV'Y]
TGJV KKVOVl&V X#<?tS TOLCCVTr]. 10
1. TOfifjs] -o- corr. ex Q in scrib. C. 2. r&v] suprascr. D. 3. 3] post d ras. A. 4. fisvroi] corr. ex (isvroig C 2
.
6. Tftryfiocroff] corr. ex Tju.rjfiaTcov D. 8. toaovrav] mut. in
Toiovroov D. 10. Y.avovCa>v] ~vo- add. A 3. In extr. pag.
(fol. 48Y) add. ty.&EGig r&v v,axcc nugc&'krikov y&vi&v v.cd TCSQI-
(jLQor]g OJQ&V ly fioiQuv i$ t D, mg.
174 KAATAIOT UTOAEMAIOT
r&v xara
Tov dice
jtegtcps-
Qet&v
ycoWaiava-
toJlutai
vcuWori
ovtixai to^oiqeiia
ytaviathva-
toJ.iy.ai
ywviatovtiy.ai
KctQKlVOV Z vy o v
qoyvy
y.y ft?
of 1Ad
Ay
g o f xd /"* "2
A s o v t o s Q n i ov
15
20
id re
ttj fia
xp xi,
r?r~ S,
'-,
i
IT;a p jua t9
c xey.n
id A? *a
To 6 T o v
26
"t
30 ff
id
iy
17
AC
o*
Ad
A* ,18
Ay xarf A
QXS
pi 4go Mod va
o9
1. iy '] om. AB C D. Ordinatio est codicum AB C, in D tres columnae sunt
cum quaternis signis. 6. /^ (pr.)] AB, N C, om. D./? (alt.)] om. D. (pr.)]
om.D. r(alt.)] IV in ras.A, om.D. 8. (o] seq. ras.A. rd]>dD. 9. r(pr.)]
post a B, suo loco B2. Ai/] vt D. r] post ^>o/
B (qui omnino numeros huius
columnae uno loco altius collocat), corr. B 1; om.D. or (alt.)] AD. 10. d (sec.)]
ABC. Ad] -d e corr. D. 11. e (pr.)] e corr. C. p] y.a D. 12. Tty] Ttg1 A.
i^-] corr. ex iy D. 15. /S(utr.)]om. D. y(utr.)j om.D. 16. xg] corr. ex
QZ B2.
Qorj] g- in ras. D. VL] v^D. 17. v] om. D. 18. e] corr. ex i D.
_ 19. vc] ft? B C. 20. *p] corr. ex xf C./9]
om. D. 21. r] om. D. o (tert.)]
AD. 22. xe] om. C. 24. Qia] DB, Qtd A, piB C. v] om.D, mut. in p B 3
.
o^o] om.D. Ac] As D. T (tert. et quart.)] om. D. 25. p] om. D. o (sec.)]
corr. ex. y D. 26." o (pr.)] corr. ex y D. 27. ,uj is D. ^;J ^a D. 28. if]tn BC. 29. Ac] xc B. c] A? D. ooa] ood D. 30. As] corr. ex ^s C. A]
om. C. 31. d] ABC.
MA0HMATIKHS 175
ycovi&v nal
OJQ&V ij [lOLQ&V
toQ&V JttQKfS-
qeitbv
yiaviatava-
tolixat
ywvovtixai co^cov
QSIWbva- yoiviat
ovtixai
Aly ox s QOO V
s I
fittr
oa. 8
iiy Ha
9? o
gva xs
QVtJ fll]
/Lrj
xrjxa
9 o
AS
va 10
QOfi A?
Ta v Q o v
of
eQtrj
I9
'I % & V 00 V d l8v p, CQV
la, f.ig
fj. Vfi
ir\
/ua
/ua o
x/? a
y o
/S] om. D. 14. ,*#] -5 1
e corr. D. /uz] corr. ex ^C C.
7] ^e C. 16. w] oc A, i& D. 18. f] in ras. A. 19.
5. v] ter om. D. 7.riy] A, fttj BCD. 8. x] v D.
^a D. 10. e (pr.)] in ras. B. ^ij] A, vt] B C, ^^ D. 13.
om. D. ,uc] jud D.
p] seq. ras. A.,1177] ^e C. 16. w] oc A,
QP&] QC,& B C. 20. id] D, in ras. A, S B C. 22. v] bis om. D. f] bia
om.D. 23. x] xa D. a (tert.)] in ras. A, a*BC. v] corr. ex t^ B 3, tf C.
24. ^i] tcB. v&] D, r^ ABC. r] om. BCD. 25. ^s] ^|a BC. 26. y]
y$ A. 27. f] om. AD.Jlij] rq D. 28. v] om. D.
176 KAATAIOT IITOAEMAIOT
Tov $10,
yamat&ra-
toi.iy.aiSvtixai
KctQuivov
? I
o o
ty (yxy
o o
y ^c
(UQ& JtfQKpS-ytoWoridrva-
roAtxatyuovaiovtizai
Z v y o v
xy va
la|i/e HP.
10
*<S H* 9 Qvy
9
A V X S
15
ft
y xa ^ i^0?Q7t
/In xe
A*? /
Jtt] [IS
oa u
re id
Sn wre
/la
20 S1
ff
ita vfi
|
9 o9 o oo
r/? re
iUe <^
25
30
i ftpA. v qoy ry
QOIJ yQ7t O0^" if
oy xTie xy
re ^e
Htf.1 10
pa9
5. o (quart, et quint.)] om. D. 6.
*rf] * D. 17. po#] ^oa BC. i] ^7-e corr. D. 25. ry] r? D. 28. oo^]^d] D, ?f ABC. SO. /ia] o BC.
juS] o/ua A, o/ua D. ay] rt^ D. 9.
A (/lw?). 18. o|^] |^ A. 24. /uffj
ooe B C. ufi] post w raa. 1 litt. A.
MA0HMATIKHS STNTASE&S B'. 177
iy [_' xy vcc.
(UQ&V
178 KAATAIOT HTOAEMAIOT
Tov SLO, vf)$ nemo tfjs Atyvnrov
&Q&V
MAOHMATIKHS STNTAEE&2 B'. 179
x|3.
'uonui,
bva- /I
tolixai OVtMycaviatava-
toliixalyuiviaiovtixai
la x/?
017 r#9 o
9 o
(6 UI& xy
06/u.eoi]fi
a
of
xs /ua
te v
t ty
10
QXC
Ta v p o v
SI
vy
Ttlf
9yra /tf
xa u
* /*/
xy tij
iy I
vtj xaoa ts
15
It
t xgf r
c vC,
o17
re 20
t s
'I i <9"u co j> d 18 v (ico v
xff rtf
? y ly
QX VS
QX6 V$
xi;
Aa
Sf tf
of A
>*>? y
ft_X^Md xg
ty 25
t Ad
*r/f?
9 firj ;
o|
/uff
x ta 30
1. A x] ^ x D. 5. ty] te D. A x/S]in ras. C. 10. e (pr.)] e A.
11. fffcnr-)] ff 5 A. g- Aa] om. D. 13.c
l"d()o/dov] IX&VMV D. 14. |^]e D. 15. l&] sciipsi, Ae ABCD. xa] -a e corr. C, x D. 16. /tf] -C e
corr. D. 18. rq] corr. ex /uq D. v] x D. 26. |] f C. 27. oa] od D.
28.Qf*(i] qvp D. 29. t] e corr. D.
12*
180 KAATAIOT HTOAEMAIOT
Tov 8i& *P68ov
coot&r
MAGHMATIKHS STNTASE&S B'. 181
id /_' (IQIQCQV /I? O.
&Q&V
182 KAATAIOT HTOAEMAIOT
Tov
wnwv
MA0HMATIKHS STNTA3E3S B'. 183
UJOUV
184 KAATAIOT IITOAEMAIOT
Tov dice [isoov TLovxov
&Q&V
MA0HMATIKHS STNTASE&S B'. 185
GDQOOV IS {_' (JiOLQCOV [l U.
tupwr
186 KAATAIOT nTOAEMAIOT
Tov
TtSQKpE-
Qsiiav
ytoWat&va-
tolixaiycjvlaiSvtixai OJQ&V
I ytavLnwe- *.,kva- vtovat
ovtixai
Z v y o v
10
oft xdita It]
9 o
vy vy
w nft
fj,y vd
Hy vg
po fian
rj
9 o
qiyoxg
xy
QVf
ga tft
9 ft
rta vg
og xd
oy i&
op xy
A s o v r o s 2KOQ7C tO V
15 fieoy/u,
a
20
*ff re
ltd t
9 o
**
Qflf
JtftVCt,
i
fia
Irj
O/9 8
ft y
9 o
Qta o
qxft e
<>va ft
oe I?V1J
xft
To | 6 r o v
25
30
ffrcf
v/ xe
la 4e
oa xJ
ta tC
9 o
Qe
od vao xd
Ydd X
vi?
qva /.//
X
odft
9 o
9ft
Q/L& X
*?'06
in1. tov di&] to dice tov B, tov dia tov C. 7. /J(pr.)] 3 B. nras. D. 9. o^] ox; D. o] 5 A. 15. i/J] ft
C. 18. A] J D. 20. o]6 A. 21. o] A. 26. o] 5 A. 27. //d] fia D. 28. o#j oe D. 29.
o] 5 A. 30. xy] f* y D. d] e corr. D. 32. o] 3 AB.
MA0HMATIKHS 2TNTAEE&S B'. 187
fl/TJ
vaqmv
188 KAATAIOT nTOAEMAIOT
y xa rr^g rcbv ycovi&v
de rotg vnor^s^voig fov rag ito%a,g r&v
xara [ii}%og xal xccra nAdrog xobg rovg
5 r&v v ccvralg <pcuvo[ievG)v litikoyiGiiovg rr\v {iv roiav-
trjv k'K&e6w ^ai^rov nod yfajypagptjdjg fyofievyv
xa& avrqv vn' otyiv itoiri66iL&a axo-
rats r&v rt%i,Q'ya6[iVG)v cog EVL
rovro rb idog faroQwis xcci
10 [toiQccg K7t%i rov fariiLSQivov T&V
nark tor di avrfjg yQcc(p6[ivov [i6rjiif}Qiv6v ,xal
ovxog rov di' ^A^e^avdQsCag yQcccpojiEvov
JtQog avccroAcig v} dv6ig iit\ rov l^rj
dt,a rb ngbg rovrov r^ilv GvvfaraG&cii rovg rwv 7to-
15 %&v %Qovovg. vvv $ rb rotfovrov cog V3toxt,[iVG)v
rcbv &6G)v jii7tlv axoAovd'ov rj'y^d^d'K^ dtdrt,
av rtQOcuQGoiif&a r^v k'v nvi rcbv v7toxi,[iVG)v
QiGiidvYiv CDQKV 6xojtiv, tfrig i]v xara rbv
ccvrbv XQOVOV l<p sregov rwbg r&v
20 orccv diacpQG)6iv 01 di avrcbv ti6rj[i/}Qi,voi,
o^ftAoficv, odccg aitfyovtiiv aMtfhcov ovroi [loigag lid
rov tGruLEQivov, xal Ttorfoog avroov
2. df] mut. in rs B 3,rf D. 3. S7tiar)[La6ici$] pr. i supra
ras. D. 4. 7r<rx'qp<9m] -at e corr. A. xara (pr.)] ttard
D. -nurd (alt.)] om. CD. 5. avratg] av- in ras. A.
v] -cc- corr. ex (iin scr. C. 1'. 7tQ<xy[icctLKs] -s
corr. ex v D 3. noir\6Qv D. 8. ins&QyuGpiv&v D. 9. TO]
ins. C 8. 10. fioLQccs] p ovtog B, corr. ex fiov C 3
. 15. TO]om. D, del. A 3
. 17. av] edv ABCD. xty] mg. D*; }f D,
sed eras. 18. cbptaa^fVrjv C, corr. C 2. ijg] ^'TTJS C,
IJTJ]S C 2. xaTa TOV~\ corr. ex xaT
J
CCVTOV D. 20. fif(7rjju.f-
givoi D. 21. an^%ovGiv~\ corr. ex enfyovaiv C 2. OVTOI]
renouat. B 3. 22. avr&v] corr. ex savr&v D 3
. ienv] om. D.
MA0HMATIKHS STNTAgESiS B'. 189
regog r vTM&TSQOs, rotiovrois t
X^V KKXCC TOV V1tOXSl[l8VOV XOTtOV
tW Ttoi&iLEv rriv iv r<p sxifytoviisvG) KUICI, rbv
avtbv KQOVOV &0)QOviievr]v, rijg psv av^^scss GvviG'ta-
otav 6 eTtifyrovpsvos r6itos avarofaxcbrsgos ^, 5
orav
1. 7} 8vtMia>rQog\ xat D. 2. tonmv C. 3. xara] corr.
ex -na D 3. 6. (isimGBcos] corr. ex (islcsws D. 6
D. In fine: Kfavdiov
ABC, KJiccv$iov nroHspctiov paftiruLa. $ D.
r.
Tads V6Tiv iv T& y' Tys JZtoAf^ca'ov
a'. jrfpl TOV [leyed'ovs trot) viav0Cov %o6vov.
5 j3'. K%"6i<S XCCVOV&V T&V TOV fjMoV [l6G)V X
y'. 3tQl r&v natf dtia&jjv xal eyxvxfaov xfoyGw vno-
d'. 3t$l tils rov
sr. 7t$l rijg agog ra xara pfyos r^^iara r&v ava-
10 iiccfacbv xccvovoitouag.
g'. xav6viov 1% ^Aiaxijg av&paMas.
rvjs Kara, xr\v tifaqv TOV v\Uov xdgodov
Tijg TOV yMov
TVJS T&V
15 'E(fG)dVllVG)V fjlllV V TOig 7COO TOVTOV
T&V T 0^00%QG)S OCpMvTG)V 7tQl T OVOCCVOV
1. P'] om. ABC, xecpdJiccia TOV rgirov D. 2. y'] AD,OJ B, om. C. t?Js] T&V D. [iad"r][jiccT;iKfi$ GVVTCC^SOOS]
D. 4. a'] om. D. Iviavafov] corr. ex ivi-
ccvGiag C. Post ^^dvov add. rf ^ (ft^ D 2) ^ D. 5. |3']
om. D. xavdvos D. 6. et 8. permutauit D. 6. y'j om. D.
8. #'] om. D. 9. ']om. D. 11. g'j om. D. 12. ']
om. D. 7ra(>odov] om. D. 13. TJ'] om. D. tfjs] t?\ C.
TOV j]liov\ f]hcM7is D. 14. -9-'] om. D.^
15. IlTotepcciov
[icc&rKLctTmcov y ABC, wfpi TOV fieyf^ovg TOV EVIKVGIOV %QOVOV D.
scpodtvpEvcov C, corr. C 2. TT^O] corr. ex Tt^6<s C. 16.
Tt (alt.)] supra scr. D.
KAATA. IITOAEM. MA0HMATIKHS 2TNTAEE&S P'. 191
xal yr^g na&rjuarix&g itQohricp&fivai, Kal In 7tol ri]g
fyxhfafcog rov dice pBticov r&v tydi&v rjfaaxov KVK&OV
Kal r&v xara p,Qog jffol avrbv Gviiflawovr&v iiti re
rr^g oo&ijg Gcpaioag Kal snl rr^g xcc&' Ka6rrjv ot'xrjGiv
S'yxexA.ilievrjg axohovfrov rjyov^s&a xal (p^ijg rovrov 5
rbv 7tQ\ rov fjMov xal r^ra r 3tQtl rag xiwtJ6is avr&v
k&lv prjdfvbs v&v KQi> wvg atirtQag
avv rfjg rovrcov JtQodiaA.rii{ja)g Kara rb
dvvapevov. Kal rovr&v d avr&v itQorjyov- 10
i6xopv rr\v rij$ fjhaxfis xivrj6G
g avev itcchv ovds roc rtfgl ri\v
olov r av ydvoiro di,%odiXG)g
a'. Ilfl rov if^frov rov VLav6iov
Ilacbrov drj itdvr&v rcov 7tQl rbv rj/Uov aitodLKvv- 15
rov rbv viav6i,ov %g6vov VQtvrag plv rcov TtakaiGbv itQl rr\v aTtotpavtiiv rov roiov-
rov diacp&vLag r Kal djtootag [icc&oiiifv av IK r&v
avrolg Kal \aaKi6ra r&f
lTtitaQi& avdylr bpov Kal cpiAaAtjd'Et,. ayi ya$ pdhGra 20
Kal rovrov tg rfjv roiavrrjv aitooiav rb dia plv r&v
rag rgoitag Kal rag i(3^gCag (paivo^dvov avto-
rbv viav6iov %o6vov V
1. (icc&7]jLtarotcoj] corr. ex iLaQ"r]^KrLY,&v D 3. 2.
TOV yhccKov CD. 3. CCVT&V C. 5. tovrcav] corr. ex ro D 2.
9. ncivxtaUg C. 11. VQLGY.O^V] oQ&psv D, mg. g. 14. a']
mg. BC 3,om. AD. TISQL %QOVOV] om. D. 15. Sri] corr.
ex Si A 1. 16. eviavGictlov CB 3
,eviavGLeov B. 17. ano-
cpaGw CD, supra -a- ras. D. 18. unoQiKs] ante p ras. 1 litt. D,anoQfias C. av] D, om. ABC. 19. Post trw ras. 1 litt. D,item post ^Imtdq^a). 21. ccnogiav] ante 9 ras. 1 litt. D. 23.
C.
192 KAATAIOT HTOAEMAIOT
jtl rcclg r% fi[iQai$ rov rrdorov
r&v 7tol rovs a
. 0&V ittlfittktel r<p
Iirdfia6iv xiva, 7toA.v%QOViov TtOisZG&ai, Kal avrtfv,
5 (o6rtQ Kal rag r&v rthav&iiwcoVj fig ra 7c6^va rvjs
rrjv rtQG)tr]v it^iKy^y^v JtoiovGrjg (pOQccg Kara rbv
dici r&v jtoA&v a[i(porQG)v rov rs faq^Qivov xal rov
Ao|oi) yQa(p6iivov xvxhov. fiptfs ^, rovro plv on
ovr&s t fyM xal rCva yivercu, rgoitov, v rotg 7tQi10 r&v ankav&v aGrfy&v 7tidioiiV' ovd yap ra 7tgi
Xivovs civv ri}s v\kiawri xal Gfkrjviccxijs nQodiaMityecos
olov r av yzvoiro di? o'Aoi> fts&Qri&rivai' Kara df ri\v
TtaQovGav BTCiGKStyiv TfQOs ovdw AAo qyovfi
<x7to(lA.7tovrccs rbv BviavGiov rov i]Uov %QOVOV15 $ rfjv avrov rov ^Atov nQog favrov, rovr^nv rov
vn? avrov Ao|6v xvxA,ov, aTCOKaraGratiiv
r rbv iviuvGiov %oovoV) xa& ov aito nvog
axivtjrov 6r][jitov rovrov rov xvxhov Kara rb $;^S
7tl rb avrb itagayCverai,, [tovas aQ%ag olKia$ rv\
20 roiavrrjs <x7ioKara6rd6G)s r^yov^vovs ra vjtb r&v roo-
TtlKCbv KOI l6r]ll
rov 7tQOiorj^ivov KVKkov. edv r yaoc5 AO^GJ, ovr oiKi,oroav
rijs till rbv avrov
1. r)[LSQcci C. dial - - Sid B. 2. nsQi] corr. ex ngos D 2.
3. TOT] corr. ex TO D* (TO! fr\v\ supra scr. D 2. 6. ir\v\
-$- in ras. 2 litt. A 1. 9. yvr\tai C. 13. Gntyiv D. ~] mg. D.
. 14. anofittnovrs-s D, corr. D 2. 15. rovrscti D, comp. B.
xj\v ywoptvri'v D. 16. vn' UVTOV~] (-it av- renouat. D 2)
vn' ccvrov TCQOS TOV AD, ugh? TOV del. A 3. 18. 6f\piov] -ov
renouat. D 2. TOV] om. A. 21. <yrjju-ficov] corr. ex Gr^islov C 2
.
22. sav] D, av BC et post spatium 1 litt. initialis A. 23.
Aoyco] evloya) ex renouat. D 2. 24. TOV] r&v A.
MA0HMATIKHS STNTASE&S r'. 193
rbv ijkiov Toitix&g TE xccl %QoviK&g tftot, agog Tovg
doi^ovTccg i)rbv [is6rni(lQivbv i)
ra [leyed"*] T&V vv^^-[IEQC3V TOV TOLOVTOV &G)Qov[ievov OVTE aMccg da%dgEV T& duo, pEG&v T&V Jcodtcov nvxhcp, povag ds rag
XKTK TO GviiftEpyxbg acpOQi&fievac; vjto rs t&v TQO- 5
ItMCbV KO.I tov$kSQW&V 6r]HlO)V' KV TS
Tig 7tl6X07tfi TO OLXIOV, OVT
TQCCV VQ1J6l, Trjg KTtO TOV O^IOLOV TtSQi TOV (XQCC
xccTaGTtjpaTOS nl TO opoiov not Tys avTils COQKS iitl
rriv avTrjv (pfgovGrjc; TOV ijfaov OVT aMag d$%ag -J)10
liovccg, KK& ccg aC(bgcci, [iccfotiTcc diaKQivovTcci,
TOV Trjv agog Tovg attA.avZg a6Toccg
aTOTtov (pttiVEG&ai did TS ahka xal
,OTi Xal
fjCCVTCOV GCpttiQU 7tQlQV\LivY\ TWO,
flaGiv ig TK 7t6[iva TOV ovoavov 15
&G)atToci,' ovdfv yag TOVT&V ovT&g e%6vTcav
Kiysiv, ToGovTov ivcu, TOV viccv6iov TOV riMo
EV 06O) TOV TOV Ko6vOV CC0TEOK AoyOV EVEKEVi)
KCtC
TLVCC TCbV CCA.A,G)V 7lA,CCVCO[lEVG)V 6 fjAfcOg JfEOLXCCTCi^tt^KVEl,^
jro/Uot T av ovTtog xal ditttpoooi ytvowTO OL EViuvdioi 20
%QOVOI,. did [iv dij TCCVTCC itQo^KEiv OIOIIE&K TOV
EVOiGXOllEVOV did TG)V TrjQIJGE&V TKtV &g EVi lldfaGTCX,
dytb Ttfoiovog diadTdtiEcog ^.K^KVO^EVOV dno Tivog
1. r/TOt] 7} TOV BC, corr. B 3. 2. yy^-thj/x^jcov] post 9
ras. 2 litt. A. 3. Q-fcoQri^vov D, TE- ins. D 2. 4. povas
d] f) IIOVKS D. 6. idv ri\ she D. 7. rig] corr. ex TS D 2.
STTtffHOTm ABCD. 8. SVQ^GEL] corr. ex ZVQSWSI, D. 9.
^?] i- in ras. A. 12. roi>] om. D, TOV nai supra scr. D 2.
13. Ante &TOTCOV ras. C. 14. fu&Uffjtf-iK D, sed corr. 17.
ro-u] -v in ras. A. 18. K$6vov~\ comp. B, corr. ex %$6vov C.
21. odcc A. '22. IVt] corr. ex fa D 2. 23. onto (pr.)]
i D. nteivos C.
Ptolemaeus, ed. Heiberg. 13
194 KAATAIOT nTOAEMAIOT
v} totftteQfas irii ryv avtrjv xal (p%ijs %()6vov
rovrov fiyBiG&ai rbv Iviav6iov rov ^iov.litsl de ftogyfisl nag rbv
f
'IiutaQ%ov i\xal nsql
avrqv rqv roiavryv aitoxardGraGw VTtoitrsvo^v^ dia
5 r&v KCCTK rb e%ijs yivopiv&v 6vve%a)v rrigriGs&v KVL-
dice PQCC%SCOV [irjds rovro
fisv Ettrjyorsg nsgl rov
/LM) avfaovg sivcci TOV %$6vovg TOVTOVS, f| (bv ual
avrol dice tcbv dgydvov xata rb |ijg vwy%dvo[iev
10 reTr}QV]x6Ts rgoitcbv re xcci foqptyttfp* ovdsvl yag
aitoAdycj dicccpSQOvrag avrovg SVQI^KO^LSV rrjg Kara rb
reragrov ejtovGiaS) aAA' sviors 6%sdbv o0G) jtagd rs
rr\v xccrcc6xvrjv xal rrjv ftzGiv rcov QQyKV&v vds%rcu
diapttQrdvsw 6ro%a6iivoi, $ xccl f'| avrcbv, (bv 6
15f
'Ijt3tccQ%os eitikoyi&rcu, [laAAov r&v rrjQtj<5G)v fivat, rrjv
yt()l rag avitiorrjrag Kpagriav. x&[ivog yag rb
itQ&rov v r<p Il()l rijg iisranr^sog r&v
xal fotftUQUf&it 0rjiiiG)v rag doxovGag avr&
xal p^rlg rsri^Qri^ai frfQivdg r xai
20 Ttdg b^o^oyel xal avrbg ^ roGovrov iv avratg
rb didqxDvov, &6re di avrag dviGoryra xarayv&vat,
rov viav6iov %QOVOV imMysi yag avrcclg ovr&g'
X plv ovv rovr&v rcbv rriQ^sov dijAov, onitavrdnaGiv yeyovatiw ai r&v svuavrCbv di
3. 7 mg- D. de] corr. ex dr) C. i] *ai] mut. in xal
f)B 3
. 5. r&v} renouat. D 8. 7. nL6[ia] BD 2
, niG^a ACD(corr. uoluit C 3
).8. pri] supra scr. D. 11. avrovs~] -ov-
in ras. A. 12. TSTKQOTOV C, sed corr. 14. dnx(jicxQTfiv D.18. a-uTo5] seq. ras. 2 litt. A, corr. ex CCVT&V D. 20. flvcct,
sv avrccls D. 23 sq. > mg. ABCD. ZOVTCOV] supra scr. D 2.
corr. ex luvd. A 1. 24. nccvrdiiKGLv -v eras D.
MA0HMATIKHS 2TNTASE&2 T'. 195
7tl [iV rojv rooTt&v ovx ait^TtCtfQ xal f}[iag xccl
rov ^o^^trldr] xccl v r rrjQrjdfi, xccl iv red 6vkkoyi<5iLK>
V XCcI & rErdorOV [lEQOVS fl[lEQag. KXQl-
dvvarai xccravoEtGd'cct,fj av&naMcc rcov smccv-
6icov XQOV&V EX rcov tExriQvi^vov sjtl rov v AK&tttv- 5
av SK rov
xgcbtov iiroitc*Qiv5)v farjfifQi&v 10
cTa rfir^i^fVrov, iv \L\V r& 1%
xccrcc Kakmitov itQi6dov rov
rov ^jUov, percc d y rrj v
rsi rri TtQ&rr] r&v 7tKyoiiV(ov ^(xotag, ddov
ag, &6r dia7i<pcwr]Xvcc(, rerdgrGt ^ag fjfiEQas. 15
sviccvrbv iv r& xa' k'rsv &ga$ gr
, ojtQ xal
TJV ax6kovftov rri xgb avrrjs rrjQtJGfi. psra de Ice rrj
r& A/3' b'rEi rr^ tQfafl t&v ErtccyoiiEvov fig rrjv rEra
rov yiEGovvxriov, dov TtQcoLCcg, &6r ro3 d' it
cpcwrjxdvcci,. pErcc $ viavrbv W roo hy' Victvr& rr\ 20
1. ct7tli7t%co~] B 3D, ayf-lnfta) ABC. 2. 'Ag^i^Sji] mut. in
B 3. 4. ta>v] e corr. D 8
. SVLKVGLCOV] -co- in ras. D.
6. Kcdovpsvr) rtTQciywvG) B. 7. Grace] cro&i C, t eras. 8.
a^Tjrat] corr. ex c^rjrca D 2. 10. [IETOTCOJQLV&V] -&- e corr. D 2
.
iGruLEQi&v] corr. ex IGJ]^SQIV B 2, tGr]^SQiv(ov D, IGJIUSQW&V D 2
.
11. Ante v ras. 1 litt. D. i'] corr. ex ^ D 2. 12.
KctiLnnov] ABC, Kcttiimtov D. MSGOQL B. 13. T]ABC, T^ Tqiu-AOGTy B 3D. 14. xfj\ corr. ex xr\ A 3
. Tr^coTiy]
B 8D, vsoprivCa ABCD a
. 15. wffw] AD, &s BCD 2. 16.
d'] 5 D. sv Tea] Bvarm D, supra a ras. %a'] nQmrca V.CLI
siv-oGrw D. ^v xat C.'
17. KVTTIS] corr. ex ravrrj? D 2.
'
18.
T$] TO* T^ B. 19. rov] eras. B. 20. *'] <T BC. iy']
seq.- - in ras. B, >Ty C (similiter saepe), /I r^iTo) D. tvt-
avrco] 8TFt D.
13*
196 .' KAATAIOT nTOAEMAIOT
d' r&v STtayonsvcov Jtpotag, oiteo xccl fjv dxoAov&ov r%
nob avrijg rriQ^ei. psrd ds y sty ra> kg' BXBI rr\ rs-
rdorrj r&v iitttyQpiv&v sGTCeoccg, deov rov HSGOVVKTIOV,
cbg v<p $'!*<6v<p
Ttdhiv diKTtsycovqxsvcci,.
5 psrd ds ravrcc exri&srai, xdl rag opoi&g dxoifl&g
CCQIVCCS fatjiisQiccs' iv [iev ro5 A/3'
Kara KaknntQV xsQiodov, Ms%iQ x'
xccl 6 XQLXOS ^5 <pri<5iv, 6 iv 'Ate^avdQSia i'6ov
exarsQOv [legovg jtaQrjvydG&r] TISQI s' &QKV &6re
10 xal ri]v avryv l6rm,8gi(x,v diaydQCOs rsrrjQ'rj
lyyiGxa dieveyxstv. xccl r&<s sepsis de
rov % srovg GviiTtsycovyKsvai, rfj itgbs to
psta de Id trj real y xal p' srei, rov Meylg rr\
[isrd rb [istiovvxriov rb sis ify ^ ysvBG&ai cpytilv
15 eaoivfjv farjiiSQiKv, OXSQ xal dx6Aov6&ov ^v rri iv rat
A/3' srei, rrjQtJGfi, xal (jvufp&vst, qyqffiV) ndkiv xai nobs
rag sv rots fyppfroig &cetii rrjoijtisis f^JCpi tov v'
srovg' yvto ydo rov 0a[iVG)& rrj Ttocbrr] Ttsol 8v6iv
^Afc'ov perd \i,ia.v tyiqwv xccl ijfiHfv xal rsraorov sy-
20 yiGta ri}s iv x& \iyr
erst, OTtso xal eitifidkkEi rotg
&t6w. ovd' iv ravrcug ccoct rcclg
1. luiayopivayv] -o- in ras. A 1. 2. de] -e' in ras. B 2
. y
I'TTJ] corr. ex y rr\v B, TQLTOV hog (corr. ex eret m. 2) D. InD numeri plerumque omnibus litteris scripti sunt. 4. ndkiv}supra scr. D 2
. 5. iv.riQ'sxai\ corr. ex fatt&atifcu D 2. CCKQI-
|3w?] corr. ex &.%Qi$fotcna D 2. 6. IG^SQLVKS D. l$'~\
I $' AC. 7. Kdhnnov] BCD et corr. ex Umtov A 1.
MB%LQ\ MB%COQ D, MS%SIQ D 2. 9. naQvyaGftji C, corr. C 8
.
. iesqf] supra scr. D 2. 11. cpqoi, D. 12. Z'] corr. ex Zy D 2
.
13. TOJ] corr. ex t&v A. y' xat ft'] jly D. MB%S{Q A. tjf]
om. D. 14. <pr)0v] -v del. D 2. 15. ^v] corr. ex ehv D 2
.
16. avfjicpwvei] del. B 8, mg. yp. cvvscpwvet,; Gvverp&vsi D.
qpTjat D. %ca (alt.)] om. D. 18. sytvsro] -sv- suprascr. C 2
. TtQanrj] AD 2,a BC, vovwvfy D. 21. ] fjrra BC.
MA0HMATIKHZ! STNTASE&S T'. 197
yfyovs rig d^Moyog diacpoya xairoi dvvarov ovrog
ov povov iteQi rag roonixdg rrjo^6ig^ aAAo: xal 7iol
rag for]pQtva$) yiyvtG&ai ri xao' avrdg
xal p%Qi> d' [iiag f}[ioag' xav ydo rcj
xcil s^axoGiodtG) [love) [ISQSI, rov dice t&v Ttok&v rov 5
farj[iQi,vov KVX&OV 7taQccAA.d%r] rrjs aKQi^sCa^ ^ ftsdig
tyxal duU$6is i&v ogydvov, rfy totiavTrjv xarcc
TtAdros 7tKQK%a)Qri6iv 6 r/Ato^ dioQ&ovrai, XQOS rots
6r][iQi,vots rprujLKdiv rerccQTOV ^itag [IOIQCCS xara pijxos
STtl rov Ao|oi) xvxhov xivri&Ms, co&rs nccl r^v diet- 10
tp&viccv y>%Qi' d' pi&S f][iQccs syyidTK disvsyxsiv. sri
& civ dia^iKQrdvoi nheov iitl r&v[irj xa&cc7tK%
xai itccQ avrag rag TrjQtJGsis dxQipovf
vv6rr]Qi'yii8VG)v daydvov CCTCO tivog (XQ%ijg rotg
V7toxi{ivoig ddcp6iv ytobg TO novijiyv iit\ TtoAv rrjv 15
&6iv %iv } yiyvojifvrjg nvbg itsql ccvra vnb rov
%oovov foAyftviag 7taoccxivitJ6G)g) &g iti ye ribv
v ry rtccAcciGroa %akx&v xoixcov v roo rov
av rotiavrri yaa v\\nlv rrjoovGi xarayaivfrai diaGrooyr} 20
rijg &6G)g ccvr&v xal [idhiGra rov [iit,ovog xal
aQ%ot,ioreQov , fog vior xal dig iv rccig ccvralg lorj-
[iQiaig iLfrcicp&ri&G&ai rag xoiAccg avr&v 7ticpciViccg.
1. ys'yovf] seq. ras. 1 litt. D. 3. ylveG&ai, D. 4.
ins. D 2. 6. farjfteQivov] in ras. D 2
. 7.r[\ postea ins. D.
xcct] xai r) D, i] add. B 2. 9. T(irj[i(x6i,v~]
-v del. D 2, TJLITJ-
B. 12. 8iaybKQxa.vi, AC, ^ta^a^TTj^st'?] D. nlsfov D.
/LIT]]del. B, supra scr. D 2
. 13. %ca] comp. B, v.cd ^ B 3.
ccKQifiovusvcav] &%Qi,fiov[ivcov ogydvcov D. 14. Gvve6Tr}Qiy(i-
va>v~\ corr. ex GvvfGrrjQiG^vcuv D 3. ogyavcov] om. D. 15.
sSdysGi D. 16. yivopiv7\g D. 17. tog inl] corr. ex mcitl C 2,
renouat. D. ys x&v\ renouat. D. 18. TtukaiGxa. D, corr. D 3.
20. duxGTQOCpri] r\ diaGTQOcpri D.
198 KAATAIOT nTOAEMAIOT
r&v \iv roiovr&v ovdfv ovd' avrbg 6
Iji7tccQ%og ofercci, rvy%ttViv a&oitiGrov ngbg rr\v VTCO-
tyiav iijg aviGorrjrog r&v eviccvGicav ^pox/ov, cbro $
riv&v rr}g GfArjvqg ^xtefyfov eitikoyi^oyL
5 gpT/tftV,
fon f\ av&iiaMa t&v iviavtiicw IQOVGOV
rbv [istiov ftsaQOvpEvr] ov [isi&va 7tQi%si,
i' xal d' psgovs IM&S fftiSQas' QTCSQ av r^v tfdr] TWOS
ofeiov, si'neQ ovrog d%e Kal ^ Q avr&v,
evGyidvov s&scoQelro.
10 psv yccQ did nvov 6vvs /
yyvs catkavcbv ad
xfafys&V) 7t60ov xcc& eKK&ri
Y]v 6
ayvs icgo^BltKi rov {LSTOJCCOQWOV 6rniiov,
xccl did rovrcov evQiGxew oferai, itorl JAW rb
avtbv a7ts%ovra rolg xa-01
'
eavrbv XQOVO
15 note de to &d%i,6TOv [loiQccg xccl d\ Gwctyst,
VrV&V) Oil, 1tl7tQ OV fivVCCTOV TOV Std^VV V
ovr&g oMycp XQOVG) rotiovtov nftaxwqd'rivai, ,rov
) cccp' ov rovg roitovg t&v dTt&ctv&v 6 "Iit-
20 KitoKaxK&Ta&iv. AcA^'d'f d avrov, on rov
dvvapsvov 7too%G)Qlv avv rov rov xara
iv rov f\kiov r6itov vitoxtfG&ctt, avtbg ig
rovro xa& xd0rrjv Tta^cc^cc^dvov rag
rolgr
r(ji,v Xivoi,g cp ccvrov
6. piaov] corr. ex (istov D 8,
-ea- supra scr. D 3. 7.
']
ovs D. 8. d%\ corr. ex d%tv D 2. 9. sitdoyigercu] corr.
ex iniloyi&to D s. 15. [loiQas H xatl f D. Gvvdysi] post
ras. C, -ye- in ras. A. de (alt.)] d' D. 16. dvvccrov] -rov
ins. B 3. 17. peconivriiQ'fjvKi A. 18. "inagios D. 20. 8\
8" D. 21. ngo%coQiv~] -co- in ras. A. TOV rov] corr. exrovroov D 2
. 23. nctqccla^oiVfov ]AB 3C 2D 2
, TttXQodafifidBCD. 24. Ig;'] ABC; dtp' D supra scr. s, quod del. D a
.
MA0HMATIKHS STNTASE&S r'. 199
xal fariiiEQCa avro&ev dijlov noiel pr)de[iiav TCEQI
GvyXQlGlV TG3V EVlCCVr&V V7tKQ%OV6ttV JtCCQCi t$\V tOV
rsrdgrov EitovGcav dicccpoodv.
G)S y&Q <p' &>6 foodsiypato$ ex plv rijg EV rep
A/3' EtEi rr}s rofays xccra K&Knt'KQV Ttsgiodov TtaQare&si- 5
ex&eiTtTixijs rrjQijfa&s evQiGxew oi'srcci tbv
rov psroitOQivov Gqudice ds rri<s iv TG) p' xal rgCtG) eteu ri}s civrijs
7fQoy'yov[ievov poiQccs d'. xal dpoi&s
fg rovs
rovrotg
[isv tovT&v
rag iv rolg sredi 10
sccgwas farjiiSQicts, LVCC
rovg iv rots [ie6ois %QOVOL<S r&v
rdjrovg, djtb ds xovrcov rovg
S) ciitb ds r&v ri\<s tffA^i^g rovs t&v a6re-
r^v p,ev sv r& A/3
r
S'TSI (pytil ysyovevai rov 15
M%LQ K% -jtQGjia^ rqv d' iv rat py' srsi rrj
rb inetiovvxriov rb sl<s rrjv k' peta, j$i' d'
rfjs EV to* A/3' h'reu yfyEvrjpEvrjS) otfag xccl Ttoiei rb
rsraorov \LQVQV 7tiA.a[ipav6[ivov ExaGrc) r&v {ira%vTec rcbv. i'7to ovv ^itjr iv nfaCovi, p^rs iv &u66QVi 20
%QOVG) rtfs xara rb d' ETtovtitas 6 tffoog rrjv nobs ras
rv
5. KccliTtnov] ABC, KuMinnov D. nectars&ei(Jivr}s] corr. ex
itccQKTi&siJLEvris D 2. 6. >dr]7mxi?g C, corr. C 2
. 7.{_'] /_' j' D,
corr. D 2; j" ins. B 3
. 8. /u/ xal tQirco] ]iy D.^
9. f] ?/_ D,^8 D 2
. opoLfos] o/Ltcos D. 10. sis tov? 7tQov,s^isvovs] mg. D.
ioyTjitovg] BC, mg. A 1; STtdoyiGiiovs D, sed sm- renouat.
15. (fj]GivD. 16. MS%IQ] p%i>Q ^ D. K'] supra scr. C.
S' sv ro5] corr. ex $s r&v D 8. 17. ^'] TQLKKdda D. ^']
mut. in TerccQtov B3
. 20. SITIEQ ovv] corr. ex snsl ovv D 2(y^.).
21. y.atu ro] xard A. litiovaias D.
200 KAATAIOT nTOAEMAIOT
xal reragrov xsxwrjG&cci, , nag ovx aroitov ra
did rcbv vxo%i[iVG)v &Q%G*V fitifaAoyiGiifva Jtaoa^ap-
fidvsiv ftobg tv\v avrcbv rCbv 6v6rr]6anVG)v avrd dta-
poAijv xal rrp> cclrCav rov iteol r^v ro^Kvrrjv
5 rov 2xK%vo<s advvdrov iiydevl [isv
*ys fivr&v t&v e^7toii]6ca TJJV
iav dwccpevcov, porous ds rats v
a)g apa aKQiflcbs Kal pi} ax
dvvarbv yap av do&iE pccMov rjtot, rag iv ccvrcctg
10 rcclg SKfofystii diaGrd^sig ri}s ^aA^v^g Jt^bg rovg
rovg lytL^oy^povs ijroi r&v
rrjv t&v g)cuvoiiVG)v rojtcov iTtfaxetyiv y rijg rov
fjMov xtvrfGscog rijg ccnb rcbv ItirjiufQiav sxl rovg
15 [is'tfovg r&v sxfofyscov %a6vovg ^ prj dhrjd'&g r} pij
xal rbvr
'l3t7tccQ%ov Gvvfyvcoxsvcci, psv xal
ccvroV) on [irjdsv iv rolg roiovroig V0rt,v
itobg rb dvrQccv rwa r& ^Atw ngotiKiirei
20 fisfiovkriG&ai d [i6vov vito (piA.aA.y&ffag prj
n r&v vtovg fig vitofyiav bjt&Gdvjnor
Vyxlv. xtyorjrat, yovv xai ccvrbg rcctg V7to&66iv
fjMov xal 6^jjvrjg <bg piug xal rijg avri\g V7tao%ov6rig
7tol rbv r^kiov Kv&pccMccg rijg 6vvattoxad't,6ra[Lvr]g
25 rc5 nobg rag roonag xccl rag farjiifotag IviavGiG) %o6vG).
1. rlrccQTOv] j' B, j D. WKivfiGftai] post %- ras. 1
litt. A. 5. iij}Sevi (iev~\ corr. ex psv (iriSsvi D 2. 6. roi-
avtr]v D. 7. dwafif'vooi/] des. fol. 68 UA, ,,deest folium" mg.
m. rec. (desunt reuera 4 folia). [lovccis] sqq. om. A. 8. PostBC.del. v.al D 2
.
9.^6|fif] D, do&i BC. 10. luJLef^satv C.
11. iyyvs D. 13. 7) rrjs] om. B. 14. Ic^fqiv&v D. 15.
cclr]Q"rivo<s D, Cr supra add. D 2, cdrj&iv&g D 2
.
MA0HMATIKH2 STNTASE&S T'. 201
xccl ovdapfi dice to l(5o%QovCovg vitoTL&sGd'ai Tag ex-
KEi^iEvag TOV r\Uov TtEQiodovg ra itE^l rag sxfafysis
<pcuv6[iEvcc dscaQOVpsv aJtoAdyco tivl diacpegovra T&V
XKTK rag EXXEipEvag vito&EGEig Eiti^oy^o^Evov^ OTCEQ
av afa&rjrbv it&vv GwEficcivEV py 6v^7taQcc^ciii^civo^vrjg 5
tils 3tegl rriv avt,6oTqrcc tov eviavdfov %QQVOV diOQ&G)-
^ei xal [nag [tovov i]v poL^ccs^ dvo ds cog&v sy-
s'x TE dq TOVT&V ccitdvrcov, nod i% (bv r^iEls ai)roi
8ia t&v g)^rls ^tv tErrjQyiiEvcw rov v\Uov Jtagod&v 10
xccTaA,cc(i@Kv6[id'cc rovg rcov artoxccrccGTCcGEcov ^^dvovg,
OVVE aVlGOV VQl6XO[lV TO EVLCCV0LOV [lEysft'OS) EO.V
OS fV XL KCil(li)
TtOTE [lEV ttQOS ta tQOTtlXa Xttl 16^-
rjiiEia, jtors d itgbs rov$ aithavEis KGTEQCIS
,OVTE aM.rjv olxEiorEQciv K3toxartt6ra6iv rijs 15
Kit6 twos tQOftMOv rjxccl far][iiQivov r}
xccl
6r}{iEiov rov dice HEGCOV r&v ^codCov
Jtl TO avTO cpQOv<5rjg TOV f/Aiov.
lV di K7tA,OV6TEQC()V G)g EVl
V3tO&E6EG)V TCC (pCCiVO^EVCC UTtodElKVVELV, <Jp'
00OV CCV 20
X T&V TrjQIJGECOV aVTlTtiTCTOV TTj TOl-
(pccivrjTcci,. OTL {LEV roivvv b ngbg TCCQ
ag xal JfQog Tccg l6r][iEQicts &ECDQOV[IEVO$ EviavGiog
E6TLV Tijg Eitl Tatg T^E r\^EQai<s TOV d'
1. fyxft/^vas D, corr. D 2. 3. rpaivoiisvcc] C J
D, qpatvo-
^svag BC. fteooQOVfiEv] corr. ex Q'tfOQOv^sva. D. rcov] corr.
ex root D 2. 5. av aUfhftfo] corr. ex ccvai6Q"r]Tov B 2
,corr.
ex KV aic^Tcog D 2. ovvsfiaivfv] -v del. D 8
. 7. fiovov r]v\
corr. ex povris D 2. 15. -9-fcop^rat.] E, jtanpeiTcu BCD. 19.
dt'] 8 B (h. e. did). 20. &Tiodiv.vvtiv] corr. ex ano-dsMVvsi B 3
,dfwvvew D. 21. avrntCnrmv C. 22. TOLVVV]
ovv D. 7 mg. D. 23. n^dg] om. D. 24. iat D, comp. B.
202 KAATAIOT IITOAEMAIOT
v yeyovev not 6Y
ds ehd66K>v <5TiV)
[iv oi)% olov T av yevoito kafielv rrjg re rov d'
av%tJ6G)g rtl Ttkeiova eiri jroog afo&rjtiiv
5 (isvovGrjg di ro kd%i6tov tr\$ dt,a<po$ag nal di,a rovro
Kara trjv dia IIKXQOTSQOV IQOVOV Gvyxgidiv dvvansvrjg
rijg svQiGxoiiewqg T&V rj^iSQ&v snov^Lag^ ijv fist rotg
xal v ekurroGiv sviccvrolg rijg avtfig &GJQZ6d'tti'
10 Aaft/fcrnuro d' av syyiGra axQifiag r\ roiccvrrj aito-
, oticp civ 6 ^ircc^v r&v GvyxQivouwcov rrjQ^j-
xal ov povov 7tl
ravrrjg TO xoiovrov Gv^eftrjxfv^ dMa xal STCL ytaG&v
r&v TtfQiodix&v d7toxara6rd0cov' ro yag naga rrjv
15 avr&v r&v TYjQr}6G)v ati&dvsiav, xav dxQificbg
voiisvov didil>v6(ia Pga%v xal rb avtb
(bg xgbg rf}v nag avrd al'G&rjtiiv ini re rcov
dia fiaxoov xal iitl r&v Si okiyov %g6vov <pat,voiis-
vav fig ttdrrova [isv 7tL^QL^6^ivov ivy iiiov itoiei
20 ro sviavGiov d^idQrrj^a xal ro ex rovrov xard tbv
^ stg
'Aa66ov.
o&v avragxfg 7tgo6r^xEi voptfav, edv, otiov 6
fira|v %QQvog JUL&V re xal (bv ye e'^o^iev nakaicbv
1. yiyovs D. 2. ccnidei^s post. ras. 1 litt. D.
&O.GG03V D. 3. TS] BC, ye B 2 D. 8. iv TtlEiQGi\ corr. exnldoGiv D 2
. 10. JiCCfLpttvoLVTo D, corr. D 2. 12. z0oi>os]
cvty BC,corr ex %QOVOI$ C 2;bis D, corr. D 2
. 13. ravrTjg] tccvt
avTijs corr. ex ccvrog in scr. D, ravrr^s D 2. 15. rcov] bis D,
corr. D 2. iisdodevovTUL CD, corr. C 8D 2
. 16. yiyvoiisvov D.
didtyevGiid] corr. ex Si&tysviia D 2. 18. XQOVOJV D. 20.
%ca] del. C 2D 2. 21. 8e] corr. ex $i' C 2D 2
. 24.
corr. ex %%a>iisv in scr. D, %a)(jiv BC.
MA0HMATIKHS STNTASE&S r'. 203
apcc xccl axoificov rrjoijtifov dvvarai jtooGxoirjGat, rfi
r&v TtsQiodix&v vito&E<3G)v S'yyvrrjrt^ rotiovrov xal
lQK&G>llV GVVEKSeVSyKSlV Kal [IYJ SKOVreg <X[IS-
ri]g JtooGTrjxovG'qg s^srccGscog, rag ds neqil o&ov
rov at&vog TJ Kal rov (iaxQ(d tivi xokkcatkadCov rov 5
Kara rag rrigriGEig %g6vov diK^^aiG36ig KMorgfag
<pt,honKd'iag t xal yihaA.rjd'Mag riyto^d-cc. WEXEV pwovv TtccAcciotytog ai re vitb r&v 7t$l Mdr&vu XKL
Evurrftiova. rrr}Qr][iV(u &Qival rgonal xal aC [ira
rovrovg f)itb r&v 7C^l '^QiGrccQftov Q(pikoiv av stg 10
rrjv GvyxQiGiv r&v xa& fftnag y^Evrj^vov TtccQcdaii-
Pccv6&ai,. VKV dl rov Ka&oAov r rag rcbv rgoitfav
dv<5diaKQirovg eivai xal JtQog rovroig rag VTC
taQaddo^Lvag Qho<5%Q<5rQOv EikYimuBvag, cog
KOI rip
(
Innate:) doxt cpaiv6&cci) ravrag {iv 7taQrjrr]6d- 15
rcclg rcbv faqiiSQi&v r^^^i xal rovrcw KXQL-
EVEKEV ratg r vxb rov *Iit7iaQ%ov ina
ccvrov xal raig vcp fftifiv avr&v dia r&v Eig ra rot- 20
avrcc Kara rr\v aQ%rjv ri\g Gvvrd&cog V7toddt, i
y[iVG)v
[idAiGra rrr]Qr][ivai,g' f| (bv
rotg r Eyyitira r6iv \iia f}[iQtt itgo-
rQov yivopdvag rag rooTtag nal fayiiEQiccg rj\g Kara
1. dvvccrai] mut. in 8vvi)tai B 1. 7. cpi3.o[iad'icc$ D. 8.
vnb rmv TISQI] supra scr. D, in textu/. ite^l TOO. 9.
om. D, yp. *ai fttQivai supra scr. D 2. at] om. D.
TOVTOVS] JU.ET' ccvrovg D, deinde ins. at D 2. 17. TOILS]
Tf D, corr. D 2. rriQijGstGi. C, rrjpTjfffcov D. 19.
O'rjoatg C, corr. C 3,
sed euan. tog] add. mg. B 3. &ocpa-
AfVrara] corr. ex a.GyalEGTG.'tag D 2,ac- corr. ex comp. axj B 3
.
22. a<f7rcbiTcog] corr. ex <xdt,GTKKT(p D3
;hie calamum mutauit C.
23. iv\ om. C. htGi D. 24. rag] ins. D 2. %ca] v.a.1 rug D.
204 KAATAIOT HTOAEMAIOT
TO d' 7tl tats t% rjfioai,s sxovtitccg. ev ply yao
A/3' k'ti rijs y' xatd Kdhiititov 7tQi6dov
tyv [isroTt&Qivrjv farjiifotccv 6"
o^^vrjv xal
5 avtrjv ysyovsvai, tr^ y' r&v ejtccyo^isvcsv rov
rov sis rfv d' (pSQOvtog' KVLI Btinv to srog goy' aito
fAfvrijg. ftfra df tine rrj rw yf
k'rsi
6 iGuv v%y' aytb r^
10 farinQiKv yeysvYipBvriv tr[ & rov 'A&vQ peta
cooav syyiGta ti\$ tov ^Atov &vatoti]s' in&vifav aaa
i] drtoxatdijtaGis f'gp' oAotg Afyvrttiaxots 6?t
tovt6tt,v tolg ava t, fi[iQas, tag ytddccg o xal
xctl ffaocitbv h'yyiGta yuas f)iiQag dvtl t&v xata
15 tOV
oa .
to 7tov6ias Y*> *>i> iitovtir to
d)6avtG)s $ ndUv 6 plv "ImtaQios (p^uv t^v iv
20 rc5 7tQoxi,[jiVG) k$' ti tijs y' xccta Kd^LTtitov 7tQt,6dov
tri ttf tov M%IQ TCQ&ICCS' KUL i<5tiv to i'tog to
dttb tijs 'Afa^dvdQov tA,vtriS' ^tg d tqv [ita td
1. rj^QK? D. 2. Kdhmtov] BC, Kdllimtov D. Ini-
ro D, corr. D 2.
~J mg. D. 10. ^crj^fpmv] far}- in
ras. C. 11. K>QUV] rj^Qccv B. 12. Iqp'] renouat. (ex vy'} D 2.
13. rovr^GTL C, comp. B. rots'] supra scr. D 2. o] 17^5-
QCC$ o D. 15. sTtifiu'kovG&v C. 16. oa d'] corr. ex o OA D 2.
17. jLua] corr. ex TtQwrr] D 2. 19.
r/
/?rap^og D. cprjGiv] -v
del. D 2.
'
20. KdUnnov] BC, KdUimcov D. 21. a^i^Gra-rrjgri&eicav C. 22.
t;y~\corr. ex TTJS D 2
. M%SIQ D. SGTIV]-v del. D 2
,SGTL C, comp. B. TO (alt.)] nccxa. TOV EKKTOGTOV D,
xata rov del. D 2. 23. TO. 'GTts] Tag its D.
MA0HMATIKHS STNTASESS P'. 205
Ores dfiot&g rr] red vty' cbro rijs '.^/UjaVdpov Tf/Uurijs
mgiv^v farnisoiav VQfaxo{iv/
y/
yevr}[ievr]v rfj % rov
IIcc%G)v [ista yiCav (DQuv syyiGtct rijg ^^^/3(>iag, cog
Kttl rCCVrrjV TV\V 7CQl'odoV 7tlA.rjCpV(Xl, T&S faag fi[lQaS
o ual d' nal K k'yyiGra avrl r&v agog rb d' sjupak- 5
AOVG&V T0t$ 6718 T6lV i^LQG)V OK d'. TCQOTfQOV KQCi
xal wrccv&cc yiyQVBV fj rijs CCQIW?JS i6rj[iQias ccitoxccTa-
6tcc<5tS rijs ttaQcc rb d' itov6Ca r\[idQK yua foiTtovGrj
rb K' [lQO$. G>6T 7fi TOV CCVTOV %l, AoyOV TCC T T
bs t& 6X xcclfj pia rjpfya ngbs vqv piav 10
rb K [iQOS) GwdyErai, dioti xal iv rots r
7tQ6rQov i6tiv rrjg xccra rb d' 7tov6iccs
Jtgbs rcc farj{iQi,vcc 6r][ila yuvoiievri rov ri^Cov ano-
xav TCQOS rfjv vjfb r&v itoi Msrcava r xctl Evxrij- 15
pova rrr]Qr]iivr]v ^Qivi\v rooTcfjv cog
rijg i)(p fj
,rb ccvrb rovro VQtj
ci,f
yyvri^vri iitl '^4^vdovs CCOVTOS 20
xccr
2.SCCQWIJV^
corr. ex sctQivrji, D. yyevvr\\Li-vi]v C, yD. ^'] t^ B, corr. mg. B 3
. 3. WQUV] rjfi^Qav B.
ayytara wquv D. 4. xr\v\ om. C. sm]\Bi<pivai D. 6.
oa 61
'] o a A D. 10. T?]] supra scr. C. TO] D, rds BC.11. TO] D, agog TO BC. 12. SGTLV] comp. B, tcrcci D. 14.
5] BC, piK D. 15. 7 mg. D. xav] B, xcu CD, y.al el
C 2D 2. Supra ryv scr. o D, del. D 2
. re] om. D. 17. ava-
C. 18. noirGme&a corr. ex TCOLGOied'a C-cc in ras. B, Ttoirjadiievot, D, noLrjaofie&a corr. ex
[ie&cc D 2. tr^g] corr. ex ryv D 2
. 19. eni'ke'koyiGiiiv'riv D,corr. D 2
. 20. yeyevvr][ievr] C. 21. KQCOIKS] ne^l xr\vD.
206 KAATAIOT IITOAEMAIOT
ds rrjv iv rc5 7tQoxi[ievG) vt,y' ri anb rijs
yiddiisfta ysyovdvai rr] la rov
[ira /3 coaas fyyvg rov sis fr^v rf' [isGovvxrtovKai fotiv ra iilv djtb ri}g snl rov 'A^vdovs dvayfyoa^i-
5 psvrjs &Qivfig tQOTtijs [itJCQi' t^S v^o r&v TtSQi Agi-i& v' k'rsi rs
gvfi, tec d% dyfb rov ytQOXsi^isvov v' s'rovg^ o i\v
a rb [id' eros ano rrjg 'Afo^dvdQOv r^vrr]s^ pt%Qt>
10 rov v^y' rov Kara rrjv rnirQav rrfgriGw fry vt,&. iv
rots [ifra^v aga rys ohrjs dia6ra6G)s ^poa r6iv, iav
% vnb r&v 7tQl EvKr^oi rov
15 opi.' y' yyi6ra avrl QpfiL' $' r&v rots <poa r<5iv
Kara rrjv rov d' 7tov6iav 7tif$aA,A,ov6(bv, &6rs noorfoov
yeyovv ^ x%i,[ivr] KitoxaraGraGis rijs Kara rb d'
7tov6ias Y\H>Qai<3 dvtil faiitovGais t& ifi [lias r}[iQas-
tpavfobv aaa xal ovrcos yyovv^ on iv oAois rots %20 k'rEGiv ras dvo itAijoMS fyyiGra fidgets o viav6io$
%o6vos 7tQokainfidvi rrjs Kara rb d' iitovtiCag. KOI dt'
7tki6vG)v rrjQrjdf&v r^ifls ts rb avrb rovro
VQl6KO^iV Kttl tQV "Iltlta
avr& 6vyxarari&Hvov b'v rs ydo r<p25 lviav0Cov [i
iy&ovs Gvyxoivas rr^v VTCQ
1. ^TTO] twv KTto D. 2. sTtsJioyiGdfiEQ'd] D 2,
BC, inikoyiGK^sQ'u D.~J mg. D. r^ ta'] corr. ex
ir\i a D a. rov] t- e corr. C. 3. MSGOQL BD. WQCCS
dvo D. fyyurtcc D. 4. icti D, comp. B. sW] suprascr. BD*. rov] supra scr. D 8
. 5. TQOTtrjg &Qivf]$ B.
&Qivf]g] e corr. D 2. p%Qt] -t renouat. D 2
. 7. Ka.\mnov\BC, KdlUmtov D. 9. v.ara to] om. D. 10. <u|y'] v|y'
D. 13. t^s] rfjs xu D. xa'jom. D. 15. y']sv B.
^
rgfaov e corr. D 2. ^TSGL D. 17.
17 EKKSifiswi] ysyovsv18. ro5] corr. ex to C, ex xai<$ r&v D 2
. 19. rotg] om. D.20. TE0w] B, exeat, CD. nlri^j] C. 24. yao] corr. ex
T B 3C 3.
MA0HMATIKHS STNTAgESiS r'. 207
rc5 v' rt, A.rjyovTi, rr\g
Kara Kdlinitov jcspiodov r -69?' eavrov rtdfav
stA.r][i[iV'fl rc5 py' s'tsi ^tjyovn rr^g rgCrrigKara KaKntitov 7tQiodov <pr}0lv ovrcog' ^d^ov roCvvv,on iv rolg @ii ers^iv ra^iov yyovv r\ rgonri rijg 5
Kara rb d' InovtiCag fa fj[ifaet, rov 6vvap<porQov &,
Kal vvxrbg IQOVQV"' jtdfav re Kal iv rti IIs^l
[iqvcbv re Kal fi^Q&v TtQOMTt&v, on, Karaftl Mdrova Kal EvKrrLova 6
ttQi%i ii^Qag rt,e d' Kal og' piag ^(ISQCCS^ 10
xara de Kdhititov i^LQag r% d' ILOVOV, iTtiktyti Kara
v rolg i& r6W) otiovg KaKlvot,, rov
miavrbv n Kal rov d' ghaGGov rQiaxoGioGra iiti-
p,dki6ra USQSI, {Mag fux,Qag, a)g iv rolg r 15
rGiv ^L7Civ Ttaga pv rov Mdrova f)tiQag i, nagadf rov KdkntTtov fj[iQav piav"' KOI GvymcpaAaiov-
pwog $ rag yvco^ag avrov 6%dov dia rv\g avayqa-<prj r&v idicov (Svvray^idrov cprjGlv ovr&g* ^vvrdra^ad Kal 7tQi rov viav6iov %QOVOV iv fiifiMcp vi^ iv 20
co a7todiKvvG),on 6 Ka& ijfaov iviavrog' rovro $
yivrau b %Qovog, iv & 6 TJAtog ditb r^oii^g iitl rr^v
7taQayivrai rjaito i6riiLQiag iitl rrjv
25
2. Kdlimtov] BC, K&klutnov D. rj) 4. OVTO>S] mg. D 2.
4. K(&(,mtov~\ BCD 2. <pj]6iv OVTCOS] etiam in textu D.
5. on] ins. D 2. 9ft^] corr. ex pft B. i-reaiv] -v del. D 2
.
ra^tov] corr. ex rd^eiov CD 2. 6. Jjro'Ufftag] post n ras. 1
litt., -g e corr. D 2.
'
<mg. D. |] Ix re D. 7. Ante
XQOVOV del. wi D 2. re] om. D. 9. Mirtov C. 10. d'} %al
%xi (-1 corr. exTj) 4' D. 05'] D, o s B, o g B 3,
o s C. 11.
Ka,limtov\ BC, KdMimtov D. d'] v,al TETCCQ-COV D. 12. ft?V]
om. C. 13. > mg. D. 15. j&iag] corr. ex ccs D 2. 17. Kdl-
ntTtQv\ BC, KdUiTtnov D. xca] om. D. 21. 6] D, om. BC.mg. D. 23. nuQuyiyvtTccL D. 24. slaecov D.
208 KAATAIOT HTOAEMAIOT
xcil VVXTOS-, xccl ov% cos of
TO d' ETtdyEG&ca ETCL TOO EL^^EVG) Tthrfoti T&V fj[iEQG)v".
QXI [iv ovv ra n>%Qi TOV dsvQO (paivo^iEVK TCEQIto [ifysd'os TOV EVIKVGLOV %QOVOV rf/
5 TJJV T&V TQOTtlXGOV XKi i0r^LEQLV6)V 6V\\JilG)V CC
GTCtGlV TtyhlXOTrjTl, 6VVT()S%Si KKTCC tV\V TG)V VVVT& TtQOTSQOV 6[LOhoyLCCV , (pKVSQQV OL[lttl,
TOVTCW $' OVTG)S %6vTG)V, IciV 7fL^l8Qi6(O^
YllieQav ELS t& * f^? 7rt/3aAAft EKK^TG) srsi,
10 fj[i8Qas s^rjxoGra devrsgcc i$, KJtSQ sav a(pE^co^
t&v Tys Kara TO d' itov6ias t& ^5 $OIIEV TOV iiti-
TO00VTOV {LEV d^ TC^^OS TCDV r][lQG)V sty (XV
qiltV G)S EVi [idhlGTCC K TCOV TIKQOVTOV15 EVEKEV E TqS ETtC T TOV i\MoV XCcl TWV
TKS 7tKQ EXCKJTK 'yiVO^lEVKS CCVT&V XCCQo
1JV JtQOftELQOV XKi &67tQ EXXl,[lEVr]V TtECpVXE 7tO,Q%lV Y]
GVVTtt&S tilS XttTa [LEQOS XaVOVOTCOLLCCg., 7tQO&6l,V [IEV KCcl
GxoTtbv T]yoviL&K dslv vnaQftEiv TOO ^a^rj^ccTixoo dsl^ai,
20 TCC (pcav6^va EV T& ovoavco TtdvTa dt' o^ia^&v ual Eyxvx-EG)V KTtOTEhoVllEVa, 7tQ06ljXOV6CCV d XCCi
Tfi TOlttVTTl TtQQ&EtiEl [idhlGTCC XCCVOVOTtOitaV
Tf}s dia Tag T&V xvxhcov VTto&EGEis doxovtirjs25 fictivEw avGoiiaMccSi ndkiv df EX T^Q [IL^ECOS xal T^S 6vv-
a'yco'yils TOVTWV ajifpOTEQCDV TCCS (pccivoiiEvas UVTCOV TCCCQ-
odovs ccTtodEixvvovGccv. LV' ovv r\\iiv xal TO TOIOVTOV
sidog EvxQrjGTOTEQOv xccl itao' KVTCCS tecs ccrtodsi&is VTtb
%EIQK kapfiavriTai, TCOI^O^E^K EVTEV&EV T^V X&E<Siv T&V30 xciTa PEQOS b[iahG)v TOV ^LOV XLV^E&V TQOTIG)
1. avto] corr. ex ccvtqt D 2. 4. TtQocsiQrj^vrj D, -G- eras.
5. aTtoHccTaGTKGiv] pr. T e corr. C, -iv corr. ex -ft D 2. 11.
corr. ex STCLOVGLCZS D 2. Deinde add. r^Lsgrnv D et
supra scr. B 3. ts] corr. ex id ftrj D 2
. 13. Ante TOGOVTOV
del. TO D 2. 14.
e&Tjpf^MMt D, corr. D 2. 25. Gvvaycoyfis D,
av del. D 2. 27. fva D. 29. TronjacbfAfO-a D.
MA0HMATIKHS STNTASE&S I". 209
rijg yaQ (lifts ccTtoxaTccGTaGfcog <xitodedi,'y[ievr]$
r|f id jZ^, sav iti,[iQfaci)iiv fg TccvTccg Tag TOV
xvxkov noigag T|, |o^i> TOfi
TOV fyiov [noigcbv o v&rj t? Ty i$ Aa
yap pfyQi' TOGOVTCOV %r}X06TO)v Tovgtovrcw itoielG&KL. Jtctfav xov fjiiQr)6iov
^K^KVovrsQ TO xd' e^oiisv TO coQiatov ^OIQ&V o
v Ip/y y a syyiGru. o^ioicog TO f}[iQiJ6i,ov
&S tov vbg [irjvbs rjufyccg A
nqviatov pOLQibv x& Ad q Ag Ag i A, 10
id ds Tag TOV a AlyvTCTianov TOVS
xarj
A. TCakiv TO viccv6i,ov 3toA,A,a7tA,a6t,a6avTs itl
Trj M? dia TO (pavr]66iivov 6v^Toov Tijg xavovo-
XCCi tt(phoVT$ oAot> XVX&OVS ^O^lV IrJTrj- 15
7tOV6taV [IOIQG)V TVS A^ X Aff X Ad A.
ovv xccvovicc Tr
vO' TtfQlS&t, d TO [lV TtQ&TOV XKVOVLOV TCC TCOV
STriQidov iisGa xivnj^iaTa^ TO df ft' TCQ&TCC TCC iviuvGia 20
xal V7t avTa TCC cDQtata^ TO $ y' TCQ&TCC [iv Ta
VyfOXKTO $ TCC r\^,QTq6lK^ TCOV [lV TOV %QOVOV TOlg 7CQG)TOtg llQ6t, TCC060^lV(DV^ T^S $ T
iv Totg /3' XCCTK Tag olxstag fxccGTcov iiti-
Kg. xaC sfaw 01 xavovsg TOLOVTOL' 25
2. r|f] ante ras. 1 litt. D. ravrcc D. 3. T|J] seq. ras. 1
litt. D. TO] totvvv TO D. 4. o v-fr] corr. ex ov& D. 6. 17^-
QIGLOV C. 7. lufiovTes D. o f] corr. ex op D. 8. O/LMHOOS]6- corr. ex D. TJIISQIGIOV C. 9. Post s^ofisv del. i\ D 8
. 10.
(jiGov Kivrifia D. ^,g(alt.)] supra scr. B. 11. a] svos D.
- e corr. D 2. 12. $ mg. D. 15. oxtooHcafoxccfrT^i'-
17. vdt-ofisv D. 19. TrifTegLdtov C, dxrcoxcadfttaer?;-D. 20. KivrKiatK] in -vrj/Ltem* rursus incipit A fol. 69.
] Is" A. 21. tap to;tec] opta m C. 22. r][i()iGi,cc AC. 23. rj)s
D.'j
TWV df TT)S D. 24. Tra^a-O'fVfos] corr. ex
|3'] SswsQoig BD.
Ptolemaeus, ed. Heiberg. 14
210 KAATAIOT HTOAEMAIOT
t
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MAOHMATIKHS 2TNTAEE&S r'. 211
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I 8?-
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Hioa. s. -
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212 KAATAIOT HTOAEMAIOT
S|8
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Qa.sr
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MA0HMATIKHS STNTAHE&S r'.
l
5-<fe
213
git
2?
o o o o o o ooo
3 'g
f 4
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214 KAATAIOT HTOAEMAIOT
o <^ <* o <
s ^Or Q/
to vu *o
111o a a.
8 00. ?
* ci *[i*!"
1
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ffl I $. f J:
MA0HMATIKHS STNTASE3S T' 215
's. X*4 ft"
to -y~n o-a.
<*$ I:8 2"
a. a. a.
S U ^
i 111o o
*T-i co ^
IH o co ^
216 KAATAIOT IITOAEMAIOT
y'. Ilsal r&v Ka&' bpakriv nal
VJCO&S6S&V.
d' ovros xal r^v (pawoiisvrjv dv&iiccMttv rov
det%cci TtgoAynrtov xalhUou, diort, xccl al rcbv
5 3tAav&iiVG)v sis ra jto^iva rov ovaavov
ci)67tQ Kal sis t& riyovpsva yoga r&v
f*fV elctiv nation, xccl syxvxAioi, ify cpvGst,., TOVTSGTLV aC
voovpsvai rtSQidysw sv&stcci, rovg aGTsgas vjxal xovg
uvxAovg avTKtv 7ti TtdvT&v catAcbs zv tolg
10 l6K<s yoviccg aTto^K^dvov^iv agog rots KVTQOISX&V 3tQiCpOQ(bV, CCi $ (pKiVO^eVKi 7tQl CC
ytccga ras &fasts xul rd&is t&v w tats 6<pttigKi$ ccvr&v
xvxAcov, di' <bv xoiovvrat, rds XLvt]6iS') ccitoxskovvrat,,
xal ovdlv dMoTQiov CCVT&V ri}s didiotrjTos rtQi rr\v
15 V7tovoov[ivr]v rcbv cpccivoiiva)v drcc&av rc5 ovn
Gviifiawsiv. rb d' cd'nov r^g dvco^id^ov
xccra dvo [idAiGTCc rds ttQcaras xal ccitAas V7tod'0i,s
v6ftui. rrjs ?&$ KLV^SCOS ccvrcbv
rbv 6[i6xVTQ6v T T& x66[iG) xal iv
20 eTtmtdcp rov did pfaov r&v fydtov voovpevov
cos ddia<pootv nabs rb xwraov avrov rv\v
otyiv, ccvrovs nrou xara[irj dpoxwrQcov r&
xvxh&v ofiftAwg V7tohr}7trov noiBiG&ai rds xi
xccrd 6[ioKvrQG)v /u-fV, ov% ccnh&s & iit
1. y'j rag. BC 3,om. AD. 3. (T] ds D. OVTOJS C. 4.
D, corr. D 2. 7. sfoi CD, comp. B. 10. fvtaffrrjs]
f cp' sndcTris D, corr. D 2. 11. itEQicpoq&v] corr. ex nsQicpegsiatv D a
.
12. ra|fig] -eis e corr. D a. t&v av-~] in lacuna minore
ins. D 2. 13. wot-] in lac. maiore ins. D 2
. dbr-] in lac. D 2.
14. oijfoV] -8v in lac. mai. D 2. K^OTQIOV] -ov in ras. 5 litt. D 2
.
16. <?'] 84 D. 17. -AUTO] wia. rd B. 20. ptGov] ptccov D.
24. KUTCC] KUXO. to C. cbr/USg] a- e corr. D 2. 8s~\ S' D.
MA0HMATIKHS STNTASE&S r'. 217
'
itl
eitlXVXA&V. KU& XKTQCCV ya.Q TOVTCOV TG)V V
vd%6[ivov (pav^STcci TO v foots ccvrovg
avfoovs (pccivsG&cu rats otyeGiv i\^&v 8iQ^o^vovg TOV
dia n<5G)v rcov ^cpdicov xvxAov dpoxevTQov TK> notice) 5
10
lav T yap iitl rijg XCCT
TOV plv XXVTQOV XVXA.OV, Cp
j CtGTYlQ XlVfiTCCt. TOV ABF4B
XEVTQOV TO E xccl did^Tgov
/,TO ds Z 6r][itov ?t
r}[lTQCCV OtylV, O)6T Hal TO
A TO KJtOyfiOTCCTOV
TO
T L6CCS yfOL(f^iCCS
T AB xccl rfv 4FTCCS BE Kol BZ xal FE xccl TZ,6Tai,, dioTi Tag AB xal Td 7tQi(pQias wa-
TOV icegl TO Z XWTQOV /
yQccg)o^ivov xvxhov dtfA^Av- 20
7tQi(f>BQiccs dice TO farjs oviSrjs Tils vrtb BEATfj VTCO FE^J A.a66ovcc [iv yCvsG&cu T^V V7tb
BZA xciToas avTobv, piova ds Tqv vjtb FZ4[Eucl. I, 16].
KV T' Bill Tils XCCT 7tMVX&OV VJtO&6G)S VOWGWVLSV 25
1. al'kd D. vn' SHSLVCOV] vnoHeifjitvcav D. 3. %Qovoigccvrovg D. 4. CCVIGOVS] &.- supra ras. 2 litt. D. 8i,Q%6Q'cci D,corr. D 2
. 5. v.vv.'kov] nvnlov KCCL D. 7. sdv\ civ D. f'x-
KEVTQOTriTa] gx- in ras. 1 litt. D 2. vnofttosoov C. 8. bpul&s\
6- supra scr. A 4. 14. J] J -to D. 18. IGTLV D. 816x1]
supra scr. D 2. 19. do|ft] dti&i B, SO^SL supra scr. B 2
. 20.
TO] corr. ex rov D. 22. rj[\ seq. ras. 1 litt. D. 25. T'] re D.
218 KAATAIOT HTOAEMAIOT
rbv per 6[ioKvroov rc5 did (U-titov r&v Z&di&v KVK&OV
rbv ABP4 Ttfol Kvroov rb E xcci did{irQov rf)v
AET, rbv d' lye9
avrov (po6[iEvov eitfavxAov, Ecp ov
xwsfacu, 6 dtirtfo, rbv ZHK5 TtEal Kvroov rb A, cpavfobv
Kttl ovr&s avro&sv h'^roa.,
rov sjuxvxhov d^icc^&
(isvov rbv ABT4 xvxhov (bg
anb rov A Aoyov svsxa sal rb
10 B KOI rov aGreoos rbv iiti-
xvuhov, orav [lev xccra r&v Zxal yavrjrat, 6 a6rr^Q^ ddiatpo-
QWS tpuvriGErai, ra> A uevroc)
rov STiiKVKkov,
orav ds Kara
15 Kara psv rov H (psos SLTCSLV
riG&ai, KivviGiv rrjg b[iaA,ijg ry AHds rov K shaGdova O^IOLCDS rr] AKtl [isv ovv rijg roiavrrjg xar' XKvroorrjra vno-
dfl o^v^^rjK tv\v [iv A.a%far7]v KIVYIGLV Kara
20 ro aitQyeiorarov jtaQaKokov&eiv, rrjv d [lE'yLG'rrjv Kara
rb TtEQi'yfioraroV) srtsl Kal ndvrore ^ vitb AZB6rlv rijs vjtb z/ZF, jil $ rijg Kar
dvvarai tivpfkdvBW. rov
rd 7t6[iva rov ovoavov
ovxsrt,
nteiova
1. /u^v] ^ D, ftD 2
. 3. #'] seq. ras. parua A. 9. ccno]in ras. B 3
. A Aoyo-u] cdoyov C. Wxi> D. 10. B] corr.
ex a D 2. 11. Ante ptv ras. 1 litt. B. xara] &u' D. 12.
ysVrjTca] corr. ex yftvTjrat A, ytV^rat D. adiaqpd^cog] A, corr.
ex diacpoQtos B 3C 3D 3. 13. tov A KSVTQOV D. 14. xorr' D.
15. Ttliova. D, corr. D 2. 17. ^X] ^4- renouat. B 3
. 7tQi-corr. ex 7iQi(pQtia.i D. 18. o^v] om. B. yy,VTQa>-
D, corr. D 2. 19. alsl D. Gv^r]v.v D. 22. fffti D,
comp. B. 24. pttdBaai C.
MA0HMATIKHS 2TNTABE&S r'. 219
cog Aoyov svXv dab TOV A inl TO 5, eav plv 6
ovT&g v tip 7ti,xvxA.G) itQirpai r^v
rqv aito rov ajcoysiov jietccflaGiv ig ra
a7toTtei6&ai,, rovre^riv aitb rov Z cog sitl rb
H, xara rb aitoysiov TJJV ^s'y^rrjv ndgodov yivBG&ui 5
6v[ipri6Tai dia rb 7tl ra avra rov re srtixvx&ov r6rs
xal rov a6rQa xwsM&ai, sav ds r\onto rov aitoyeCov
rov adregos [isrdfladig slg ra TtQorjyov^sva rov iiti-
xvxAov yivY\rui, rovrtGnv cato rov Z &s eitl rb K^xara rb cutoysiov avKitakiv
rj skaftfarr] jtdoodog aito- 10
dia rb st<s ra svavria r^ rov
rov dtiTSQa Tors psTaxivEiG&at,.
rovrov d' ovr&g %6vrcov (p%rl$ xdxiva
,on r 7tl [iv Tcbv di66a Ttoiov^evcs
d[Kpors'()ag Tag vjtod'6tg ravrag svde^erai 6v[i7t- 15
&g v rolg rtfgl avr&v anod^o^v^ iiti d
Kal rfl avrr^ x%Qy[iVG)v dvG)[iaMa xal ptaTK)V XXl[lVG)V V7tO&6G)V d()X6l, Xal OTi Ttdvra tk
xaTQav avrCbv ditaQaMdxT&g dno-
T&V avrCbv koyov v d[KporQaig TtQis%o- 20
TovT<5ri,v orav, ovs-yjti koyov rj ftta|v T&V
XVTQO)v sjtl rijg xar' fxxwTQOTrjTa v7to&6G)g r^g re
ofa&g xal rov MXWTQOV xvxhov agog rr\v x rov
XVTQOV TOV XXVTQOV) TOVTOV #7? TOV koyOV Ttl T^g
Xar' 7tlXVxA,OV V7tO&6G)g i\X TOV XVTQOV TOV BTCi- 25
XVX&OV JtQOg T^V X TOV XVTQOV TOV CpQOVTOg aVTOV
Tl V 00G) %QOVG3 TOV XXVTQOV
2. noiziTcci B. 3. &7toyiov~] e corr. D 2. tig
\fd corr.
exel\GTcc.
A 1. 5. KKTO] -rd supra scr. D 2
. 8. efe] sni D.10. s\aG%i6Tri A- 18. aex&jfi] -ft renouat. inter duas ras. D 2
.
21.i-'zy
D. ^] mg. D 2. 23. Supra rov add. HSVTQOV
rov D 2. 24.
s'xj]] A, t^i BCD. 27. ?Tt lv\ corr. ex tort, D 2.
220 KAATAIOT IITOAEMAIOT
6 aGrriQ cbg sis v
d[iTd7tTG)Tov ovra dia7CQQVrai, v ro^ovrcp xal 6
TOV 6[i6%VTQOv rfi otysi xvxAov
cog ig rd 7t6^va [iTaxi,vov[ivo$, 6
5 rov 7tiKvxkov t6oTa%G)$, cbg ^ievroi rrjs XKTCC rb KTCO-
yeiov {iTafld6G)s sis ra TtQorj'yov^vcc yiyvoiiwys.
On $ TOVr&V OVT&S V7COX^VG)V TK CCVTK TtSQl
Mccrfyav r&v vnoftfafcov (paivo^sva 6v^ri6srai^ dice,
l$Qa%G)v (podv6o^iv did t Tcbv hoy&v avrcbv xai
10 [ira ravTK xccl dia r&v ^cpodvo^iVG)v iv ccvroig eitl
TOV fikiov ava)[iaMcis agid'ii&v.
j TtQ&xov, on xcc& xatQav avrcbv1} ft-
diaqiOQa yCvxcci tys o^aA^g KIV^O<S TCKQCC rqv
15 t&v a6TQ(ov voeirai, orav % qpcavo^V?? didtiraGis ano
rov aitoy iov TsragrrjuoQiov dnoAappdvr], xal on 6
anb rov artoyuordrov p>%Qi rrjs Eiorjpwrig ft<?^g
nagodov %QOVO<$ psi'Cfav 0x1 TOV dnb T^S [ifaris 7tl
TO 7tQif
yLorarov. o&v 6v^aCvi Kara [iv rv\v r&v
20 XXVT()G)V V7t6&6l,V t, Xal XaTCC rV\V T&V
de, orav ai aito TCOV dnoyficov avrcbv
ra 3tQor]i
yov[iVtt yivovrai^ rbv dnb ri\
TOV anb
TT
3. $LeQxsTcei, D. 4. 8'] 8t D. 5. Ante cog del. piv D 2.
g] rrjs rfj$ B. 6. yivofisvrjs D. 7. > mg. D. 8.
alt. v corr. ex Q C. 9.rs~\
corr. ex dH D 2. 10.
did] seq. ras. 1 litt. D, om. B. kpofovoi&rov] AD, -svtov
euan. B, ecpodevpevav C, scpoodsviisvav D 2. 11. rov ^Mov}
fjUctKfis D. 12. uvr&v] -co- in ras. A. 13. ofta/lffc] -?)-
e corr. A. 14. &vd>iLcdov~\ corr. ex av^aliav D 2. 15.
diaGTucis] -G- del. D 2. 16. 6] ins. D 2
. 19. o^cv] corr. ex
ontQ D 2, supra scr. yg. oitfQ. GVV^KIVEL A. 22. ytWi>Tca] B,
yivovxai AC, ylyvwvTui D. 23. ytVfd^at] -I- e corr. D 2.
MA0HMATIKHS STNTAEE&S r'. 221
H,s6r]g snl rrjv \Lsyi6w\v dta rb Kara rb aitoysiov
iv SKarsQa rrjv i\ct,%{&syp xdoodov
8s ryv sis ra sitopsva r&v sitixvxkcov rag aitb rov
aitoysiov Jtot,ov6av nsoLaywyag rcov atirsQwv avdnakiv
rbv ajtb rijg fieyfatrig XLV^SCSS snl rr\v iistfqv %QOVOV 5
a yivsG&ai rov anb T^g ft(?^g iitl Tqv
a rb xal svrKv&a Kara rb anoysiov rr\v
drj jto&rov 6 sKKSvrQog rov dtirsgog
o ABF4 Ttsol Ksvroov rb E Kal did^isroov rqv
^ stp* rjg si^fp^G) rb KsvrQOv rov
^(pdiaKov, rovrsGnv rb Kara rrjv
ofyiv, Kal stirK) rb Z, Kal dua
rov Z rtobg oo&ag ycoviag rift
AEF dia%&i6r]g rrjg 5Zz/ vjto- 15
%^ ra/lrfi&m 6 dtfrfiQ STcl r&v B Kal
>,Iva drjhovon reraorrj-
tyri rov A anoysiov. dsinrsov, on nobg
rotg B nal z/ Gruisioig 17 psyfarrj yivsrai diayooK ryg 20
yag ijrs EB xccl
r]E4. on
ov avsj^t] koyov i\
vitb EBZ, y&vCa TtQog rag
d oQ&dg, rovrov s%st, rbv koyov f]rov ytaoa rr^v avco-
1. TO (pr.)] supra scr. D. 2. tr\v\ r B, T* B 3. 6.
ovci\ ABC, ttdcoovcc B 3D (renouat. D 2, supra est ras.). 7.
did] corr. ex S$ B 3. &x6ysiov] -siov renouat. B 3
. 9.
nag. D. 6] punctis del. D, sed puncta eras. 12. ^codianovD. TO] om. C, ins. B 3
. 19. A] renouat. A 4.
-i- ins. A 1
,corr. ex dsiKTociov D 2
. 20. yCvErai r]
Df 22. 17] ins. D 2. 23. av\ supra scr. D 2
.
corr. ex fyei D 2. rd$~] om. D. 24. rov] supra scr. D 2
.
222 KAATAIOT I1TOAEMAIOT
[ICiMcCV dittCpOOOV 7tQl<pQl,a 7tQO$ rOV 0&OV
Civr6d'v yivetcti (puvsgov, 7tidi]7tQ % p,v vytb AEBycovia rriv rv\s b^a^g xivijciscas vnotzivei
fjd vrtb AZB %v\v rr\g <jDan/o^Vt?
5 o%ri d CCVT&V fanv % vnb EBZ ycwicc [Eucl. 1,32].
j^ on, rovtov ixarfyccs &My y&via H%(QVcci, xgbg rg TOV ART4 xvxAov 7tgi-
ia 7tl rijg EZ v&iccs.
6vv6rccTG)6av yag ycoviat, ytQog rots xal K10 6y[itoi,s i]
vnb E0Z xal % vitb EKZ, KOI
&G)6(X,V fyt 4 XCcl
f]K4. 7t\ OVV
y&vov jj [i%G)r ntevQtt vnb tqv [i%ovct y&viav vito-
relvi [Eucl. I, 19], pstfav $ farw y Z rijs Zz/
[Eucl. Ill, 7,3], peftcov forai xcci % vnb 4Z yewfa
15 1% -INTO z/@Z. fay $ 6nv % vnb EJ@ vy vnb
[Eucl. 1, 5], 7tiitQ xccl % E rr] EzJ i<$nv
V\vjtb EZ.
6rlvf]z/Z rrls KZ, yLit,G)v itfxlv Keel
r\ vjtb
20 ZK4 rrls vitb Z4K' fay ds faxiv r\vnb EK
Tfj V7CO E4K, 7tl7tQ Xtti fjEK TtdklV 1% E4
fay xal XoLTCr] O.QK % VTCO E4Z, rovrfanv y vitb
EBZ, rijs VTtb EKZ 0nv
2. rpccvtQov} -o- in ras. A 1. 4. AZB~] A- in ras. 2 litt.,
-B ins. D 2, supra scr. a. Post avfo^dlov add. xii/i^coo?
in ras. 1 litt. B 3. -fijrepo^] v- add. B 3
. 6. dij] corr. ex84 D a
. 7. TtQOs] TtQos I itQOs B. 10.i] (pr.)] ij
re D. 12.
VTtb rrjv iLtcgovcc ntevQav 17 [iia)v ycovicc D. fift^cov] [tei-
cav<x C. 14. JZ~\ mut. in JZ A 4. 15. ^@Z] mut.
in &JZ A 4. tan D, scri D 2
. *%] %r\ C (ut saepe), xf\i C 3.
16. EJ TTJ E D. 18. Supra nfi&v scr. Harrow A 4. larlv]
comp. B, -v del. D 2. 19. [itigcov SGTLV (pr.)] om. D. 20.
ZKzf] ZK4 yaviu peifrv D. ZJK] ZKJ C, corr. mg. C 2.
!(mD, eGTlV*. 21.E4K~\EJKolyI). 23. JerrtD, comp.B.
MA0HMATIKHS 223
OVK ccQtt dvvatbv a.'k'ka^
via<s, need' ov
6v6rtJ6cc6d'aL yco-
^T&V 7tgbs rots B xal
(f,
on, xal17AB
TOV <X7tb rife kK%i<5rriQ KivriGs&g Ijtl xr\v 5
[isifav <5tlv T^ B FI ^t'S rtQi'Xi> tbv
O
dvtil rats to didyogov rv\q dv&iiaMas 7tQi,%ov6ai,s
7tQirpQlKl^ 7tl,dlJ7tQ V] {llv VTfO AEB yCOVlK [1%O)V
6rlv op-iHfe, tovrfativ vrjs VTtb EZB, rr\ vnb EBZ 10
BET ticcttcov t$ avrf) [Eucl. I? 29].
VXV tOV KCtl 7tl Ti}s
t^Kl TO
<3TG) 6 [JiV
r& notifies xvxkos b ABP rtfgl 15
XVtQOV TO 4 XCX.I dl(X[JiCT()OV Tr]V
A4B, b d' V T(p KVTG) 7ClJtda)
(pQOllVOS 7l' CiVTOV 7ttXVXAoS
6 E Z H 7tQl KWTQOV TO A^ Ktti
V7tOXi<5&G) K6TVIQ HUTU TO H, OTCCV 20
TttUQTrHLOQlOV CC7tt%G)V
TOV XCCTCC TO dsCO /yLOVKOI 7t&V%&G)(3ClV i]
T AH HOI 4HF. Afyco ,OTL %
(pCC7CTTCU TOV 7tlXVxA.OV' TOT yCCQ TO ItkslGTOV
didcpogov TJ\Q b{iaA,rjs Kivtfdf&s TCKQCC rr^v dvG)- 25
1. (lei^covccg C. ycoviccs avariJGaGd'ai D. 2. xat] ins. D 2.
3. ar](ji8Lois 4. TtfQicpSQSia] ~mg. D 2(nfifievov}. 4. TIEQI-
etiam in textu D. 6. sorL D, comp. B. 10. tovr-
comp. B, -v del. D 2. Post EZB del. yavtcc [leigcov
eariv dQftfjs D 2. 11. <T] ds D. -cfjs avT^e D, corr. D 2
.
17.8'~\ ds D. 21. T\TfT(XQTTl^6QLOV C. 23. fTtl^V^fOGCCV C,
corr. C 2. Y.a.1 (alt.)] %ul f) D. 25. dpalfig] corr. ex b^aUg A 4
.
224 KAATAIOT HTOAEMAIOT
pcdov. itd yao % plv opccM} ccTtb TOV unoyeiov
itQi,%Tai, vitb rfjg VTCQ EAH ycoviccg' i6oTa%8>$
o re atirriQ rov IrtfavxAov xal 6 7fiKvxA.og TOV
ART xvx&ov dia%ovTai' TO ds didyoQOv rr\g opaArig
5 xivr]6G)g TtaQK rr)v <pcavo[ivriv vxb Tr\g vnb A4Hy&vias 7tQis%Tcci,j (pccvsQov^ on xal
r\ vitQO%ri tys
VTtb EAH y&viccs ftgbg ri]v vjtb A4H, rovrfanv ^VTtb AHz/ y&vitt) rfjv (paivo^vrjv TOV a6rQo$ aitb
rov anoyeiov SwGraGiv 7tSQiB%et,. &cir aitsl vit6xi,Tcci,
10 avrrj TttaQTrjiiogfov, OQ&r} ply forcci, uai ^ vxb AH4ycovia, g)anto[ivr] de dice rovro [Eucl. Ill, 16 cor.] xal
f\AHT v&tcc rov EZH miKVKkov. % AT
^tt|v TOV A KSVTQOV XCtl
6Tiv dicicpoQcc TOV naga rriv av(x)[iaA,iciv.
15 xal xaTK TCC CCVTCCr]EH JtQi,(pQi,cc^ iJTig rtQi%t,
KCiTCC TYJV fVTCCVd'CC V7tOKi^lVrjV 7tl TOV 7tlXVxA,OV
TOV KTcb Trig A,cc%i6Tr]g Kivr]<5G)g iil xv\v
ov, [ifiZ&v i<5r\v Tr\g HZ.,
TOV anb Trig [i6r]g mvr\<5(ag Tcl rr\v
20 dvfil Tccig AT ytQig)Q^cag., 7CiJtQ) av
2. KivriGig] -r]- e corr. D 2; supra est ras. Supra EAH
ras. 1 litt. D. 5. vno (pr.)] post ras. 3 litt. D. Tfjs vno\ins. D 2
. A4H] AHzJ C, corr. mg. C 2. 7. tovreGTiv] TOV-
in ras. D 2.
TJ] om. C. 8. AHA\ corr. ex AAH B 8. 9.
MOTS fTtft] corr. ex >ISQ D 2. 10. >rca] sari D. 12. EZH]
corr. ex EZ B. AT ago] ydq seq. ras. 2 litt. D,ayct.Q
tt D 8.
13. TttQLClp^QSLK] COri*. 6X TtCpSQSlU D 2. ^SXK^V SCpCCTCTO-
pivr\s\ supra scr. D 2. 14. iortv'] comp. B, -v del. D 2
. TOV]seq. ras. 1 litt. D. Kvcopuh'av] a -ICav inc. fol. 66 m. rec. B.
15. EH] -H in ras. D 2. tjtig] ij- corr. ex v in scrib. A.
16. KMTCC] v.a.1 ynxrd C, nut ins. D 2. 18. u&arp] peGrjv
KLVTIGIV B. %QOVOV] -v e corr. D, deinde eras. son. scrLv]
comp. ins. D a. TT)S HZ] -s H- e corr. D 2
. 19. \Ltyt6tr\v\
-yi- e corr. D 2. 20. ^cc^iaj^v BD, corr. D 2
.
MA0HMATIKHS STHTASE&2 T'. 225
AH xal dydyco^isv rr\ EZ TCQOS
rrjv AK, feat, ftcv ywovrui ijr VTtb KAH ycwicc
rfj vnb AAT [Eucl. VI, 8] xcclf}KH 7tSQi<pQia ry
AT 6^ota, rccvrrj ds rov svbg rsraarr][ioQiov [isftcov
l<5tivi\ EKH, eAK06G)v ds % ZH' OTCSQ edei, 5
on, ds xal 7tl rcov Decree [lEgog xivrfdEcov Icp KK-
rcov vjto&6EG)v v rotg I'Goig %QQVOI<S r& ccvra
yiv&iui rtdvrcc itQi rs rag 6[iccA.&g
xccl rag (pKivoybtvag xwtJGsig xal 10
sn rccg v7tQo%ag ccvr&v^ rovr-
rb Tcaoa rr\v
Evrsv&w av
156
r&vdice
ASTi'Gog ds rc5 ABT opoxsvroco, 6 EZH
rcov A xal xEvrocov xal rov E aitoyfiov f\ EAA, 20
xccl cc7to2,r](pd'Ei6r]g jtl rov 6^oxvroov rv%ov6r]g itQi-
tpQiccg T^g AB xsvroG) rc5 5, dia(3rrj^ian ds r& A6 KZ 7tlXVxA.Og) XCCi 7tt
> V%&CQ f}KB A.
Eyoa(pd'\.Al
^ai\ H.G- (
1. AH\ JHB.i'o- e corr. D 2
,o
2.-d- corr. ex o in scrib. C.
B 3. rf? (pr.)] se(l- ras - 1 ^*- ^xat] ware xat B. xal
<fj4. opoia] supra scr. D 8
. 4.
6[ioict xy AP D 2. 5. EKH~\ E- e corr. D, EK B. ajrep
BD, corr. D 2. 9. ytyvttui D. 11. Toure'crt?] -v del. D 2
,
TovrfffTt B. 14. KccTU[id&oL] seq. ras. 1 litt. B. 15. TOO]corr. ex rtbv D. 17. 8s] 8' BD. 18. ro5] corr. ex ro CD 2
.
20. T&V] corr. ex TOV C 3. E] E^4 C.
'
22.
^E] %ai diacTrifiari, BD. TW (alt.)] TOO I'ffoo TOO B. 23.
D, corr. D 2.
Ptolemaeus, ed. Heiberg. 15
226 KAATAIOT HTOAEMAIOT
on 6 ftev atirriQ vq? mareyas r&v
jtl rqv Z ro^v rov SXXSVTQOV xai rov 7tixvxA.ov
ndvr&s Kara rov faov %QOVOV ivejflrftetai, rovrstirw
at y iteQUpfyftai o^oiai h'tiovrai, JMijfais
5 rOV XXVrQOV Xai'Y]AB TOV 6[lOXEVtQOV K
TOV sitixvxAov, 1}
de diacpOQK rijs 6ftA^^
itaga rr^v avco^ia^ov noilrj (paivopwr] rov
ua& exarsgav r&v vtto&sGe&v b^oia xal
10 7t&v%&GM)av *yaQ ijre Z@ xal
v\BZ nal h'n
% z/Z. iti rsr^ajt^vgov rov B4&Z ai aitevavrCov
ittevQal faai eltilv uarQa xaroa, ^ i&v Z rr^
rj$ BZ rr\ z/@, rtccQaAArjA.6
/
yQa[iiiov h'tirai rb
rroa7tA,VQov. faai ccocc falv ai y y&viaL ijre vitb
15 E0Z xal ^ vitb A4B xaifjvnb ZBK [Eucl. I
; 29]'
totfr' insl itobg rots xwrooig ti<5i, xal rag vitorewo-
[ivas vn' avr&v 7COiCpOias b^oiag aMrjAais yivstiftai
rr^v rs EZ rov ZKKtvrgov xal rv\v AE rov dpoxwroovnal rfy KZ rov zitiKVKkov. xar' a[i(poroas aoa rag
20 M,vtJ6i,s v r<p fa(p %g6vG) lid TO avro drmeZov rb ZV%fi'tfo'rai, 6 a6rr}Q xal rr\v avrrjv rov dia [i6G)v
r&v ^G)diG)v uvxhov 7tQi(pQiav ccTtb rov aitoyuov rr^v
AA <pavri6rat, dtfA^Avthos, k'tirai, rs aKokovftoQ xal rb
1. vcp'l B, y^. scps supra scr. B 3. 8.
rj] postea ins. D. 10.
. C.om. C. JBZ] ZB B. hi\ r)hi C. 11.
BJZ& C. 12. stciv i'occL D. SKKXEQCC] mut. in succrsQcti? D 2.
xar%] supra scr. D. 13. BZ] ZB B. A&\ A C.
i'cTccL] 'iGri corr. ex scnv D 2. Bz/Z@]ABC, Bz/@ZD.
14. ca] fTTft >tai j/aHc<;| at D. y] om. B.-fj]
fTtfl %at
Jyanal at rpftg ycovicci ij B. 15. xat (alt.)] ins. C. ZBK}-BK e corr. D 2
,ZB^T facu B. 17. yiyvsadui, D. 19. v.ara C.
20. rd (alt.)] seq. ras. 1 litt. D. 23. HGXUI p. 227, 1. nagd]supra scr. D 2
(yp.). 23. %Gtcti re] I'arat C, cocrf D 2 et suprascr. C 2
. v.a.1 TO wa^a] etiam in textu D (-& renouat. D 2).
MA0HMATIKHS 2TNTABE&S T'. 221
Ttaoa TY[v avG)[iaMav didcpooov TO avrb xa& exarsgav
r&v v7Co&6G)v, itidr] t^v roiavrrjv
till \i\V Tife XCCT
VTtb rrjg vitb 4Z y&VLag, iitl de rijg
xar 7ttxvxAov VTCO rijs into 5z/Z, KOI a^rca de
TS nod vaM.a% yCvovtai dia to jtccQK
rriv Z Tfj B4.
dtfAov d\ oti xai litl TtccGcov rcbv diaGrccGewv
avra TtccQccxoAovd'tfGei, 7taQccA,A,r}A.o/
yQcc[i[iov itdvrots
[isvov tov 4ZB TstQccrttevQov xai yQacpopevov rov 10
SXX8VTQOV xvxhov vit ccvr^ rye; XCLTCC rbv
rov ddrsgos psTccflccdGa)^ orccv oC Adyot xcctf
rcjv VTto&etis&v opoioi re xal faou GvpflKivcod
on, de, xccv opoioi povov G>6iV) avidoi ds tip
ra avra ita'kiv cpaivopeva 6v^yj6sra^ tpavsgbv xal ovr&s 15
faro yaQ aGavt&s 6 plv o^ioxsvrQog r&
o ART nsgl XSVTQOV rb z/ xal did-
)xa&' r^v ajtoysioraros re xal itSQiysioraros 6
^ rr^v AAT^ 6 ds Ttsgl rb B sitixvxhos
a3t%a)v djtb rov A aitoyeiov r^v AB rv%ovtiav itsgi- 20
xal xsxwiJGd'G) b atirriQ rrjv EZ TiSQicpEQeiccv
tiav yivQ\LivY\v drj&ovon ry AB dice, rb l6o%Qoviovg
1. TO] seq. ras. D. 2. tr\v\ rr\v plv BD. 4. JZ] J-
in ras. A 4, z/ZED, z/ZD 2
. 5. vno (alt.)] addidi, om.ABCD. Ez/Z] corr. ex EZ D 2
. I'GUL] I'G- renouat. A 4.
6. yivovTUL] fLvoix av B. 8. 8'] 8s D. 10. 6>z/ZE]AC, Ez/Z BD, @z/EZ Halma. 11. vnb tccvrrjg D. 13.
Gvpficcivovoiv C. 14. fiovov] post -6- eras, i A, -6- in ras. 2
litt. B. 15. TK KVTO] TK ccv- in ras. C. 16. ysvriGsxai] GV(I-
fiiJGopev B (supra -do- ras.), noiriGo^sv D. 17. nsgi 19.
AdF~\ nag. D 2(Ksfysvov). 18. TS v.cci Trf^tyfidra-rog] om. CD.
21. xca] 6 EZ %at BD. wf\G%v> C, corr. C 2. 22. cffl
seq. ras. 1 litt. D.
15*
228 KAATAIOT HTOAEMAIOT
sivat, rag r&v xvxh&v ajtoxaraGrdGsig, xal
<3av ijrs 4BE xul r\
BZ xal $ z/Z.
on ftv ovv facet, rs sltiiv Ttdvrors rj rs vnb AAE,
ycovict notr]
vrtb ZBE, xccl on sjtl rijg z/Z sv&stccg
5 6 &6t$ig <pavri6srai) Kara
ravrrjv rqv vxo&sGw avr6- H
ds
Kiyw $', on, xal $LK
ri\<3 xccr' sxxsvrQorrjrcc, sdv
10 rs [isi,G)v sdv rs shdrr&v
YI6 sxxsvrQog rov ABP
diLOxsvrQov, rrjg rs r&v k6-
yov 6{ioi,6rr)ros povrjs vito-
xsiiisvrjg uccl rfjg r&v cato-
15 xarcc6rd<jSG)v fao%Qoviorr)ros
sitl xr\$ avrijs jtdkiv sv&siag
rijg z/Z (pccvtJGsrat, 6 atiriJQ.
ysyQacpftG) <yaQ psftcov piv, &g scpaiisv,
o H Ttsgl XSVTQOV STtl rijg AT rb X,20 6 AM Ttsol ndvrQov d^ioicsg rb N, xal
rijg rs z/MZ@ XKL rijg z/AAH sit^v&K xai
r\MN. inti <5nv, dig <%
4B agog B Z, ov-
rog ijrs K itpbg K4 xccl % MNxqbs N4 [p 219,21],
xal ycwia fji)7tb 5Zz/ ycovia rf] vnb M4N fay dia
2. TE] re BZ -AOL r) BD, corr. D 2. z/BE xca r]
BZ v.ct.1
i]\ om. B, JBE nccir] D, corr. D 2
. 3. TS] om. B. etai
BD. 13. &7COKi(jivris C, sed corr. 19. Y.KVTQQV] KSVT(O D,
vivify D 2. llaxTcov BD. 20. AM] corr. ex z/M B.
ofioicos TO] -ff TO e corr. D. IxjUq&etrifoj in -&SIG&V rursus
inc. m. 1 B fol. 68. 21. TTJS (pr.)] corr. ex tr\ A 1. Post
dAAH lac. paruam ob naturam pergameni C, ULTIEL svravza
mg. D 3. 22. sTtEi 23. MN] xng. D. 22. ineC] s 3tt D.
BZ 23. MN itQos] postea add. A 1.
rs
MA0HMATIKHS STNTASE&S r'. 229
rb itccodUrjAov flvai, iv\v z/A rf/ BZ [Eucl. I7 29],
faoyaovid itiuv TK y rofyoovcc [Eucl. VI, 7] xal at vitb
rag avdkoyov jtAsvyas ywvivu facet,fj
re vitb B4Zxal
fjvjtb 4K xal
i]vitb AMN' jrapaAA^Aot ago,
ffalv at B4 xal K xal MN sv&elai, [Eucl. I? 28]. 5
co6rs nal ycovi'at, T]VTtb A4B xccl ^ vjtb AK xal
ilvjtb ANM teen sfaC [Eucl. I, 29]. xccl sxel itgbs
rots xwrgois efal r&v xvxA&V) onoicci, etiovrai xccl cci
iii ccvrcbv JtSQKpSQSicci, rjre AJS xal H xccl AM'
iv roj faa agcc %QOVG) ov povov 6 rs B7tCxvxko rqv 10
AB rtSQUpfysiccv xccl 6 atirriQ ryv EZ dis^^v^cc6iv^
AA xccl jtl r&v xx8vrQWV 6 aGrrjg %v\v rs H xccl
rqv AM dLshyAvftcos h'tirca,, xal iitl rijs ccvrrjs sv&sias
itdvrors r?i$ 4MZ dice rovro ^scoQ^tj^srai xccl
xccra [lev rbv STtixvxkov enl rov Z tiyiietov yiv6\ntvQS, 15
xccra ds rbv [ist&vcc fxxsvrgov iitl rov,
xarcc de
rbv B^drrova sitl rov M, xccl sjcl nccG&v r&v
d'?
ort XML, orccv fayv ytQicpQiccv 6
dtti,A.r}<pG)s cpaCvrirui dno r rov dnoyftov xccl 20
rov 3tQiyiQV) i'Gov 6rcci, xa& xccroccv &<5iv rb
itaoa rfv CCVCJ^CC^LCCV didyoQOv. iiti r ydo rfi$ xar
fxxfvrQorrjra^ ccv 'yodipcj^iEv rbv ARTA xxvroov
xvxhov 7t$l Xvrgov rb E xccl did(irQOv rr^v AEF
2. GTIV] comp. B, mut. in Ictl &QK D 3. y] A, om.
BCD. TQiywvcc] -Ly- e corr. D 2. 6. i] (pr.)] scrips!, at
ABCD. i] (alt.)] om. D. AK@] AK B, corr. ex AJK D.
7. TJ] om. D. ^(7t] comp. B, corr. ex SLGLV D 2. 8. at]
ins. D*. 9. 7J H v.ali] AM D. 11. dwJL$U;#e D, corr. D 2
.
13. a-uT?)?] supra scr. D 2. 14. Sid] 8iav C. 19. faces
itQicpQias D. 22. Int re] corr. ex sneiTtsg D 2. 24. AEF]
AETJ C.
230 KAATAIOT HTOAEMATOT
did rov A dnoysiou rr\g OIJJE&S vitoxeiiisvris id ccvrijs
xcctd to Z Gypstov xal did rov Z r^v BZ4 rv%ov<5a.v
diayayovtss rtisv%G)[iEv tds EB xal E4^ ai rs yccwo-
[isvcci, ttdgodoi i'cfcci*r xdl Kitsvawtiov 6ovtcci) rovr-
5 i^riv ijr vito AZB y&vCa rijg aitb rov
xalr\
vnb .TZz/ rn$ UTtb ro#
TO r itagd rqv dvco-
didcpogov to avtb b'tirai,
did to fayv eivai rr\v JJLEV BE10 tfl E4, rfy df VTtb EB Z y&vCav
rr] vjtb E4Z [Eucl. I; 5]* &<5rs
t<j}avr& diayoQG) rijg (pcavo^Lvr]g
-,tovtEGtiv rrjg v(p
r&v^vTtb AZBxalrZJ15 y&VlCOV 7tQl%OlLVri$ , [lEi&Vtt [lEV
rov A Kitoysiov rr^g
6ova df rr\v ditb rov F3tQicpQiaV) did rb xal ri\v /
,ova Eivcci rr\g vitb AZB, rit
20 rijg vnb FZ4 [Eucl. I, 32].
xal litl rr\g xar
rov iilv 6[i6xEvrQov
XEvroov rb ^ xccl didpErgov rrp> A4F, rov d'
ETtixvxhov rov EZH XEol xEvrgov rb A, xccl diaya-
25 yovrEg rfiv 4HBZ rwYovGav ETti&v^&uEv rdg AZ
trjv coco
rrls o^a^ijg
v vrtb AEB ycovCav
$ vjtb TE/1
av ya-xvxhov rov ABP
2. Y.uf] v.ca SiuyuyovTsg D. BZJ] corr. ex Bz/Z D. 3.
SiccyccyovTsg] om. D. 4. re\ ins. D 2. 6. VTTO] v- renouat.
B 3(propter fig.). 7. Post nccQci lac. ob naturam pergameni C.
Item ante fcrjv lin. 9. 13. TT)S 14. AZB] mg. D 2, r^g
V7tb ABZ in textu D, AZB supra scr. D 2. 16. ^KGGOV BC,
corr. C 2. 18. 7i8QL<psQiav] om. D. 19. AZB] corr. ex
ABZ D 2. 23. d'] 84 D. 25. JHBZ] corr. ex JBHZ D 2
.
MA0HMATIKHS STNTAgEfiS T'.
xal AH, 17 p&v TOV Ttaod T^V
7tQiq)Ql,a fjAB
fj
231
0Tai V7tOX[,[lVr]
TOVTStiTLV av T XaTK TO
HTI
6 dtiTriQ, xal i'Gov d dite%G)v
(pavrj6Tai, aito T TOV xaTa TO dito- 5
TOV did [l6G)V TG)V
,OTav
r\xaTa TO Z, xal dab
TOV xaTa TO TtSQiysiov, OTavft
XaTO, TO H, Ttid^7tQ 'Y] {lV dltb
TOV dnoyMov yaivoyizvri 7tQi(pOia 10
3tQid%Tai vitb Tfjg V7CO 4ZA y&-
Trjg T oftaAij^ xivrJ6G)s xal TOV
jcaod TV\V dvo)[iaA,iav diayoQOV r\
dab TOV itQifyiov (paivo^vri 7t$i%Tai, vitb Tijs 15
ZHA y&vtas' l'6rj ydo i<5tiv xal avTrj Tfj T drtb
TOV TCSQiytCov 6ftaA?J xivr^6i, xal TK> jtaod T^V dva)-
yiakCav diaq)6oG)' l'6r]d i6xiv xal
j]VTtb
ytnvia TTJ vitb ZHA [Eucl. I7 5] did TO xal Tqv
r AH i6r\v ivai. co6T xal VTv&v Ttu'kiv 6vv- 20
dyBG&au, OTL TO* avTKt diacpooc)) TOVTB&TIV TTJ vjtb A4Hy&via, [iM&v piv fanv
fj nobs T& ditoyuG)
Tijs cpai,vo[ivr]S) TOVTBGTW ^ V7fo EAZ ycovia
v D, 2. TtSQicpEQfia i]}corr. ex
C 2D. 7] (alt.)] ins. D 2. 6. tf^tmW] corr. ex Grjusiov C 2
.
15. <^] d' D. 16. VTCO] om. C. SGTIV] comp. B, -v del. D 2.
17. TOJ] corr. ex to C 2. 19. TO] om. B. 21. TOVT&TTH;]
comp. B, -v del. D 2. AJH] AJB D. 23.
p. 232, 1. ovoris] supra scr. D 2.
AZzI] AZIZ23. rovTEGTLv] r D 2
. 24.
232 KAATAIOT HTOAEMAIOT
rijs avrr^q ovGyg, rovrfanvrj
vitb HA z/
rijs vjtb AHZ [Eucl. I; 32]' 07Co
ft'. lisp! rqs rov ^At'ov (pccivo[ivrjs
5 Tovrcov drj ovros itQoexrd'i[iVG)v
xccl rijv jteol rov ijfaov (paivo^svr]v avopaMav svsxev
rov [iiKV re swat uccl rbv aito rijjg Aa%i6rr]s M,vij0G)$
7tl xr\v [i6r]v %$6vov ^i^ovcc TCOISLV 7tKvroT rov aitb
rrjg [i6r]S && f^v p&ffavtp' xccl rovro yao10 ov vofaxonv rotg <pai,vo{jivois' dvva,6&ca [ilv xal
Sia ri}s xar7
3tixvxAov [iwroi,, orav Kara r^v aitoy
ccvrov HQi(pQiav ^ rov ^Atov [ird(lcc<3i,s lg ra
rtaoyyoviifvcc ytvyrai,, v^o-ycoroov (f av
15 cc(p&rlvca rr} xccr xxvraorr]ra V7to&6
over] xal vjtb [nag) ovyl d vnb dvo KLVijtifcoV) 6vv-
roivvv rov rbv koyov rfjs 3tol rbv
xxvra6rr]ros VQiv, rovrstfnv rCva.
20 Aoyov k'%i r\ iira%v rCbv uwrocov rov rs xxvroov
xccl rov Kara, rr^v oifriv xzvraov rov dia p^cw r&v
tfpdi&v xvuAov nobs vnv &K rov Ktvrgov rov Mxevraov,xccl hi, xara notov [Jidhidra r^r^La. rov dia [i8<5a)v r&v
xvxhov rb cc7to'yi,6rar6v itinv rov XKvraov
1. TTJS uvrfis ovorjs] etiam in textu D. tovxicxi D. 2.
D, corr. D 2. 4. *'] C, om. ABD. 5. ^^vno^nr^ov D.
9. cvfupcovov 6V] corr. ex cvfirpatvov D 2. 12. xara] f)
a. D, rj add. B 3. vr\v\ corr. ex TO B 3
. 13. 17] om. D.14. 8' KV fVj] corr. ex av D 2
. 19. tovtEGTiv] comp. B, -v
del. D 2. 20. T(] om. C. 21. TOV (alt.)] -o- corr. ex co in
scrib. D. 22. KVV.I.OV] -v e corr. D 2. TOV (pr.)] supra scr. D.
MA0HMATIKHS ZTNTASE&2 T'. 233
,dsdeiurcti pw ravrcc xccl rc5 'l7tTtdQ%(p
, rbv lv cutb
rv
9/3/.
/
,diCC [IOVG)V tOVTCOV tiibv Cp(Xl,VO[lVG)V CCTCQ- 5
ri]v {lev ^isrcc^v TK>V ttQoeiQrjiiev&v XSVTQCOV
sv&siccv ixo<3toT8TccQTov fyyiGTci ftf^og ovGccv ri\g ex
iov XSVTQOV rov sxKSvrQov, TO d' aitoysuov ccvrov
rrjg &Qivij$ rooitijg rp^atftv xd/.' $y-
oi&v 6rlv 6 dice [L6cov tcbv fcaditov KVKko$ r%. 10
xal rovg
tovg avrovs iyyittu uai vvv ovrccg VQfoxo[iv,
dia rovro xai, QTI Tqv avrriv ad ftztiiv b
rov v\Uov Kvukos GvvrriQti ytQog ra rgoitiKa xal far}- 15
vtQov t\\Liv yCvzG&ai. VXv d rov
3tccQccA,A.i[i[ivov ii>oa tov roiovrov roitoV)
rb &O)Qr]iicC) 3toirj6o[id'tt xal avrol rr^v rcbv
lizv&v del&v &s fal MXWTQOV xvxhov %Qrj6d[ivoi, 20
rots ccvrots (pcavo^voi^ rovr6riv, a$ scpa^sv^ ro3 rbv
lv dnb Kivf farfQiac; pfyQi &QLviis T^ojr^g %oovov'
jrbv d' djtb &Qivi\g rQOTt^g
Qiccs 9j3^. xccl yag diet rcbv
vq? rjii&v xara rb v%y' frog 25
1. (TTjftftcov C. i7t<x()%(p A. [ista] (Jifccc na.GT}<s D, na.Gj]g
add. B 3. 3. rov 5.
/_'] mg. D 2. 5. tinodeinvvet, B, ccno-
dsiv/if-i C. 11. SB] seq. ras. 2 litt. A. 16. yevso&ca D.
18. ^nersQcov A. icptodsvofisvov B; sfpoSev^ivaiv C, co corr.
in o; scpoSfviisvov D, corr. D 2. 23. ^SQKS] -i- eras. C. 24.
234 KAATAIOT HTOAEMAIOT
ditb ris 'Afa%dvdov T&VTig iGiSi&v rs xal
GV[l<pG)VOV TO T&V dl,a(3TCC0G)V Jthijd'Og T&V
VQi<5XQILV, 7tidlJ7tQ, Ci)$ (pCC[lV [p. 204, 10;
2057 2; 206,2], ^ plv iisToitoQiv^ faqpfQia yzyovsv rr\ #'
5 TOV 'A&i>Q [iTd Trjv J]Mov dvccTohrjv,
5' TOV Tlaytov psTa Tr\v peffrjiiflQfaV) cog
de
ia TOV GOQI {iTa TO
XCCi TCCVTrjV [lV Tr^V dlCC6TCC(Jl,V, TOVTEtiTlV TrjV KTtO
10 ccQi,vijs faypfQias 7tl TJJV
v (id/_\ tufc&fafat&f&Ki d9
is TJJV CCTCO Tijg &Qivijg7tl Trjv Qijg ^TOTtcoQivr^v far][iQiav Tag koi-
sig TOV viav6Lov %QOVOV ypfyag fyyuGTa gftL'
etiTG) drj 6 did [i6cw T&V t,(pdiG)v xvxhog 6 ABF415 nsgl xwTQOv TO E, xccl ditfx&coGccv Iv ai>T& dvo 8id-
ttgbg oo&dg d^iq^Kig did TMV TQOTtM&v uccl
r][ita)v ij TS AT xali\B^J
',vitOKSiG&o
de TO [iV A IdQLvbv <5r][itov TO df B frfQwoVj xccl
id ^ilg dxohov&cng.
20 OTl {lV OVV TO %VTQOV TOV XXVTQOVTG)V EA KCil EB
TOV TO ply ABFTOV ftfLtdovs TOV IviavtiCov XQOVOV Keel did
TOVTO [li&V dltolc(,^dvLV TOV XXVTQOV25 KVXliOV, TO dl AB TTCCQTrjUOQiOV XCCi KVTO
1. i6r}[iQL(bv] D 2, l6Jip,SQL&v D, iGrniSQivfjq ABC. 4. yi-
yovs ry D, -f T- renouat. D 2. 7. r$] rf) AD, rf]i B et C
(77
e corr.). 8. ia'] i- e corr. D 2. iiBGogi B. 11.
/_']corr.
ex s D 2. &EQwfjs] &- corr. ex a in scrib. C. 16. a/UUj-
lcu<S~] ycoviag tiiltfiais V.KI D. 18. or](iiov~] -ov e corr. D 2.
'
20. yitvrQov} v.- in ras. A. 21. EA] -A renouat. D 2. 23.
om. D. 24. zptfpti] nvukov rpfjiiu D. 25. 7ilelovci\rs D.
MA0HMATIKHS 2TNTAEE&S 235
xal
rov xxevroov XKoa TO BF rEraarypoQiov. rovrov ds
ovr&s %ovros vjtoxffa&G) TO Z Grjpetov xwrgov rov
XXVTQOV) XCCi $1-
[iv fjdi 5
rcbv
rov
f) EZH,KsvroG) ds r& Z 10
9-co 6
rov r\Uov xv-
xlos 6 KAM, 15
xal dta rov Z
AT $ N&O, rfj ds B4 % 77P27,
xai Ti riffi&Gccv xd&sroi, ccjtb pey rov & iitl xr\v
N80 Ji TT, fab $ rov K 7tl r^v IIPZfjK&X. 20
roCvvv 6 ijfao$ rov @KAM nvxhov dficck&s disg-
{18V &K 7tQKpQl,CCV diCC7fOOVrCCi V
dl KArcclg 9d'/.
oicov 6rlv 6 xvxhog r, iv d rats ^$Ll poioas 25
?r ccv rb ilv &KA
3. TO] corr. ex rrj D 2. 18. N&O] corr. ex N8 6 C 2
,
~O e corr. D 2. 20. NSO] corr. ex TVS? 6 C 2
. K] e corr.
D 2seq. ras. 1 litt. K$X] K- e corr. D 2
. 21. &KAM]-A- supra scr. A, &- e corr. D 2
. 22. K\ corr. ex K& D 2.
23. xr\v /_'] mg. A 1. 25. Iv] -v e corr. D 2
. /_'] renouat.D 2
. 26. Supra Tec scr. F D.
236 KAATAIOT HTOAEMAIOT
&vvayL(p6tEQd ds to re N xccl TO AO tcbv
psta to NTIO fywfafaw noia&v d jc, ^ ds di7tA.fi
[Eucl. Ill, 3] XSQUpSQSlCC 7% NT]
NT tC)V aVt&V
d x. &6t teal ^ {ilv vn' avt^v sv&siccfj
T toiovt&v
5 6tai d A/3 lyyiGta, otcov stitiv ^ tov sxxsvtoov did-
f]ds i^ii^sici ccvti]S i] T, tovttGtw 17
7g. ndhv snsl to 0NIIKokov iioiQ&v e&tiv yy #
?etitiv ds xal to N
fi ~i,to ds Nil tstccQtrjiioQiov [IOLQ&V 9, xal
10 ply stitai UK itSQiysQeia poiQ&v o v#, ^ ds
avtijs ^ KTIX xsQiysQsicc poiQ&v cc ~vy. &6te xccl 17
fti/ vjt avtr^v sv&sta ^ K<&X toiovt&v sGtai, ^ dy
OiCOV Ititlvr\
tOV SXXSVtQOV dlK[ltQOS 103C 9 ^ ^' l}ft^-
^ioj avtijs f} jRC0, tovtstitiv % Z&, t^^idtov aft.
15 t&v d* avt&v sdzfyd-rj xalfj E& sv&sta ft 7g. xal
sjtsl tK an' avt&v Gvvts&s'vtcc Jtoist to <XTtb ti]S EZ,
[Eucl. I? 47], fatal, xal avtri [irjxsi, toiovt&v ft K&L'
syyiGta, ot&v stitlv ^ sx tov xsvtaov tov sxxsvtoov %.
i]aoK ex tov xevtoov tov sxxsvtQov xvxAov tstQccxcusi-
20 xo6aitha6iG)v Ititlv syy^ta tri$ [ista^v t&v xsvtacov
avtov ts xal tov
1. cvnyorsQcc ^C^corr.C 2
. N~] @N D. AO] in
ras. A 4. 2. ftf-ra ro] BC et post ras. 2 litt. D, mut. in r&v
stg TO A 4. NIIO] seq. ras. 2 litt. D. x] A, x ncti WKTE-
QOV (isv ago, avrav f'crcci, poiQ&v $ T BCD. 3. 7tQi<pSQi,ci]corr. ex nsQicptQiu A 1
. 4. x] ins. C 2. T] TT D. _7.
Ante ^ ras. 1 litt. D.&NUK D. 8. olov] om. B. 9y]
-y in ras. A. tGxiv~\ comp. B, /j supra scr. D 2,om. D. tro]
TO ptv D. 9. z] corr. ex y A. jito^wv] om. D. 10.
&TCU] ^rtv C. JT.S:] XH D. o] 6 BD. i] --9- euan. D.11. 7CQicpQiu 12. #$JT) mg. D. 12. fi^v] om. D.
K$X] K&X TCfQKptQSLa (comp.) D. tf] jitf AC, ut sae-
pius. 13. *'] ds D. 14. Z#] SZ D."
17. Post ufaydel. tpfiiLu D 2
. 18. TOV (pr.)] supra scr. D 2. 20. KSVTQCOV]
comp. supra scr. D 2, HSVTQCOV i] B.
MA0HMATIKHS ZTNTASE3S r'. 237
itu, O'L&V f}EZ zdeiffiri /3 x&l_\ roiovrov
xal $ Z& vd"la a /3, xal olcov aga 6rlvfjEZ
neCvovGa px, roiovrov k'tirai xal
ftg k'yyuSra) r\d
3 fV avriis 7tQi(pQi,a rov
xvxhov itsgl rb EZS oa&oycbviov roiovrov 5
oi&v <5rlv 6 KVX&OS r%' xalfj
vitb ZE&CCQCC y&vtcc., oi&v H,BV sltiw ai dvo dg&al rj, roiovr&v
6raL/Lt-9
1
,o'i&v ds ai d doftal T|, roiovrcov xd A.
BH itQi(peQELa, tyv TtQoriytfrai rb Kara rb H ait6yi,ov 10
rov B &QLVOV rooTCixov 6r][Liov, poiQGbv i^nv xd A.
Aotjrov df, itidfj rb [iv O2 rsragrrHioQiov xal rb
21N xdroov [loioav i<5xiv 9,
[iv OA 7tQi(pOi,cc avrtf r xccl
[loio&v /3 I, r\d MS ILOIQ&V o v^1
,xccl ^ [iv 15
AM 7tQt(pOi,ci 6rai ILQIQGOV ytg ^vcc, 07$ M lioi-
o&v nrj {ifr. AAa rag [iv ytg 'vu poiQas 6[iaA,&s 6
^iSQ%srai, v fifisQCUrS nri xal17 ', rag $ ^ ^
iv Yi\Ligtti 9 xal 77' syyitira' &6r xal rr\v [ivT/l 3toi,(psai,aV) ijns 6rlv CCTCO [ifron&Qivijs farj- 20
2. T]v\ corr. ex rj C 2. 3. TOVOVTOOV D. Post BGtca add.
%l f ri>L' C, del. C 2. *uC] supra scr. C\_ Z8] ZZ D.
5. EZE] ZEE corr. ex ZS D. 6. rf] r- e corr. C.
ZES] ZE- in ras. D 2. 7.
6g&a A. 8. <?] post ras. 1
litt. D. 9. TO -Aivrgov D, corr. D 2. fab] -v del. D 2
,
comp. B. 10. 7iEQi(pf
Qici A. yv] corr. ex j\ C 2. 11. SGXIV}
-v del. D 2, comp. B. 13. SHKTSQOV] -o- mut. in co C 2
,sed
rursus corr. t<?ni/] icn D, comp. B. 14. rs\ in ras. D 2.
0N] corr. ex ON D 3. 15. o] ovSsv D. 16. [IOIQ&V (alt.)] ^
supra scr. A 1. 18. tftt'^STca] corr. ex SQ%STKI D 2
. 19.j\'~\
ob D, oydoaj D 3.
238 KAATAIOT HTOAEMAIOT
xal yf
, TYJV ds 4A, iJTig
TO, 7COO-
10
6 r^hog v
aitb
fjHSQCUS 9 Kttf\ ytfttt* *w SVQrjTKl,
xi[iva 6v[i(pG)va)S tots vitb TOVf
l7titda%ov
5 KKTCC ravras ovv rag
TQOV, itoaov 6rlv rb
itaga rr\v
xfai 6r][iioi,$
OVTOV 6V[l/5lJ6Tai,.
StiVCD dfj MCVTQOgABT rtQi ndvrQOv TO
dia rov A fatoystov
(p fy 6T& TO XV-
TQOV TOV fydiaxov TO Ej xal
15 agog OQ∾ y&vtag xr\ ATf) EB, xal
X TOV XVTQOV ,TOiOVTCOV 6rlv
xwTQ&v /3A xaTa TOP TTQaxaiixo6a7tA.a6tova
xal OICDV aga i6t\vr\B^d vrtOTtvov6a ^x^ TOLOVTWV
k'tiTcci, xalr\ pkv z/E v&la
, YJd' ji avTijs rtQi,(pQi,a
TOIOVT&V d jiZg syyiffta^ oi&v 6rlv 6 7tQl TO B/1E OQ&O-
ycbviov xvxhos T%. cc)6T xal % vno z/BE ycovia, iJTig
TO 7ikl<5TOv didyoQOV Tijs avco^iaUa^ ofay pivai dvo og&al T%, TOIOVTCOV 6Tau d
jilg,QIK>V d'
1. 7j'] 7j A, rj D. ^rig lettv\ -s Iff- et -tv in ras. A 1.
2. ano ^90-] cc- in ras., cetera in mg. A 1. rr\v\ om. D.
3. TJ'] r\' AC. 4. lyo[i8voi$] 7iL^^oyi6^VOisD, 5. KQO-
TQOV~] ngoTSQcov A, TtQmToov D. 6. Ivtt D, comp. B. 8. xLai\
seq. ras. 1 litt. A. rotovtrov] corr. ex roiovro D 2. 13.
6Tca] fart D. 14. xat] &nb rov E xat D, %ai ccnb rov ED 2.
_ 16. sni&vx&co BC, corr. B 2C 2. BJ~\ corr. ex BA C 2
. 18.
f] post ras. 1 litt. B. 19. BJ] corr. ex BA A. 20. d']ds D. 24. <T] 8e D.
T8)V
20
MA0HMATIKHZ S r'. 239
at d oo&al T|, roiovrov/3 xy. r&v & avrcbv
xal i\ yLV VTCQ BE4 oo&r} y&via 9, r\ds far]
dvtilv vjtb B4A drjAovon 9/3 l&y. xal Tt\ nobg rolg
xvrooig sfalv rj [isv vno B^dA rov xxsvroov^ f}ds
V7tb BE/I rov tydiaxov, %o[iv rb psv rtfalGrov did- 5
tpooov rov itaod ri]v dvcopaMav poiQcbv /3 scy, rcov ds
ttQi(pQiGbv, TCQOS alg rovro yivfrai,^ rqv ^ihv rov x-
xvrgov xal 6[iaA.r}v IJLOIQ&V 9/3 ~wy dnb rov dTtoyfiov,
rr^v ds rov tydiaxov xal dvco^ia^ov (paivoyitvriv rCbv
rov rttaorriiioatov, xa&ditso xal 7tQorQov dttdu^aiisv, 10
lioia&v 9. (pavsQbv d' sx r&v TtQOSfpcodfv^vcov^ onxard rb dvnxsC^svov r^iij^ia ij {ihv (pawo[ivr]
ndoodog xal rb Ttfaitirov didcpooov ri\
xard rdg 60 [totoag., f\d? b^a^ri xal xard rov
sxxsvroov xard rdg &, Af. 15
Lva ds xal did r&v
csg cpayiV) rdg avrdg it-
di,G)[iv tivvayoiisvag xal 7tl
xard rov snixvxhov
orav oi avrol Aoyoi, xafr' ov siotf- 20
Xa[lV TQOTtOV) 7CQl%G)Vrai) S0TG)
b [isv bpoxwraog re* did [ifa&v
rcbv t,G)di(Dv xvxAog b ABT Jtol
xsvrgov rb z/ xal did{iroov rr)v A^tP^ b d' iiti-
xvx^og b EZH rtol xvroov rb A^ xal ^froo ditb rov 25
1. icn D, comp. B. 3. 9|3] ^ ^9(3D. 8. p
corr. ex ILOLQO.V D. 11. cpavegbv d' fx] in ras. B 2.
[itvCOV C. OTi] OTIY.UL D. 12. T[Lfj[l<x] r)^ltlVV,^LOV D. 14. KCCtO.
n,oiQcts~] et in textu in ras. et renouat. D 2(ao /not'^ag) et supra
scr. D 3. <T] ds D.
^
19. wta TOV] KKT' D. 21. nQii%ovxai CD,corr. D. 22. 6 jLttV] om. D. Sid 23. gcodicov] wdtaxcoi D.
24.T1J1/] corr. ex TOV C 2. a*] 6s D. 25. EZH] E- corr. ex N
uel H A 4.
240 KAATAIOT IITOAEMAIOT
TOV 7tixvx&ov ev&Sicc 4ZB, xal iit-
AZ. yivBtai dq aticcvTag [p. 219, 21] sv
T<p AJZ TTQKXKiLXO<5aTika<5CG)v rjAd
rr}S AZ, wGre xai, otW ItixlvTIAz/ {worsivovea ^%,
5 TOLOVT&V itttkiv xal rijv psr AZ yCve6&ai ~s, r^v ds
7t avrijs 7tSQi(pQiotv roiovrcov djitg, oi&v fGrlv 6
Ttsgl TO AdZ QQ&oy&viov ygcccponsvos xvxhos ?>' xal
i\vitb AdZ CCQCC y&vitt) oi&v psr efaw at dvo OQ&al
T%, TOLOVTC3V tGXttl d jdg, Ol&V $ CCi d OQ&CCi T%, TOl-
10 ovrov /3 ~uy. TO [isv rtfalGrov CCQK SidyoQov Tijg avco-
TOVTEGTW f AB rtSicssia xal
15 Tils
7ti7tQ fab
OlQ&V 9, ^
EAZ ya)vcc,
titto AZdCCA.'tj, 7tQV itdkiv 9/3
VTtO
20
EvXv ds TOV xai Tag XKTK {iQog avco^id^ovg
xd<5TOT
ZCp' fXCCTSQOCg TG)V V lJtO&<3G)V,
CCV [U,ttg T&V X-
XCCi T&<
1. 7t&v%a) C. 13. snfasQ A, corr. A 1. AZ/J] corr.
ex AJZ D 2. 14. 8s (alt.)] om. B. 15. vno] D, om. ABC.
EAZ] D, corr. ex EZ A, Ez/Z BC, corr. C 2. 9^" xy] in
ras. B 2. 16. f' mg. C, om. ABD. TJLKTU e corr. B 2
. . . .,
. . .,
supra scr. D 2. rr/g ccvcofLaMas] T&V CCVCO^K^I&V nccvovoTtouag D,
corr. D 2(79.), r&v ccvoD^id^cov uavovoTtouas e corr. B 2
, y^. nsglT&V HUTU USQOS rfjs avmiLKlias B 2
. 17. STUGntyecog] ABC,T&V HUTUom. D. 19e corr. D 2
.
B 2. 17
-si- e corr. D 2. 20.
MA0HMATIKH2 STNTASEQS T'. 241
S6TG) drj 7CQC3TOV [ISV 6[lOXVTQOg T03
6 ABF TtSQl XSVTQOV TO z/, 6 d' sxxsvTQog o
EZH 1tQl XSVTQOV TO @, ^ &dl? <X[l(pOTSQG)V TG)V XSVTQOV XCCi
TOV E ccitoysiov dt,d{isTQog % 5
EA4H, xal aTtoArjcp&siGrjg Tfjg
EZ TtSQicpSQstag STCS^SV^CD^CCV ij
TtQ&TOV % EZ 7tQl,(pSQSia [IOIQOOV
ovtia Aoyov svsxsv A, xal sxfH.r]- 10
rjg Z xa&STog sit
TOV z/ ^ z/JiT.
TOIVVV f)EZ 3tQLCpQSl,CC VTtOXSiTCCt, {lOlQ&V A, XCCi
VTtb EZ CCQCC y&vitt) TOVTSGTIV y vjtb 4K^OiCDV [ISV 1<5W Oil d OQ&al T%, TOLOVTCOV 6T\V A, OiG)V 15
ds ai dvo oQ&al T%, TOIOVTCOV . xcclr\ ^LSV STtl Tr^g
CCQCC rtSQlCpEQSLCC TOiOVTOV 6T\Vjj,
OIG)V 6 7CQi TO
oQ&oy&viov xvxAog rj, ^ ds sitl Tijg K T&V
sig TO fuiixvxkiov [Eucl. Ill, 31] ^x. xccl ecu
VTt CCVTCCg CCQCC V&EtCCl, S00VTCCI,'Y] [ISV AK TOLOVTOV 20
f, oTov <5T\vi\
z/@ v7COTLvov6cc ^3c, ^ ds K T&v
CCVTG3V QV VS' 030TS XCCL ol'cOV S0Tlv Yi LiV ^
ft A, fjds Z X TOV XSVTQOV |, TOIOVT&V XCcl
fj
6Tcci K Ti, % ds K T&V CCVTOJV ft I, rj ds KZ2. ABT] ABT4 B. 6. EA4H~\ EA&J D. 7. EZ]
corr. ex ES D 2. sn^sv^coGav BC, corr. B 2 C 2
. y] at D.
8.rj]
om. D. 13. EZ] corr. ex EA D 2. 14. vno (pr.)
-7} (alt.)] mg. C 2
. EZ JK] mg. A^. r] (alt.)] ins. D 2,
supra scr./
D. 15. text D, comp. B. I] D, in ras.
A 4B 3 C 2. \1.^K\ in ras. A4
. 18. K] K B. 20. vn}V7t6 D. 21. ioxlv
j]\ corr. ex. IGTL D 2. 22. ^y vs] in ras. D.
23. I] in ras. A4. 24. K] K D. X0Z] corr. ex KZ D 2
-
Ptolemaeus, ed. Heiberg. 16
242 KAATAIOT IITOAEMAIOT
oA?? /31. xctl sjcsl ra ait avr&v 6vvr&vra
rb cbro rf}s Zz/ [Eucl. I7 47], <5rat, ncti
j]Zz/ vito-
xEivovtia rotovrcov/3
la fyyitira. nal otav CXQCC 6rlv
fjZz/ ptt, roiovr&v 6rcci xal % [lev AK sv&sicc
/3 x>5
r\d' en? avrilg ttSQicpsQeicc xoiovt&v
/3 t^, oi&v 6rlv
6 itsQi rb Z4K OQ&o'ycoviov xvxhos T%' coGrs Kalfj
4ZK ycovfa) OLCOV \iiv efaiv cci dvo ogfrctl T^6tlv
/3 wy, otcov ds ai d opftal r|, roiovrcov
a ft. rotiovrav aga stirlv rb TCCCQK rfjv
10 rors didyoQOv. r&v dy
ccvr&v i\v ^ ^#6 E&Z&' xal Aowr?) [Eucl. I
7 32] CCQCC r\vnb A^JB
r\AB rov ^cpdiccxov Tt
on de, nav aMrj rig r&v yovi&v do&i], xccl ai
15 Aoirtccl do&tjtiovrcci,, cpavegbv avro&sv s'^rai xa&srov
u%ftei6ri sitl rtfs avrils xawygaipfis ^o v & 7tl
rfjv Zz/ rrls &A. Mv re yap rqv AB rov
do{ivr]V) rovr6nv rr\v V
rovro <5rai xccl 6 ir\ z/
20 A Ao>og ddopvos [Eucl. Dat. 40]. ddo[isvov de
Kul rov rrls <<4 nobs Z tofhttferat xal 6 TTJS @ZA [Eucl. Dat. 8], dia rovro 81 flo^v dfdo-
rijv r vito ZA y&viav [Eucl. Dat. 43], rovr-
rb TtaoK rr^v avco^ia^Lccv diKfpOQOV, ncd rqv vjtb
2. 4'orat vno-] supra scr. D 2(vno- etiam in textu D).
3. i'yyiGTa] i'yyiOTK ol'cov i]dK r\v a Ts D. 4. ?; (pr.)] bis B.
QK r)ZJ D. 6. 6 TfEQi] corr. ex OTCSQ C 2
. Zz/^] 4ZK D.
8. TOIOVZCOV T|] supra scr. D 2. SGTL D 2
, comp. B. at]in ras. A 4
. 9. sari'v] -v del. D 2, comp. B. 11. ?]] post
ras. 1 litt. D. vnb AJB~] corr. ex AB D. 17. 0A] -A e
corr. A 4,
<9z/ B. idv\ &v D. 18. TOVTBGTI, D, conip. B.
19. 4A\ FJA B, B4A B 3. Ante 8ia del. dtdo^vog
psv D 2. 21. z/6>] yl@ e corr. A 4
. 22. fo'] corr. ex ^' D 2.
MA0HMATIKH2 SXNTAEE&Z r'. 243
jrovr6riv rrjv EZ rov xxvroov itQiq)aiav.
av rs rb Jtaga TYJV avo^ia^iav didyooov vito&coiis&a
dedopsvov, rovr6nv r^v VTtb
ycoviav, ttvajtakiv ra avra
dsdo^isvov [tv dice
rovro rov rijs &Z nobs A k6-
yov [Eucl. Dat. 40],
cd rov rr
xa rvrtjg z/@ 7tobg A Adyov [Eucl. 10
Dat. 8], dfdoe&ai, d dia rovro
xal r^v vxb 4A y&vi'av [Eucl.
Dat. 43], rovr6nv rrjv AB rov ,q)diaxov 7tQicpQiaV)xal rriv vnb EZ [Eucl. I
7 32], rovrtenv rrjv EZrOV XXVrQOV 7tOl(p0iaV. 15
3tdA.iv <5rG) b [iv b[i6xvraog rc5 dia n&covb ABT 7Col xvroov rb z/ xal did^roov rrjv
b dl xara rov avrbv 2,6yov faiXvxAos b EZH& ital
Xvroov rb A, xal cbroA^gp'frffctf^g r^g EZ 7Coicp0iasr ZB/1 xal ^ ZA' vnoxsiG&G) ds 20
fjEZ 7tQicpOia r&v avr&v [ioi,Q(bv A" xal
aito rov Z xdfarog iitl xr\v AE i] KZ.7tfl
fjEZ itQicpQia {lOiowv 6nv A, ft'iy
av xal
i\ iiev vnb EAZ ycovia^ oi&v \iiv i<3iv ai d da&al
dj, roiovrcov A, otW d ai ^ oo&al T|, roiovrcov 25
xalr\ {ilv 7tl rrjg ZK rtOig)Qia roiovrov 6rlv
1. TOVT&6TI D, comp. B. 6. Z] Z D. 8. 8s] 8" D.
Z] Z D. 11. 8s Sia] -s 8- e corr. A.^
12. rtjv] x^vrs D. 13. rovrsGTi D, 'comp. B. 14. TOVTSGTL D, comp. B.
16. SLU ps'euv'] faSicwai D. 18. EZH] corr. ex ZHD 2
. 21.TJ] supra scr. dX 22. AE] A D. KZ] ZK D.
23. EZ] ZE D. sett D, comp. B.
16*
244 KAATAIOT I1TOAEMAIOT
I, oicov 6 rtQi TO AZK oo&o'ycbviov xvxhos T, 17d'
7cl Trig ^K rc v hoirtcov is TO rnnxvxA,iov [Eucl.
Ill, 31] ~QK.Kcd
CCi_V7t CCVTCCS UQCC V&iCCi 60VTCCi<Y\
[lV ZK TOiOVTCOVI",
Of
lCOV
5 6TiV r\ AZ diK[lTQOS ^>%,^
j]$E KA T&v CCVTCOV ^vy
V' &6T XCCi, OiCOV <5T\Vfj
ILV AZ V7tOTiVOV(5CCft A,
07$ A4 X TOV X8VTQOV
10 5? TOIOVTCOV 6TCCi Kttlfj
jlV ZK V&EiCC CC ij ^ 6s
KA TCOV CCVTCOVft I, fj
d
TK ait avT&v 6vvT&evTa
15 7fOii TO CCTtO TY\ Z B Z/
[Eucl. I, 47], C)Tcci xal %
Zz/ {lljxi TOiOVTCOV |/3 la,
oicovTIZK i\v cc T. xccl oicov CCQOC 6Tiv ^ z/Z vno-
TiVOV0CC ^JC, TOiOVTCOV fCjTCCi KCCi7] [lV ZK V&iCt
ft
20 5^5 ^ $* 71 CCVTrlS 7tQifpQiK TOiOVTCOVft 1^, o'iCOV
6 7tOi TO 4ZK OQ&OyCOViOV XVX&OS T* CO(5T KCtl i\
vjtb Z^/K ycovicC) oicov ftfV ffaiv at dvo ooftccl T|,
TOiOVTCOV 6TiVft 1/tj,
OiCOV d' CCi d OQd'Ccl T, TOiOVTCOV
CC &. T060VTCOV CCQCC C)TiV ItttliV TO TtCCQCC TT}V KVCO-
25 {icchiccv dittcpogov T^S -AH 7tpicpOiccs> tcov d' CCVTCOV
1. d'] A, j$eBCD.
S._Ji] D, in ras. B 3,S A, corr. ex
^ C 2. 13. |p^ 1] corr. ex f seq. ras. 1 litt. D 2
. 14. <rw-
Ti&svxct D, corr. D a. 15. TO] TOV BC, corr. C 2
. ZBz/]z7Z D. 17. Z//] ^Z D. 18. -^v 5] corr. ex rj va C 2D 2
,
a in ras. A 4. ^Z] Zz/ D. 21. 6] ot
rC. ^] ins. D 2
.
23. e'crt D, comp. B. d'] ds D. 24. ZOCOVTOV D. fart D,
comp. B.
MA0HMATIKHS STNTASE&S r'.
i]v xal % vxb EAZ ycsma A*
fjvitb AZ^d y&viK, TOVTSGTLV
KOV ltQl,(p0l,CC) ILOIQ
litl Tils xxVTQOTrjTOS
ds Kal Hv&dde, xav
6ovrcci, xal cci homed
245
[Eucl. I, 32] 'dga
TOV tcodia-
do&rj
TovT6Tiv
$$0- 5
7tl TijS
ditb TOV A 7tl Trjv z/Z Tijs A A.
av T yao xdfav rrpt
TOV ^CodiCCXOV ',
vitb AZA y&vi'av, 10
dl& TOVTO &TCCi XCtl
b Tijs Zj4 nobs AA Aoyo? [Eucl.
Dat. 40], ddo[ivov d a'| aQ%ils
xal TOV Tils Z4 xgbs Ad do-
d"i]6Ttti xal b Tijs dA nobs AA 15
[Eucl. Dat. 8]. dice d TOVTO xal
[Eucl. Dat. 43], TQVTZGTIVi]AB ?toi,cpQi,a TOV
Ttccod xv\v dvco^ia^LKv dicccpooov, xalj]
vitb EAZ[Eucl. I, 32], TOVTS6TIV
?5EZ TOV 1UXVKA.OV 3tQL- 20
<pzoicc. dv T TO itctQa T^V ttvcopccMav dt,d(poQOV VTto-
+a Ssdopmov, TOVTBGTW T^V vitb A/IB ycoviav,
sv did TOVTO xal b Tijs
AA nobs AA A6yos [Eucl. Dat. 40], dfdopwov d '|
TOV Tils x//A Ttobs AZ dod"*J6Tcci, xal b Tijs 25
1. AOITTTJ] ncti \Qntj] D. 2. Tovr^cnv rf\ rovrscti D. 4.
] post -o- ras. 1 litt. A. aTtodsSfiyfievKtg] -cci-
in ras. D. jrTjAtxoTTytoff D, sed corr. 8. sav] &v D. 10.
TOVTEGTL D, comp. B. 12. TCQog] corr. ex 7tQ6 A. 13. ^e]8' D. 14. Azf\ corr. ex AA B 3 C 2
,AA D. 17. AJB] corr. ex
AJ A 1. 22. ro-uTf'ffTtBD. 23. -g do-] e corr. D. 24. A/f\ in
ras. C 2,dA D. TZQOS 25. d A] supra scr. D 2
. 25. TT^O? AZ]supra Z scr. A post ras. D 2
,eadem uerba supra scr. D 2
,sed del.
246 KAATAIOT nTOAEMAIOT
ZA XQOS AA [Eucl. Dat. 8], dia de TOVTO xalij
TS
VTtb AZd y&via dedo^vrj 6x0,1 [Eucl. Dat. 43], TOVT-
l (pcavo^svr] TOV ^cpdiaxov 7tOig)Qici^ ualfj
EAZ [Eucl. 1, 32], rovrtenv % EZ rov iiti-
5 XVX&OV 7tQt<pQlCC.
JtdhlV 7tl
XXVTQOV
LA.1j<p&(O COIQ TOV H 3lQt,fytOV
TOV XXVTQOV i\ H Z 7CQlCp-
10 QSltt V7tOXl,[lVr] T&V KVTG)V ftOt-
Q&V A, xal jtv%&(a6av ijT
xaiI] Z@, xcd
G* anb TOV z/ Inl TVJV
15 7Cir\ZH 3tQl<pQl,a [lOLQCOV 0TLV A, iY]
KV Kttl
% vitb Z&H y&via, oi&v piv i6w ai d oa&al r|,
TOLOVTCOV A, OiG)v $ ccC dvo OQ&al rj, TOLOVTCDV (j.
K)6T Kttlf} yiV 7tl TT^ Z/K V%"lO,g 7COi(pOLCC TOi-
OVTCDV <5Tlv 1, Oi&V 6 7tOi TO 4K OQ&OyWVlOV
20 xvxhos rf, rjd' 7tl Tils K T&V AoiTt&v [Eucl. Ill, 31]
ig TO fjnixvxfaov TprjiiaTCdv ~QX' xal ai vnoTivov6ai
aoa avTag v^Lca ZGOVTCU % plv /IK TQIOVT&V,
o"lG)V 6TIVfj4 dlK^LTQO? ^3f, J]
dl K T&V KVT&V
^y vl. xal oi&v aocc i<Sxlv fj {ilv z/@ vTiOTeCvovGa
25 ^ A, 17Se 0Z K TOV %VTQOV |",
TOLOVTCOV <3T\V Xttl
1. rs] om. D. 2. AZJ] AZ BC, corr. C 2. 9. HZ]
H- in ras. D. 12. Z6>] 0Z D. 13. @Z] "Z' B. 14.
T)] A, in ras. D 2, TJ dt BC, corr. C 2
,^ eras. B. 15. sari D,
cpmp. B. 16. Z0H] H C, H C 2. 17. ^vo] |3
corr. ex
t(3D. 21. T^rj^drcov] om. D. i>7roTtiVo'u<Tart] corr. ex ano-
C, corr. ex vnoTtivovca D 2. 23. iorlv ii\ corr. ex
t D 2. 25. SGTL'V] comp. B, tcrca D.
MA0HMATIKHS STNTA3E&S T'. 247
4K v&ta a I?, f)ds &K o^otog ft I, % ds
KZ Tcbv hoiitav v v. xal sitel TO, an? avT&v GVVTE-
ftevra xoist TO aito rifc z/Z [Eucl. I, 47], stirai xal
ccvTrj ptfxEi, TOLOVTCQV v va syyitira, oi&vf\4K fa
a 7s. xal clew aoa stirlv % z/Z vnoTSivovGa ^, rot- 5
ovrcw xalri per /IK s'titat, /3
Ad AST, f)d' id avrijs
TOIOVTCOV ft xj, OltOV 6 7tEQ\, TO Z/ZJf
xvxAog T%' &0TS xalfj bub 4ZK y&via,
OLCDV [lev BiGiv ai dvo OQ&al rj, toiovrcov <5tlv/3 x^
oi'ayv d* cci d OQ&al r|, TOIOVT&V a id eyyiGra. TO&OV- 10
rcov aga sari TO naga Tqv av&iiaUav didyogov. xal
7tsl T&v avT&v VTtoxsiTai xal$1
vitb Z0H ycovta A,
ztirai xal17
vnb jBz/F o/b?, TOVTS'GTW % FB TOV co-
diaxov TtSQKpsQEia, yioiQ&v ha id.
xaTa Ta avTa ds xal Iv&dde fafityb&fckis T^g B4 15
xal xa&stov Bit avTqv ax&sfarjc; Ti\g A, edv TS rv\v
JTJB TOV ^G)dt,axov xsQifpeQSLav d&^tsv^ TOVTSGTIV T^VV7tb dA ycovtaV) do&tfGSTai, [ilv dia TOVTO xal 6
A Myos [Eucl. Dat. 40],
1. &K~\ corr. ex OK D 2. ojtiotcog] -o- e corr. in scrib. C.
r] corr. ex Hi C 2. 4. Supra v va scr. v^ v pd D 2
. ^v a]
corr. ex17 va C 2D 2
. 5. xat] H^' BC, corr. C 2. 6. 1^]
fa, f in ras., D 2,
^ supra add. D 2. As] Ad in ras. D 2
,s
supra scr. D; cfr. p. 249, 20. d'] 8e D.a'uxr^s]_C
2D, afajv
ABC. 7. ^ZX] corr. ex JZ A 1. 9. dvo] A, J3_BD,
dy C.,
fifrtV] comp. B, BGxai D. 10. d'] d D. a td] corr. exA D 2
. roGovrmv} corr. ex rotfoftrov D 2. 11. iGti\ AD 2
,ct
comp. B, fWiV CD. 12. Z&H] corr. ex ZH C 2.
]
C.D, XQIKKOVTU D 2. 13. %GTUI\ corr. ex <mi>
mut. in BJH C 2. 14. g^g ^ orayfaoi| fol. 70 r
D,fig. seq. fol. 70V
. 15. TO. avra.'] corr. ex ra-ura D 2. BJ]
BA C. 16. rf] corr. ex yg D 2. 17. rwciGxiv\ comp. B,
-v del. D 2. 18. @JA] corr. ex J @A D 2
. ycoi/mv] corr.
ex yavlu C 2.
248 KAATAIOT IITOAEMAIOT
dsdopEvag rtfv re vTtb
Dat. 43], TovT6Ti,v TO ycccoa rrjv
de % uQ%ijs xcd TOV tr\$ 4 nobs Z do&rjfcTai, xal
6 T-r}sZ nobs A [Eucl. Dat. 8]. dia TOVTO 6"
[EucL
didcpoaov, xal rfjv VTtb
[Eucl. I7 32], rovrtenv
HZ rov SXXSVTQOV TCSQL-
T TO TtKQK T^V KVG3-
v dicupoQov dcbjisv, TOVT-
10 BtiTiv
Tttt'klV
KOI 6 T^s Z rtgbs A[Eucl. Dat. 40], dedo(i&ov tf %
agyfls xal TOV Tils Z XQOS 4 dofhjtierai, xal 6
15 d Ttgbs A [Eucl. Dat. 8], dice d TOVTO
TVJV T vitb 4A y&vfav [Eucl. Dat. 43], TOVT-
TriV -T-B 7tQl(pQiaV TOV Z&dlCCXOV, Kttl XV\V
V7tb ZH [Eucl. I7 32] 9
TOVT&TLV T^V HZ TOV x-
KBVTQQV 7tQt<pQlCCV.
20 Oi)6(XVTG)S fal tyS XQOXl,[JiVr]S tOV b[lOXVTQOV Xttl
TOV 7tixvxkov xaTccoacis &oHi<frfaig ajtb TOV
av-TOVTO
T AH xal
anb TOV H inl rr\v Ad r^fto r\HK. Insl ovv
25 ita.'kivi\
H 7tQiq)aia IIOIQ&V IGTIV A, efy av xal
1. Ss] S' D. J] J D. 2. Z] corr. ex ZE D. 3.~
Z BC, corr. C 2. 4. xovrtcn D, comp. B. 6. rovr-
6Ti D, comp. B. 9. TovrtoTt, D, comp. B. 16. dA~\ corr.
ex J&A C 2. TOVTOTL D, comp. B. 18. TOVTSGTI.D, comp. B.
23. Supra JHB scr. Z D. xa-O-frog] ante -g ras. 1 litt. D.
Se\ 3' D. 25. H] H B. icxiv] s- e corr. C, comp. B,lent D.
MA0HMATIKHS STNTA3E&2 T'. 249
&AH ycdvCtt) QiG3v \iiv i<5iv at d OQ&al T^TOLOVTC3V A, olcov ft at dvo dg&al ri; 9 TOLOVTCOV jj*
6Tlv,Ol&V 6
7tl Ti}g HK <
JtQl(pSQlK TOiOVTCOV
sgl TO HKA OQ&o'y&viov xvxhos T|,
3]d 7tl Tfjg AK TG)V koiTt&V 5
[Eucl. III? 31] ig TO fiiiixvxfaov
QX. xal T&V vit avTag aga v-
&EI&VYI [lV HK <5TaL TOIOVTGJV
|, OIG)V 6TWTIAH V7tOTLVOV6a
03c, fjd AK TCOV avT&v 97 v. 10
xal oi&v aga 6Tlv y pv AHv&ia
/3 A, TId Ad x TOV
XVTQOV 5 5TOiOVT&V Xal
Y} [lVHK h'GTai a T, 07 ds AK b^oC(Qg
ft I, TId KA T&V koiTt&v v v. xal frtd Ta 15
(for' avTcov 6vvT&VTa TCQIBI TO anb Ti]$ 4H [Eucl.
I? 47], (irjxi, aga <5Tcu xal avTrj TOLOVTCOV v va
fyyiGTa, otcovrjKH v&ia i\v a i. xal oiov
aoa itiTlv r\4H vnoTsCvovtia ox, TOLOVTCOV sGTai, xal
TOIOVTC3V /3 tt, otcov 6 7tol TO 4HK xvxhog T%'
xalTI
vitb H4K y&via, oicov(i
r
v ffaiv aC dvo
t rS, ToiovT&v i<5rlv 3 xt* oiwv d' at d
2. 5.Ss D. ^o] B. 4. HKA] AHK_D.9. AH] JH BC, _corr.
C 2. 12. ^17] far} A.
in ras. D 2. 13. |] post lac. 4 litt. B, post lac. 11
litt. C. 15. r] I AC. i] 8s KA\ renouat. D 2. 16. GW-
tifti-vra. D, corr. D 2. 17. ctvrj] R _ 18. f-v&eta] om. D.
riv a] corr. ex 77 va C 2. 20.
J3^ Ag] (SW? D. 9s] d' D.
21. JHK] 4HK oQ&oywviov D (co corr. ex o D 2
).23.W D, comp. B. d'] ds D.
AB itoi(pQia.
250 KAATAIOT HTOAEMAIOT
r|, roiovr&v cc id eyyiGra. ro&ovr&v KQK e<5rlv rb
didcpooov KKI wrccvd'cC) rovr6nv
xcii jti r&v avrcbv vitoxeircurj
VTtb KAH y&via A, <5ra,i uali\ vnb BHA oAr}
5 [Eucl. I, 32], tjtrtg itQis%i rrjv (pcuvoyidvYiv rov tydicc-
xov rtQig)Qiciv j iLOiQ&v Aa id 6v[ji(pG()VG)g ratg 7tl
xara ravra df xal v&dd
rrjv z/J5 r^g AA^ idv re rrjv rov
AHA y&viccv, dofi"ij6rai
dia rovro 6 ri\g HAAA ttyos [Eucl. Dat. 40],
dedo^ievov d'J
| aoxrlg xal rov
15 rqg HA nobs A4 dod"iJ6erai
Keel 6 rqg z/A Ttobg AA [Eucl.
Dat. 8]. dice d rovro dedo-
Hvag %0[iv rtfv r vitb A4Byaviav [Eucl. Dat. 43], rovr-
20 6nv rrjv AB TieQicpeQeiav rov
rtaoa rr\v av&inaMciv diacpooov,
xal rrjv VTCQ @AH [Eucl. I, 32], rovretinv rrjv H rov
eitiKVK^OV 7tQi(pQiKV. KV re TtttkiV %Y\V AB 7tOl><p-
Qiccv d&nev rov itaoa ryv avo^ialiav dicupogov, rovre^nv
1. a ia-cLv] supra scr. D 2. sort D 2
, comp. B. Deindedel. e'GTLV &QU D 2
. 3. r) (alt.)] ins. D 2. 4. KAH] HAK D.
5.IJTLS~\ ij- corr. ex v D 2
. 7. f'xxfVrpo-u] ifx- supra scr. D 2.
8. TKvrdi TCCVTCC A, TctvTct mut. in xa. UVTCC B 2 C 2D 2. 10.
TOVT^GTIV] comp. B, -v del. D 2. 14. V.CCL 15. A4~\ supra
scr. D 2. 15. HA] H- corr. ex N in scr. D 2
. 16. A A]renouat. D 2
. 19. TOWEGTLV] comp. B, rovricri D. 20. TIJV]in ras. 1 litt.D 2
. 22. &AH] HA0 D. TOVTSOTI, D, comp. B.24. XOVXGT;L D, comp. B.
MA0HMATIKHS 2TNTASE&S I1'. 251
TY\V VTtb AdB ycoviav, avcc7tcc2.iv coGavr&g doftijtisrai, [iv
dice rovro 6 T% AA ngbg AA Myog [Eucl. Dat. 40],
S M& v rn ^^ ngbg AH do-
xal 6 rr\s HA ngbg AA [Eucl. Dat. 8]. did
de rovro dsdopsvas e^opsv rtfv ts vnb AHA y&viav 5
[Eucl. Dat. 43], rovrdenv r^v rov %G)diaxov 7tQi,<ps-
QsiccV) xal TYJV VTtb &AH [Eucl. I7 32], rovTsGtiv xr\v
H rov ejtMvxhov itQi(pQia,v. xal dddsMrm ^ivra TtQorE&dvtK.
dia rovrcov rcbv &0)Qrj[idtG)v dvva- 10
xavovoTtoiiccg t&v 7tQis%6vcG)v
rag sx rijg dva)[iaMas tcbv cpatvo^isvoov
dictxQiGsic; Ttgbg rb f'J broC^ov ku\i$ix.vsiv rag
rcov Kara {isgos diOQ&ooGs&v TtqhixoTrjtccs ccQsGKet, [ictMov
<YHLIV YI ralg 6ftaArg jtSQicpegsicug TtaQaxsL^isvag e%ov6a 15
rag TCKQCC rrjv avaiiaMav diacpOQag did re rb xar'
avrdg rag VTiofrBGeig Kx6kov$ov xal dia rb artAovv re
xal V7ti(loAov rijg xa&' sxatira iltrjycxpoQiag. h'v&sv
rolg rtQ&roig xal iiti rcbv dgi^^icbv
r&v faagrjiidrav xal iitl r&v xard 20
r[ir][iidrG)v itho >
yi,<)dn&a dice roov
ojtiavrcog rotg a7tod$i'y^voig rag xd<5rr] r&v
xafrohov d ra kv Jtbg^aTto'EiOig rfrarroia xal
1. A4$] afid D, ctdp D 2. 2. A A] corr. ex AA D 2
. 3.
om. C, ds C 2. 5. s^co^sv C. 6. TOVTSGTLV] AC, comp. B,
C 2 D. 7. rovTEcnv] ACD, coinp. B, -v del. D 2. 10.
$rj] ^TJ TT^S D. 8vvu^ivTf]<i\ corr. ex dwdpscas D. 12. tag]rd C. 13. ^K^dvfcQ'ca D. 14. diajQ&djGEcov A. KQSGKSL]seq. ras. 1 litt. D. 16. KMT' avrdg\ corr. ex Y.KTO. ravrctg D 2
.
18. fvsTtifiolov] mut. in vm]fiol.ov D 2. t/>T7<piqpO(Hag C,
corr. C 2. 21. Eiti-loyrjGdiit&ct C. 23. STf^KUovoccs] pr. I
del. D.
252 KAATAIOT HTOAEMAIOT
7tl rov r]kiQv xal TCL r&v aM&v diei^o^v fig
, fog yiv6&cci, ri]v TtKQa&eGiv sri ccvr&v
^, ra dl agog rolg rtQt,ytotg ig T[nj[iara A,
cog xal rtl rovrov yiv6&ai, rr\v 7CaQd&6iv dia {LOIQCOV
5 y, 7tiSri7tQ psi^ove'g i6iv aC itQog rolg ttQiysioig
toig i'Goig T[irj[ia6t,v diafpOQOV t&v
rolg ctTtoyEioig yivopwcov.
TK^OIIW ovv Kul TO Trjg Tov fjMov10 xavoviov 7tl 6Ti%ovg [ilv nukiv
jil^,6eM8ia ds y,
ra ftfv XQ&ra dvo 7tQid%i rovg KQi&iiovg T&V
ra xgbg TG> anoysiG) fi rerKQrri^oQia^ r&v
fav A ra ngbg rc5 TteQiyeiG), rb ds y' rag xcc6tq>
15 r&v 64aAwv aQifr[i&v 7ti,paA.A,ov6ag (uol^og ti}g
acpaLQ6K)g rov TCCCQCC rqv uv&ii(x,kiav dicupooov.
<5ri, rb xavoviov roiovro'
6. eTtLficdovTcov D, corr. D 2. 7. TftT^tatft D. 9. rov
v] rjUccKijs D. 10. ceMdici] ju^rj D. <oi>] cog D. 11.
D. 12. If] dsnansvTS D, ut saepe. GTL%GOV] -co-
e corr. D. 13. ra\ -d in ras. D 2. 14. 1] a BC, corr. C 2
.
TO d] AD, ji BC. y'] y ABC, rgirov D.ra,<s] corr. ex
TO. D. 15. ^TtlficdovGCCS D. 7tQ06(X(pttlQGCQg D.
MA0HMATIKHS 253
1. 5-'] B, om. ACD.?/Uax??] om. D.
^ D. 2. ,orat] AC,om. BD. a'
/?' y'] om.
D;habet in lin. 4. 6.
</?] -/#e corr. D 3
. 11. tec,
tov artoysiov dvo tftaQtrj-
mg. A 4, artoysiovet mg. et
inter coll. 12 B s. 12.
^uy] corr. ex Ay B2 C2.
14. r] seq. ras. A. 15.
aqrf] -9<? in ras. A. 16.
OTtrj] corr. ex ff^i? C, -7t;
in ras. A. 17. Gilp\ -itfi
in ras. A. 23. ovtj]
Ortrj D. 31. a] ftD.
32. a^a] a- e corr. A.
34. tbt. tov ftsQiyeiovia mg. A4
,
et mg. et inter coll. 1 2
B 3. /s] D, -c in ras. B 3
,
/# A C, corr. A1. axe]
-e e corr. A. 41. o] e
corr. D. 42. o] corr.
ex a D. ry] e corr. D.
43. o]5 o C, corr. ex
a D. /ug~\ e corr. D.
44. o] corr. ex a D.
A#] e corr. D. 45. o]
corr. ex a D./I/?]
e
corr. D. 46. o] corr.
ex a D. 48.;]
e corr. D.
49. (iTt"] corr. ex /) C.
xivijastuv
9
9?
.
D*
tflTJ
ait*]
aogoo
avs
ovfi
o/ug
a/uy
old
axrjay.s
ax
otyOl
o to
o x>/o mp
y.a
y.y
xy
y.a
y.
? *a rj;
a wa /<^a [.id
28
10
15
25
:JO
-10
KAATAIOT IITOAEMAIOT
xccrd rqv ^6rjv rov fjA icdgodov
254
g'. Jleol
AoiTtov d' ovrog rov rfjv iitoyftv rtfs o^a^g rov
fjMov xwiJ6G)s 6v<5riJ6cc<5&ccL Ttobg rag r&v xard
5 excctfrore TtctQodcov fastfxetyeis STtonqGcciis&a xccl
roiccvrrjv lK&6iv dxoAov&ovvrss psv xa&oAov
ini re rov ^Cov nctl r&v aMcav ratg vcp'
avr&v axQL{$e6rccrcc rsrrjorjiisvais TtccQodons^
ovres ds oat ccvr&v rag rcbv STtoftav GvGrcttiEig ig
10 rr^v KO^V ri}s Na(lovcc66dQOv Patiifoias dice r&v ctito-
xivij<5G)V) acp' ov XQOVOV xal rag
rov
*x r v f / ~ jE7
(7TO) 0^ O JI1/ O{lOXVrQOS TG)
15 di: [i6cdv XVK^OS 6 ART iteQi
xevraov rb zJ, 6 d1
xxvroos rov
y]kiov xvxA.og b EZH 7Col xvroov
TQCOV xal rov E dnoyeiov
20 rgos % EAHT, vitoKeiG&G) Serb -B'
B 6Tr]u,EiOv rov Z&diKxov rb iiero-
ItCQQLVOV, Xdl 7t%VX&(n6'CCV [lV
rjre BZ^J xal ^ Z, xd&rog de dno rov litl
rr\v Zz/ txf&rj&sfaocv YIX&G* ^ K.
25 Insl rb ulv B
om. D.1. T] B, mg. A 4, %, mg. C 3
,om. D. 2. ST
3. 6'rog D. rov (pr.)] om. D. rrjg 4.
rov ii'kLov ri]$ diKxkfjs GvGTrjGac&ai, v.Lvr\6Kcog D. 5. 7toi7}6o-
ps&K D. 9. Ss an'] 8' V C, 8' D supra scr. &n '. 14 TWSiu [jiGcov~] r&v (pSiay.G>v D. 23. ndO'eros] -g add. D 2
. d\8' D. 24. &K] corr. ex K D 2
seq. ras. 2 litt.
MA0HMATIKH2 STNTASE&S r'. 255
rCbv XiqkCbv ap^V, TO ds F itSQiysiov rag rov To^orov
lioiQctg e/_', 17
BF CCOK TtsyKpfysia [IOLQ&V itinv |f
L xalfj
VTtb BJF CCQCC ycovia, rovrfanvfj
vnb
4K, otcov {iv i<5t,v ecu d ood'cal T|, roiovr&v f A,
OLCOV ds aC/S OQ&al r|, roiovt&v ghcc. &6te xcd
jj5
lilv iitl rils K sv&stas TtSQUptysia rowvr&v fGrlv
pAa, oi&v 6 7t()l rb /J&K OQ&oycoviov xvxA.o$ r|, ^
d V7totivov6a avrriv sv&elar\&K roiovr&v Q& t/3,
OICQV 0TLVi]
/4 dlCClltQOS Q%. oldOV CCQCC 6xlvfj
filv z/@ v&ia, rj
$ Z v7toTivov6a ^3c, roiovrov 10
Kol17 pv &K 0rcci d Ay, ^ df fV aurijjg
rotovr&v d x, otW fV-rtv 6 ^^>l TO ZKT|. o5<?r xa^
17vjco ZJf yowia, olcnv
at dvo 6()0-al T|, rotovrcov fVrtv d x, otrai/ df
at d opO'at tr, rotovrov/3
i. irwv ff ctvrCbv f]v v\ 15
VJTO EAT y&via % A* Ht Aot^i) [Eucl. I, 32] CCQCC r\
VTIO Z@H) rOVXBGtiV rjZH rOV XXVrQOV 7tQl<pQl,(X,
itixiv %y x. orccv agcc jtl rijg yLsroTMOQivris
y 6 r/Aios, rov pey itzQiysiov, rovrfanv r&v
rov To%6rov poiQ&v /_', jr^o^y'ircu ^6cog xivovpwog 20
X) rov $ aTtoyeiov ,rovrttinv rcbv xccra
2. /.'] Z D. 3. I] in ras. A. Ez/T] corr. ex BTz/ C 3.
4. |e] s'dTtv |e D. 5. ^] f(7rlv ^a D. 8. ds] S' D.
?j] om. D. K] @- e corr. C. 9. ol'cov] v.ai otcov corr.
ex %ai wv D. J&] corr. ex z/E D 3. 10. f] in ras. 2
litt. D 2. 11. @K] @- corr. in scrib. C, deinde del. etifofa D.
84] d' D. 12. 8] post ras. 1 litt. D. @ZK] Z&K D.
13. TJ]ins. D 2
. @ZX] <9_Z^D. 14. 5vo] g JB. IGTI'V]
comp. B, -v del. D 2. 16. e] -f e corr. D 2
. A] seq. ras. 1
litt. D. 17. Z&H] Z- corr. ex ? C. 18. |y] -y e corr. D 2.
^19. zovreevw] comp. B, -v del. D 2. 20. /.']
^A D. 21. d<]d' D. TOVTSGTL D, comp. B.
256 KAATAIOT HTOAEMAIOT
rovg 4idv[iovs {IOLQ&V s I, aitfysi
[lVK {lOLOag (H ft.
romov dr} &coarj&vros<) sitsidrj r&v ev rats
rcus flpiv rrr]Qr]HVG)v i^iq^Qi&v pCa TKtv a
5 A,rjcp&i6(bv yfyovev l(5ruLQia [isroTtcootvr} rep 1% srsi
[isra dvo syyiGrcc
a CQQCCS rijg ^is6r]aft^ias^ d^Aov, on tear'
exstvov rbv %QOVOV 6 ijhios [isGws xivovpsvos aitstysv
rov ccitoyeCov Kara rbv swcsvrQov xvxhov slg t& sno-
10 {leva jioiQag pt? ji.AA
7
ajto [ilv rifc NafiovaGGagovrr Gvva-
ysrai xar Afyvrtrfovs vied, aitb de rrjg'
rffavrris p%Qt> rfjs AvyovGrov j$a6iteia$ rr) (J9d, aitb
d rov a hovg Avyovarov nar Alyvnriovs rijs iv
15 Tc5 co& a [i6r]n@OLas >^ytsid 1
^ rag
ILSO'vuifiQiag 6vvi<5rd[Le&a, p%Qi> tov 1% srovg'
vov 'A&vQ'
yisra dvo falftiQtv&$ COOKS
?l yivsrui o%a xal f][ioai, |sr xal cooai,
/3* nal ano rov a f'rovg ctoa NafiovaG-
20 GCCQOV Kar AlyvTiriovs rijg iv rf] rov G)& a
rr}s xxi[ivr]
xal
Jg nal COQCCI, i<5r][iQi,val /3.AA' iv rco roGovrco
6
3. ngajTcus] -TCCIS add. D 2. 4. rjfiLv] seq. ras. 2 litt. D.
fcriiiSQi&v] -i- in ras. 2 litt. D. 6. *A9"oq\ 'A- supra scr. A 1.
8. "n,8Lvov(jiEvos C. an8i%f: D. 10. aAA'] ccihd D. 12. /tar'
AtyvTt-tiovs] om. D. 13. Avyovcrov] -y- corr. ex T A. a9$]ff- eras, in extr. lin., add. init. sequentis A 1
. 14. a'] TT^W-TOV D, ut saepius. 15. a'] vovfjuiviccs D, T?)g add. D 3
; rov^r]-
mg. B 3. 16. t^'] corr. ex f C. 18. yCvovrcci D. 20.
y B. a'] VOV^TIVLK D.TM
MA0HMATIKHS 2TNTAEE&2 T'. 257
6ia x syyiGra. kav ovv rats tijs xara
[iro7tG)Qivr)v i(Sr^LQiav aito%rjs anb rov
aitoysiov rov SXXSVTQOV poiQaig jng ft 7tQO6&cbp,8v
vbg xvxhov potoas r\ xal anb rCbv yt,vo[isvG)v cupe-
rag 6ia xe ftot^ag rijs nark rbv [iera%i> %QQVOV 5
rc5 a' srsi, Na(iova66ccQov xar Alyvnriovg
li6rjiipQias aytEGrcbrcc ^LSV rov cntoyeCov rbv v\kiQv slg
ra sjtopeva xad^ bpabrjv yiiv^Lv [loigas 6% t?, site-
ds psting rbv 'Ijfhfav rijs poiQccs %rjxo6rK 'jis.10
rj
f
. Jlsgl rrjs
av s&sA&iiev r^v KCI& snccGrov
QQV&V rov viUov rtKQodov
rbv OvvKyoyiSvov dnb rfjs snoxijs %Q6vovrov V7toxi[ivov TCQOS rqv v '4A.%ccvd(){a &QCCV 15
ts ra rrjs bpaArjs xwrjGEcos xavovia rag
rolg ol%ioi,g a
r&v rijg arto%fjg 6% i H,OIQ&V xal
r&v yvo[iVG)v xf$aA.6vrg oAovg xvxAovg rag
acprjGoiifv attb r&v v rolg didvpoig poiQcbv A si$ 20
ra 7toiiva r&v tydicov xaC, OTCOV av X7t6r] 6 &rov
1. ovv\ comp. ins. D, del. &qu. TKIS 7775] e corr. D 2. 2.
D.D. 3. Kitoysiov} corr. ex
-f* sv({>D 2 in loco minore. 5. xs] %' D. 7.
QOV AC, Na^ovvccGaQov D. a '(alt.)] 6 a C, vfo^viK D, vov-
^TIVLK supra scr. B 3. 11. TJ'] mg. AB, om. CD. 12. occous]
o- e'corr. D 2. av] D, sdv ABC. &&a>iisv C. 16. rd]
tag D. 18. 7to%fjs D. 19. yivopsvtov BD. f'ot^aHovreg D.
20. ILOLQ&V 8 I] ? I' \L D. 21. ^(o8i(ov Hat] corr. exD.
Ptolemaeus, ed. Heiberg. 17
258 KAATAIOT nTOAEMAIOT
d rbv avrbv apiotyioV, rovr0ri,v rbv ditb rov dno~
ysiov n>%oi> tils ftf'tf^g Jtaoodov, i6Vyx6vrg sis fb
rijg dvconaMag xav6viov rag naoaxi,^vag r<p
poiQag v r<p y' GsfodiG) Kara plv rb itgCbrov
5 rov aQiftpov jrwrrovrog, tovr&xiv
yGhovyiSv anb rv\ Kara r^v
.)Kara ds rb $' GsMdiov rv%6vros rov a
rovr0rtv vftsgyteGovros ^yt poious, Tt^o^^o^ev rift
lisGr) nagodcp nal ovrcog rbv <xxoi,f}rj xal cpcciv6[ivov
10 ijAlOV VQ1J6O{lV.
Ta pv ovv Jtsol rbv rjhiov povovvr iGriv ax6A.ovd'ov d
y
av sly rovroig
L dia f$Qa%O)v nal ra 7tgl rijs r&v vv%&r]-
15 [itoav dvi06rrjros oyeikovra 3tooA,r](pd"YJvcci, dia rb ra
psv xr&i,iiva iftLiv nad1
'
Zxatirov arth&s ptGu KIVV\-
para ytdvra xar faag v7tEQO%a$ r^v Jta^a
pdviv &s xal rcbv vv%d"rj^Qcov itavrcw
ovr&v, rovro dsfti) ovrog %ov &G>Qt6d'ai,. rrjg
20 roivvv r&v oAcov (Srgofp^ dpaA&g re cbroTfAovfteV)?^
xal jtgl rovg tov farjpfQivov xoAovg nal rijs roiavrrjg
d7toxara6rd<30)s Kara rb 6rjfiicod0roov tfrot,
rbv 6otovra r) Jtobg rbv ^i6ri^iftoivbv A,a[if$avo
xotipov plv rtfOHyrgocpij d^Aov on, pia ttirlv rj rov
25 avrov GyiiEiov rov far][iQi,vov dno nvog rptfparos
ijrot, rov do^ovrog ^ tov ii6r][if$()ivov iiti rb avrb
1. xovrsGnv] comp. B, -v del. D 2. 4. Tcg&rov] a B. 8.
PTT] rag Qjt D. 11. #'] mg. ABC, om. : D. 16. iv.nQ's^va. D.17. itdvra] om. D. 19. f%cov C. 21. rf/?] corr. ex rots C.
26. [isofippQivov'] comp. e corr. D.
MA0HMATIKHS 2TNTASE&Z P'. 259
VV%&IJ[IQOV ds anfabs v\rov
twos rptfuaros r^roi rov bf%ovrog fyrov
rtdfav 7tl rb avrb d7toxccrcc6ra6i$. bjiaAbv [ilv
ovv vv%&ri[iaov yivtxai did rccvrcc rb itQi%ov Ttdoodov
r&v rfjg [lias TteQidroocpris rov faypsoLVOV %QOVG)V r$ 5
nccl k'n vb IQQVOV efyxotfrcbv v& syyiGrcc, oticc ev
t<p rotiovrcp [i&cos 6 tJAtog smxivstrcct,, avcbpcdov ds
rb iteQifyov Ttdoodov r&v rs rijs fttag JtQi6roo<pris
rov fari^Qivov %a6vG>v r% xal k'n r&v ijroi Gvvava-
rov 10
rovro dy rb 3tQo6dia%6[ivov rov
rots r% %QOVOI avitiov dvdyxr] yiv6&u.i did r
q)aivo[ivr}v rov r\Uov dvaj^aUav xctl did rb rd fact
rov did ii6&v rcbv ^cpdicw xvxkov rprjparct ^ iv 15
%o6vois [itfrf rbv boi&vrcc {irjr rbv
xdroov [ivrot, rovr&v
rov vbs vv%d"miQOv dtacpoodv rf[
6rd(5G)S nuQd rrjv dvcopahov dvfitcciG&qrov itoil,
20
Ttaad [iv ovv rr\v ijhictxriv dv&[iccA,Lctv rb yiativTvi/
yivro:i didcpoaov 3tl r&v ditb pices rwv pfaav rov
1. 17] tv 17 D. 2. (iar)iiQivov] /t D. 3. Post avro del.
liti D. 5. r&v] TCOV TS D. tGJiiiQivov~] $, D,a add. D 2
,
lit saepius. 7. TW] om. C. 8. T^g] corr. ex rfj A. 9.
GvvavacpQa)[iEV(ov C, sed corr. 10. GvvpsGovQavovvToov AC.12. TO] om. D. 13. Tot?] -015 in ras. A 4
,-or- e corr. D 2
.
ccvdynrii A. 15. TOV] corr. ex TO C 2. y.vY.T(.ov] corr. ex
Avnlav D 2. 17. tovTcov~] r- in ras. A. rijv p. 260, 23. -&]
mg. D (W^fvov), ad lin. 21 pleraque cum mg. recisa; rv\v 18.
iv etiam in textu. 23. r&v (pr.)] ins. D 2.
17*
260 .KAATAIOT IITOAEMAIOT
sroav diaGraGEcov ra
ovrag Gwayopwa w%&tf(iSQa dioitisi r&v
%Qovoig dL' xccl d' k'yyitirK) aAA^Aov ds rots
XQOvoig #/.', din rb xal r^v rov r\Mov <pccivoiLvrjv
5 TCctQoSov nccQa TJJV 6|itaAi)v Kara [lev rb agog rc5 aito-
JiiniKvxkiov $' d' [IOQCC$ skteiTCSiv, xccra ds rb
r& itQt,yiG) Jtfaovd&w rcclg ccvraig' naya ds
T&V GwavaroAcav ty GvyxccTccdvGswv ccvG)[iaMav
rb TthsiGrov ywsTcc&diccytOQOv iitl r&v vnb r&v XQO-
10 TtiKcov Gynst&v acpoQi,o[ie'vG)v fftiiKvxM&v' xal
ai sxarsQOv rovr&v rwv
r&v [isv o^ia^cbs &(OQOV[IVG)V %QOVG)V
rolg SiK<poQOi<s r^g [isyiiSr'Yjs rj Aa%i6rrjs f}[iQKS
r^v i6r}iiQi,vijv, aM.tfA.cov da, olg ^ {isyfatrj r&v
15 Q&V -ijvvxrcbv rye; s^cc^i^rrjg diKtpSQSi. staga ds
rcsv GvpiisGovQccvriGscov avidoTrjrcc rb
yivstui diKyoQov sitl r&v dvo [icifoGrc
rcc xarQ&&v apar&v l<5rniQiv&v (Ajpe&M^ xccl rovrov yap
20 rcc 7tgbs rots rgojuxoZs 6vva[i(p6r()a r&v [iv bpah&s
&SG)QOVIIVG)V 8ioi6i %Qovoi,s d /.' tyyiGrcC) r&v ds
agog rolg i&r^tEQLVotg 6vvan,(porQG)v Tt&kiv %oovoi,g
^, dia rb ravrcc p
1. diaoraGEcav] r&v 8iK6ra.GE(ov B, SLUGTO.G D. 2. OVTCO D.
5. TO] x D. 6. /.'] e corr. D. <T] g A D. TO] x D. 11.
&vacpoQcci D. 12. 8(,oiGovGi D. pTt XQOVCQV D. 14. de,
Oi?] dlOVG D. 15. VVKX&v] B 3, QQ B. 17. ScQdXKT7](lOQLu]
D. 21. Sioidrjoei, C. ^] TSTQCCGI vctC D./,'] B,
A CD, rjfiiGeis A 4. 22. GwcciicpOTsgoLS comp. D. 23.
^] B, ^ lyyufra B 3. 2
r exetev fol. 73V D. ^ta p. 262, 5.
fjMov] mg. sup. fol. 74r D, usque ad cvviGTa^B&K p. 261, 3
recisa.
MA0HMATIKH2 ZTNTABESS T'. 261
/to/tofV, Xiva df rep foot 6%sdbv nteovd&iv. i'v&ev
xal rag iv rats no%al a$%ag rcbv vvx&rjpSQ&v dnb
TG)V {l00VQCCVYi6G)V 6VVl<5ra\Ltfttt, XCCI OVX CC7CO TG)V
KvaTok&vYI
dv6(ov TOV r\^Cov dia TO Tqv [iV ngbs
tovg 6giovTag %'O^ov^,dvriv diacpOQav xccl [i^Qi itoh- 5
<p&dvLV KCCI ^ ivai rr^
rcbv
ds JtQos TOV ii6yii(lQivbv t^v avrriv T
vKL xara naticcv ol'xqGw xal [irjde rovg x r^js fata- 10
as (Swccyo^vovs tov diccyogov %()6vovs
rovrcov ^i^os vfjs r nu^a xr\v
xal rfis Maya rag 6vii[i6ovQavri6i,g TO didyogov iicl
T&V KKT ai(OTas Tag ir, f
vas diaoac; VTQI TIOG- 15
[i6ov IH%QI Xrjk&v T^^aTos^ TigoGd-fTixov ds TOV
dab Z!XOOTCLOV ftf^^t p&ovf
Tdoo%6ov, dia TO xdTgovTG)V KKi^eVG)V T{ir][ldTG)V TO TtfalGTOV rTOl TtOO^TL- 20
acpuiQEiv itaoa [iv Tr\v rjAiaxrj
iQccg y zyyitira xal diTQiTOV, rtaoa $ Tag
3. KTIO] ni D. 5. xat] om. D. 6. OQ&V C. 7.
"C. x%\ rriv A. 13. ^t'ov] rj- oin. C. 14.
D.D. TO] ABC, xb ntefa-tov B 3 D. 17.'
D, comp. B, v$QTr\%6ov AC. 19. fifWu] om. B. 'T
vSgrixoov AC, ^ -' (LECOV B. 21. TJ] upa ij D. 22.
TQLTOV C, Io D. 6VV[LGOVQClVri6eiS A, [L60VQCCVri<>Sl$ D. 23.
F seq. ras. AB, r A 1
D, f C. cog] tog to D. 24. ow-D.
262 KAATAIOT UTOAEMAIOT
rcbv
agog ply rd 6[iahd %$6voL$ rj xal y', rovrfanv a
L' M;', agog aMyAcc ds r&v dMhaGiov %QOVG)V 7g
rovrs'tinv WQCCV a xai &'. rb ds rotiovrov sal
5 fjMov %ccl rcbv aM&v TtaQOQ&iiEvov ovdsvl av
xccrcc^ccTcroi rrjv r&v nsgl avra
,7tl ds Tys Gehtfvrjg di,a rb rrjg
|fcdAoyov av ijdrj rr}v diatpogciv d
xai (J>%()i' y s' [nag ILOLQKQ.
10 wcc ovv Kdl ra xcc&' drtoiccvdrjitors diccGTaGiv di,-
cc vv%d"ij[iQa) heya) ds ra ccitb [isGrjiiflQias rj
sjfl ^is^rj^^QiCiv rjeitl IISGOVVXTLOV, et$
rs rr)v jtyoreQccv 7to%rjv xccl rijv VGTSQCCV
15 didoiisvys t&v vv%d"y]iiQG)v dLKGrdtiscos, xara
<3rlv rov did [isG&v r&v tydiov xvxkov poiQcbv 6
?j/Uo 6[iahG)s rs Xivov^isvog xal dvo^d^cog^ sitsira r^vdnb rqg av&pdkov, rovrstirw ri}g (pcuvoiisvrjg, sni rr\v
cpccivo[isvr}v didtiraGw r&v rijg snovGiag ^OLQ&V20 sfasrsyxovrsg stg rdg sit' 60-9% rijg GyaiQcig dvcupogag
rov
2. x] om. D. ZOVTSGTI, D, comp. B. a] AC,BD. w^aff] comp. AC.
_3. r3} r ABD, T seq. spat. 2
litt. C. 4. xovTSOtw atQccv a xai] xal $>QCC$ (li&s D. to
5. r\Uov\ etiam in textu D (ro postea corr. ex did}. In fine
([<>** mg. D. 5. alcov C. 6. ccvrov? D. 9. y e'j r ?'
ABC,rqiCav 7ts[i7tTcov D. 10. oinoLKvd^nore C. 11. Z^yoo] corr.
ex ttysi, in scrib. C. 12. Int (alt.)] om. D. 13. 6taorXZa C.
&vcdva>(jiv~\ post -co- ras. 1 litt. A, -co- corr. ex o CD 2. GY.S-
ipmiisQ'a C et uoluit D 2. 14. xara re] corr. ex v.aQ'KnsQ D 2
,
yg. v,a&K TB mg. D. 16. iazlv] comp. B, -v del. D 2. 18.
&vco[Lcdiccs D. TOvreGnv] comp. B, -v del. D 2. 19. rfj$
STtovGtag] -s - e corr. D 2. 21. noooi. C.
pr. ftadd. A 1
, GVV^EGOVQCCVOVGL C.
MA0HMATIKHS 2TNTASE&S T'. 263
at rye; dvcopd&ov dt,a6rd<5G)s, &sxal kafiovreg rqv vitQO%fiv r&v rs SVQE&SVTCOV
xal r&v ryg ofiaAijg diatitaGecos
C re to rtQi,%6[ivov iifys&o
r&v Tijg i)7tEQO%rjs %QOVG)V rovro Tthsiovoq 5
fJLSV SVQLdXO^lSVOV TOV TG)V %()6vG)V aQL&[lOV t
r& didojievG) rcov
ds acpEhovpsv an? avtov,rbv yevopevov %QQVOV %o{iv stg ra dpaka vv^rj-
,& xal ^Qri^o^e^a ^dh^za agog tag 10
rCbv iv rots xavodi r^g 0s^vrjs [ifacov
. svxaravorjrov d' avrod'sv^ QXI xal dxb rfjg
v vv%&r]iisQG)v VTtodrd^scos tvt, KaiQina xal
%QOVG)V 3tQo6&a<pai,Q'6G)g avdnakiv yivoiisvrjg. 15
rti%ev pivxQi Kara rrjv fyiTE/
Qav jto%riv 6
rovT<5nv res a k'ri NafiovaGGaQov xar
a' rfig ^s6rni^iag^ b^al&ns {ilv
[p. 257, 6] aTtBd^aiiev, 'I%&vcov ka o ~^s^
dl y poiQas xal q b'yyuSra QqxoGra rcbv 20
1. cog] -g ins. D 2. 3. duxcrdoEmv D, 'corr. D 2
. 6.
BC 2D, KQL JL A, &Qi&ii6$ C. 7. StSo(iEvcp'\ rnut. in
in scrib. C, -v del. C 2; dedopsva) D. 9. rov] corr. ex TO A 1
.
D. ctg] tbv sis D, rov add. B 3. 10. xal
a] corr. ex g KSXQ<r]6'oped'a D 2.
ai12. $'] 8t D. 14. Post
D,del. vTto D 2. 15. nQOGcccpsQEGecos D, corr. D 2
. 16.
-v del. C 2, 7ti% D. 17. tovtiuii D, comp. B. Ncc-
D. 18. toO1
] -ft ins. D 2. a'] vovpr]Viu D. 6fta-
Zco? C. 19. &nedetoii,ev D, corr. D 2
.
^]om. D. o] om. A.
In fine KlavSlov TlroJiSfucfov ^a^rj^ar iv.fi? cvvrd^scos A, KKuv-diov nxotepctiov [La&r]ii(XTi'xris Gwrdt-scas $i$Uov y' B, KluvSiov
y C, Urotencciov ftaab^cmxcoi/ y D.
4'.
Tads k'vstitw V r& d' rijg ntote[iaiov
ra itQi rr\v
5
f}'. itsgl r&v TteQiodw&v %Q6v&v rr\
y' . negl rcbv xccra pegog bpal&v xivtfescov rife
rag
10f
. Qti xccl rti ri] KitkriQ vJto&6G)s T^g 6Aivrg ra
civra (pccLv6^va TtoiovGivrj
t XKT'
rrjra xalij
xccr' iitiKVK^ov.
xccl catAijg av(D[ittMKg
15 5'. rtQi r^g dioQ&GHSfag t&v pfacdv TtccQod&v rvjg
pijxovg r xctl avapaMccg.
trig Jto%ijg r&v dpcd&v -r^g 6&rjvr]g xivt]-
[iijxovg T xal avG)[iccMag.
&'. 7tQi xi^g dioQ&GxSf&g rcctv xccra nhdrog
itKQod&v rilg^6Xr]vrjg xal ri^g eTto^g avrcbv.
1. ^d'] om. ABC, Utotepa.LO'v (jLtt&rmccrw&v A D. 2. xijs]
r&v D. j^a-9'T]ftaTtx7)s 0tott<$|ea>9j (iafi"r}[JiccTiyi(bv D. Deindeadd. ~j C. 4. a'] et ceteros numeros om. D. dti] dri C.
TrjQrjGsajv] -G- corr. ex p in scrib. C. 13. anodsi^is] corr.
ex anoSs&s A. Tfjs (pr.)] t- corr. ex s in scrib. C.
KAATA. IITOA. MA0HMATIKHS STNTAEEaS A'. 265
'. ifjycpotpoQia xai xavoviov rr^g TtQ&ryg xal o
ia'. on ov "JtKQK rag diacpooag r&v v
Ttaoa rovg 7tt,A.oi
yi,6(iovg ditjve'yxsv xara rov
rijg GeAqviawfig &v&- 5
a'. 'Ano noCov del trjQiJGs&v ta Jtegl
'Ev r<p TtQO rovrov ^vvrd^ccvrsg^ o6cc av %i i'doi
ovta 3tQl t$\v rov r^Mov xivyGiV) aQ%6[ivoi 10
TS xatcc i$\v sepsis aKokov&Cav xccl rov tteoi rijg 6s-
Aoyov itQ&rov fj'yov[i&cc Ttoo'
cag etv%v TtgoGitvai rcctg r&v fig tovvo rrjorf
%Qtj66iVi aMa agog ply rag xa&ohov
vaig pdfaGra 7tQO<5%LV r&v ajtodt|fG3v, oticct, py 15
[iovov IK rov Tifaiovog %QQVOV, aMa xal an' avr&v
r&v Kara rag 6&r]viaxag Kfohl}ig rrjQtJ6ov kayipa-
vovrai' dia [lovcav yaQ rovr&v axQificog av 01 ronoi
ri\s 6^tjvr^g VQi6xoivro r&v aAAcov, oVeu ijroi, dia
r&v 7tgbg rovg anhavflg adrsoag jtaQod&v vj dia r&v 20
ogydvcov T)dia r&v rov r\Mov fxfafyf&v
itokv 8iafyv<5&i]vat, dwapfacov di,a rag
ryg 6^tjvrjg' Jtobg ds ra xara [ioog
xal artb r&v akkov ydr] rri^6C3v TtoiziGftai rr\v iiti-
1. -Adi (pr.)] lac. 12 litt. C. 3. ia'] cci B.
e corr. C. vno&EGscov] om. D. 5. iris crtriviKyifis &vco-
s] om. C. 7. a'] om. ABCD. 11. <p^ff] corr. exD 2
. 12.[ii]']
corr. ex ps in scrib. A. 13. nrjdt D.D. 14. %QIJGGLV] corr. ex XQTJGIV C 2D 2
. xarar-
i/>ig] post -r\- ras. AC (^ eras.?). 19. 6'aca] corr. ex OGU D 2.
22. nQccMd&is A.
266 KAATAIOT IITOAEMAIOT
6xit>iv. TOV yap ajrotfrt^arog, 6 vcydtitiptsv v\
T^g Gshtfvrjs djtb TOV XVTOOV Tijg yifc, pr\ ovTog
xal TOV xaTa rbv ^cpdiaxbv xvxhov TrjfaxovTov ,
6lf][llOV JtQOg ttVTO MyOV %LV TO T?jg
5 dvdyxrj Tqv ebro TOV KSVTQOV TY\$
ev&slav 7tl TO, TOV dia ^e(5ov T&V fcodt'aw xvxkov
, agog r}v ai axQi^flg Tt&Qodoi, rtdvrcov VOOVVTKI,
OS afadyGiv Tr\v ccvTyv yivetiftui ndv-
TOT Tl] CCTtO TiVOQ falCpCCVffas T^S Y^S) TOVT&TLV T^S
10 Oll>G)S t&V OQ(DVTG)V) 7tl TO XVTQOV
paA,ho[ivr), ngbs r}v ri (paivo^v
QBlTKi, dhh<X OTCiV [lV XCCTtt XOQVCpriV TjTOV
)TOT [lovov [iiav xal tv\v a,i)xr
T^V dno T TOV XVToov Trjg yijg xai Tijg
15 ofa&s TOV &&QOvvTog 7tl TO xwTQOv T^g 02,tjvr]g xal
TOV ^cpdiKKOV xf}aM.o[ivr]v ,OTCCV $ anovsvsvKvia %
07C(D&dlJ7fOT TOV XCiTCC XOQV(pr}V T07COV, dltttpOQOVg T
Tag %M6ig T&V 3tQOXi[ivcov
xal dice TOVTO TTJV (paivo[iwr]v rtdgodov ^ TVJV
20 yivBGftui Tr] dxoifet Jtgbg aMag xal ahhag &6ig Tijg
aoiivr]g T&V did TOV XWTQOV Tqg
avdhoyov Talg Jtr]A.ix6Tr)6i Tcbv vnb
TK)V [JlV
1. o] ov D. 2. pri] -r\ e corr. D 2. 5. ccvdv,ri A, corr. A 4
.
^ff] TTJS yiis rovTSOTi TOV ^cpSwAov 8ia TOV V.KVTQOV r^g D,corr. D 2
. 8. yiyv0&cu D.'
9. rovrtcm D, comp. B. 10.
TOW] 6- corr. ex a> C 2. 12. aU' D. 77] om. D. 13. r}]
D, % r) D a. 15. xat] corr. ex vard D 2
.
'
20. yiyvEGdai D.
rri'v C, -v del. C 2. &Gtis v.ocl aUcc? D. 22. ccva-
D. nt\kiv.oxT\6iv B, TIT^IY.QXJ\IGI D. 23. sy-nXtjosmg C.
24. Gv^i^Tf]Y.sv D, -v del. D a. sntityscov A, corr. A 1
. iv.-
fatipscov yivopivaiv] om. B.
MA0HMATTKHS STNTAgE^S A'. 267
VTtb rfjs <y&r]viaxi}s vTtodQo^rjs xal
ijris E'lLTtfarovGa ELS rov dnb rijs oifjs&s
XG)VOV TtOLEtrai rrjV ^%QETUtixorrjew, [irj xavra%rj ravras [itfrE rots
rots %Q6voi<2 coGctvt&s aTtorsA.EiG&ai, pyre 5
di' as SIQIJXCCIISV ccfoiaS
rijg Gshrivrjs [irjts Kccra rcbv avt&v {ISQ&V rov
rowvrrjv dicccpogav EX t&v
Zv rov yi,vo[iE'vov Jtsol rr\v GEhtfvrjv Extent- 10
V rtd&ovs p) (3VintccQccA.appdvovros rqv rCbv do&v-
rcov ofyiv sis inv ufafav fov (tofl&Mfyiavo
yccg fj ^E^VYI ndvrors VTtb rrjs
EitEidav xccra did^LErQO
rbv {LEV ukkov %QOVOV cpccivsrcci, JHLLV ohr] 15
dice rb TC&V rb 3tQo6A,a[i7t6[ivov ccvrijs
apcc xal r^iiv rorE rtccv TtooGvsvEw,orav
$E ovr&s diaiiErQrj&f] co6rs ELS rbv ri\$ 6xici$ ri\$ yr\
XCbVOV EpTtEGElV XQV CiVriltEQlCiyO^EVOV CCEL X& ^AtCO,
rors yivErai a<p&n<5rog avahoycos fccis rijs EiMtrcoGscos 20
Eiti6xorov6r]s rijg yris rats fov rjMov
xard ndvra rd
3. itKQdlivGBcos C, corr. C 2. 4. rccvrus] corr. ex rag CCVTCCS
D. 5. ^LIJT (alt.)] corr. ex ^ D 2. 7. /u-rjrt] corr.
V del. TJex (ir]d D 2. Post KVT&V del. TJ C 2
. rov rjlfov [itQobv D.
8. cpaivopsvrjg] D, cpatvo[iV(av ABC. 11. 6vvnciga'ka[i^d-VOVTOS A, Gv^nsgi.'kci^Kvovrog C. OQOVTCOV C. 12. Gv^iTtrm-
-eg in ras. A 1. 13. cre&ifi/q] -e- in ras. A. 14. KQO-
C, corr. C 2. %ara] fort. V.KTU rr\v xara. 15. TOV
mg. D 3(v.Eiptvov add. D 2
). i]piv] -t- in ras. D 3.
16. 7iQocluiin6pvov~] -p-jiopwov e corr. D 2. 17.
-ft,- in ras. D. 22. TO] supra scr. C 2.
268 KAATAIOT HTOAEMAIOT
xal rots pey&ftffy xal rots r&v diaGrdtiscov
ravra dfj nabs rqv xa&6A.ov sitfaKetyiv r&v
roTCov rijg tffA^V^g, AA' ov r&v yctivo-
5 [isvcov, 0(fL^,6vrc3v jtccoaA,a[Ji,(ldv6ft'at, , sitsidtfitsQ xccl
to Tsraypsvov xal rb opoiov rcbv ardxrav xccl avo-
dvccyxatov avsi'rj
jtoovjtoustGd'cci, rats (J&v &k-
jQiJGsGi cpa[iv prj dstv 6wy%Qrj6&cti, r&v iv avrcclg
dia rijs otys&s i&v ryaovvr&v10 /iaVov, [novais & ts r&v sxAefys&
v avrats ovdlv ngbs rqv r&v roncov xccrdhrjilHV 17
fiil>is 6vppdM.rai,' o yaQ av r^^icc rov dice ufacov
rcbv fydicov 6 ijfaos X%G)V fbafax'rjraL xccra rbv
li6ov %aovov rrls bctefyftogi w co rb rijg 6J.rjvrj$
15 xvroov vnb rov rov tyiov xara [lyxos dxoifltbs &$rcc dLa^roftrcct., rovrov d^ov6ri rb xara
(p^t xal rb ri}s GfAtjvrjs xwraov nabg
xara rbv avrbv [i6ov %QQVOV
ft'. Jloi
20 *Ay OICQV fiv ovv rrjQtjGf&v rd 7tQi rr^v
rovrov xccrd rb rvncodfs
1. [iy8&6iv] -v del. D 2, [isys&eGi B. 3. 8i] itgog] -77 n-
in ras. A. 5. snsi-d^TiSQ] -17- in ras. A. 6. rfrctyptvov] -y-in ras. A. avo[ioicov] -co- corr. ex o C 2
. 7. ngovnoKfiod'ai]-v- in ras. 2 litt. D 2
. 8. cpa^isv fi^jj corr. ex cpKpev C 2, -fisv
(i- renouat. D 2. dstv] -e- corr. ex
r\in scrib. C. 6vy%Qf]Gd'ai]
-y- in ras. D 2, -fj- corr. ex t C 2
. 9. TT}QovvtQ>v~] seq. ras. 2
litfc. D. 11. avrccis] rccvraig D. tiardlirflpirV] corr. ex. ex ft C,AC 2
. 13. fu^i'cxrjrat] -77- corr. ex ft C, ex e D. 15.
xov TOV~] A, rov BCD. 19. 0'] mg. AC, om. BD. XQOVOV C.
20. ol'aiv] ofioicov C, cup' ol'cov [i8V ovv mg. C 2. 22.
BD, sed pr. c eras.
MA0HMATIKHS ZTNTAEE&2 A'. 269
rbv ds rgoitov, xa&' ov is 01 Ttakaiol rats rcbv aito-
ov 7ti{loA.ats %gri6avro, xal xa%? ov civ
r&V TtQOS rd (paLVO[lVa
5
litsl toivvv av&iiKh&s [ivXKTK rs prjxos KOI TtAccros xal
rbv dice [ifacov r&v Jcodtov xvxAov aid dtQ-
pijr agog rqv xara rb Tcharog avrov xagodov
%G)Qls $ vi}S VQ6G)S TOV rijg avcs- 10
avrr}s djtoxccTctdratixov %QOVOV xccra rb dvccy-
XKLOV ovd rag r&v akk&v 7tQi6dovs hafetv oiov x
Jcv ywoirO) xara jtdvra [nsvroi ra [iQr] rov ^cpdiaxov
rd r y,B6a xal ra piyiGta xal ra skd%i6ra dia rcbv
xara [iQO$ rrjQiJGfcov yaiverai xivov[if
vrj xal xara 15
ndvra ra H,QYI poQiordrr] xal von&rdrr] xal xar
avrbv rov did [ifacov r&v tydtov xvxhov
01 nakaiol iiafrr][iari,xol %$
o6ov ndvrorefj 6e^vri rb foov xivrjfi-iJGErai, xara
rovrov povov rr\v dvco^a^iav anoxa&i<5rdvi,v 20
dvva[ivov. 7taQarL^^iVOL di]
fao[jiv airLag ^
{iiqvcbv didtiratiis t6o%Q6vi6$ r yivoixo Tcdv-
ror rats rov i'Gov TC^tjd'ovs dia6ra66i, xal i'6ovs
xvxhovs itQi%ot, xara [lyxos r^roi o&ovs ^ [ird nv&v 25
4. v%QriGT6zQov~\- corr. ex o D 3
,-ov mut. in av D 3
;
iQT}6r6TQQv B, sed u eras.; ^v%ccgi6r6rK^ov C, corr. C 2
.
ftu] mut. in Ttotov^s^a D 3. 8. TOV] AB 2D 2
,r&v
BCD. KMov] corr. ex v.v-A\tov D 2. alsf] AC, foi BD.
9. TO] om. D. 14. ra. re] noi ra. D. 16. itavzcc] om. BC.Y.UI (pr.)] rs KKI D. vorLcordrrf] D, vonordrri ABC. 17.
pscov C. yivovofjLsvr] D. 20. novov] om. B. 21.77']
ds D. 22. a.trias\ supra scr. D. 23. yivoixo D, corr. D 2.
270 KAATAIOT DTOAEMAIOT
bko6%SQ<3reQOV [lV OVV 01 STt
rbv %QOVOV rovrov vns^d^avov slvcct,
V <p7te xal yr'
dice rotiovrov yag fyyitiru ecb
v d7tOTEA,ov[ivovs
[iv tfA'fr, nhdrovg ds
(Spa xal ETI,, oGccg xal 6ij
KVXhOLS SV 1& 7tQOl,Qr][lEVG) %QOVG)
tt3toxara6Ta6G)s ccvrcbv TCQOS tovs
&(QQOviiEvr]s. xdl.E6av da rbv %$6vov rovrov
10 ftSQiodixbv &s itQ&rov sis [iiccv aTtoxardGrccGiv ayovra
rds dicccpogas t&v xiviJGecov. xccl wcc
avrbv 6v6rt]Govrai^ srQiTtkttGiaGav ras
y' fj[iQas nut 6%ov fftifQcbv dgi,d'[ibv ^ fttyvz, ov EXCC-
fadav &zhy[t6v' xal rcc ahku df opoicos TQi,7tA.G)6ccvrs
15 6%o
[iVxccl En,, o0Ks xal 6 ijhos eitihaiipdvEi rolg vd
A/3.
psvroi Ttdkiv 6 "l7titaQ%o<3 ijfa'y&v dito rs rtibv
20 XahdaVxcbv xal r&v xa& favrbv rrjQtJ6C3
fyovra ravra dxQip&s- ditodixvv6t,
cov E^e&Ero rrjQiJGEGOV) on, 6 Jtotbros dQi&[ibs r&v
3. xat] om. D. tooov D. 4. $s] 8' D. 7.
(iEV(p\ KQOKeipsvo) D et supra scr. B 3. *"*] f8 C, T seq. ras. 1
litt.' A, r A^, dipoigov supra scr. D 3, 1$ B, h aUco I vfi o
xui cdrifi'ss mg. B 3. 10. n^fbrov} corr. ex ngbg TOV B 3
. 12.
UVTOV r)(ieQ&v D. GVOT^GOJVTCCI] B et supra scr. D, cvaT^aovrcct,
ACD. TQl1t).K6lKGKV~\ TQl7tld)6KVTS D- 13. %at] Om. D.
] D, iiu D 2, fluids U D 3
. 14. l&iUwov corr.
ex l&leiynov D 2. TU aUcc Ss] T&Ucc 8' D. 15. ds] $' D.
16. ? c - 19 - ^eSff corr. ex Ifrsv A 1. 21.
MA0HMATIKHS STNTASE&Z A'. 271
di oG&v itdvTore 6 ixfamnxos %$6vos iv
foots iirjtilv xccl iv foots XiinljfjLatfiv dvccxvx^Eirat^ ku,
6rtv xal enys: r\^L8Qcbv xal Alices cooas i6rmsgivi]S) iv
acts ^vas [iV aitaQri^o^evovs vot0xiyd(?if, okas de
drtoxarciGrdGEis Sepoy, q)diaxovs ds xvxAovg 5
OIQCCS f /.' tyyiGxa, o6ag xal 6r^
xvnkovg keCitEi, ndkiv cos tf}S tt
CCVT&V ngbs rovs anAccvets UGTEQo&sv stigfaxsi, xcci rbv ^VLKIOV (JLE'GOV %$6vov
rov rtQoxi,[iEvov r&v fiiiegcbv nAyd-ovs 10
rovs fititfc pypas fiiLEQ&v 6vva i
y6[jLvov K& Ace vi]K
iv [iv ovv TGI ro6ovrc3 %QOVG) rccs cforo EX-
EAyviccxris inl EKkE
dicccfrccGEis artodEixvvEi,, &sTO ttTtoKaftiGrccGftai rr^v <xvco[iccMccv ix, rov itavrore dice 15
rov rotiovrov %QQVOV rovs * rotiovrovs privets
'xccl rats facus xccru
l'6as 7tiA.tt[i(}(Jcv6<d'cci, polkas tvfi /_' <xxoA,ovd"G)s rats
rov ijAiov Gv^vytcus-
EL $ ns pf} rov ana ixkefyEGis 0E^vt,axijs iitl 20
ctQi&yiQv r&v nqvcov titifyrofy, ILQVOV de rov
O tivvodov tj navtizkrivov iril rqv bpoiav
1. IxAetTTTtHog] s- ins. A 1. 2. firioi'v] -v del. D 2
. v.ivr\-
HUGLV~\ nivri- corr. exftrjorfc
D 4. Ji] in ras. A, [ivQiddcov D.
3. tcxiv] corap. B, -v del. D 2. >tcu'(pr.)] t|3
nctl D. rt] corr.
ex ITTJ B. 4. ,tfffg] I).G^ C. __ 9. SVQLG^L] -ft in^as. C.
tov\ tr\v A, rov per D. 11. vrj]
B et e corr. D 2, VT] AC.
13. &cxAn/>u> D. 14. SiaGTKGfis] -i? in ras. D 2, supra -GT-
ras. &Tto8wvvi\ -et in ras. A. Sfi^ov] corr. ex dffia D 3.
yivsG&cci C, yevEG&ctt, D. 16. rov'] om. D. roGovrovg]i'covg D. 17. ras I'GK? D, corr. D 2
. 18. fio^ag] ante -Q-ras. 1 litt. A. 21. en^rroT in extr. lin. A.
272 KAATAIOT HTOAEMAIOT
EVQOI civ en ijrrovcc rbv dxoxaraGranxbv rijg re dvco-
[iaMa$ xal r&v ^rjv&v doi&nbv Aa/3cbv rb [tovov avr&v
xowov [isTQov STttccxciidexaToV) o Gvvdyei,
GvcC) dvcopaMas de a7toxara6rd6i 6%$. ovxen
5 6 3tQoxi[ivos %QOVO$ VQi6xro xccl tr\v Kara
drtoxardGraGLVfy yaQ avrajtodoGig r&v x-
rag dia6ra6is povov rov re %QOVOV xal
r&v xard ftijxog TtSQiod&v q)atvro 6c)ov6a rag 106-
rrjras, ovx&i, $ agog rd peytftvi xal rd$ 6[ioi,6rriras
10 r&v btitixotifescdV) dcp7 &v xal rb xAdro$
fidvercu.
ijdrj pivtQi yt^oxart^^vov rov rijs
ditoxaraGrarwov %QOVOV 7ta^ad'^ivos JtdAiv
dta6rd6is iirjv&v 6/iOtag xara Ttdvra rag axgas %-
15 AefyfiS %6vrcDV xal rots iieydfteGi, xal rots %QOVOI,S
rcbv 7Ci6xortJ6G)v ,iv alg ovdlv eyiyvero didtpooov
itagd rr\v dvo^aUav^ &s &i& rovro xal r^v xard
TtAdros ndoodov d7toxa&i,6rau,vr]v
xal rrjv roiavryv itEQiodov dytaor^o^evrjv iv
20
6 [iv ovv rooTtos, w Ttybs rag roiavrag xara-
fyatftiavro oC nab fni&v, roiovros rig yv> on,
de ov% dxhovg ovd' fvitootfros ,(UAa jroAA^g xal ov
rrls rv%ov<5r]s dfdkitvog 7fL6rd0os^ ovr&s av xaravorj-
25 6ai[iv. wa ydo d&pfv dxyiflcbs fcovg aAA^'Aotj rovg
1. IJTTOVCC xov\ r\trov D. a.Ttoy.ara.G'tiY.ov D. 2.
fiWV C. 5. qVQlGKSTO D. 7. TtQOS tU<a SiCiGtOCGSKs] Om. C.
jLtovov] avT&v fiovov D. 10. aqp5
] e corr. D 2. jur/J om. D.
13. ccnoKK-cccGtiyiov AD, corr. A 4. 15. psys&s6i \ -s&eei,
renouat. D 2. 16. syivsro D. diccyogciv C. 18. dsfawaiv]
-v del. D 2. 19. fATjai D. 20. ?gxy] AB 3
, swy BCD.22. e^tyaro A, corr. A 1
. 23. ovds C.
MA0HMATIKHS STNTASE&S A'. 273
rav 8ia6rd<5eG)v %oovovg voi6K0d'CCi,.)ito&TOV ^ikv ov-
dw bcpskog TOV roiovTov[irj
KK\ TOV f}Mov TO nagcc
rr^v avopaUav didyoQov vj {lydsv t)TO ctvTo itoiovv-
Tog xatf xccTQCiv T&v dt,a6Tcc6O)v. i y&Q pri rovro
$ rt,, &$ gyqv, naga xr\v avoyia- 5
civrov didgjogov, OVT ambg gdrcu iv rots
faces rtfOLdoonag n^noiri^vos ovrs
<xv yaQ hoyov VXV %aTQdiatiTK6G)v ftfO
1
'
oAovg xccl rovs fcovg
%aovov$ jt^cc^dvrj TO rftiiGv TOV EVLCCV- 10
6iov IQOVOV, v d TGI T060VT& Xi,xxivrjtivog 6
idtfTCiGiv aitb Tij
,XCCTCC $
aitb Trig KCLTCC TJJV IIao&voV) KCCTK [iV ri]v TCQQTSQKV
ka66ov 7iiA,r]cpG)g 6 rjhiog l6tai TOV r][it,xvxMov poi- 15
g&v d [_' d' fyyiGTa, xaTa $ TYJV dVToccv
iftMKVldUov Tcctg avTCilg potocug' &6x xccl Tr\v
v Totg faoig %aovoi,g fteO-' ohovg xvxhovg xccTa
TJJV naoTaccv did(3TK6iv Bitsi^fpdvaL {loioccg QO dr
,
XCCTCC $ TTjV dVTOCCV QTtd i! $'. dlV OVV CpCC[lV 20
TOVTO ito&Tov %iv Tag dict6Ta6ig 7tol TOV ij&iov
6v{i(lf}r]Kbg TO r^roi ohovg CCVTOV xvxhovg it^ii^iv r)
XCCTK [LV TY]V TQCCV TG)V dlCC6Ta(5G)V TO KTCQ TOV
aitoyzCovi
r\\MKVK/
kiQv iiti'kapft&vBiv, XKTK $ rv\v TaavTO (XTtO TOV TtEQiytLOV, 7J
CiTtO TOV CCVTOV T^tj^LKTOg 25
XKTO(XV TG)V 8ltt<5Ttt6WVJ]
TO
5. yi'voiTO D. TKXQK] pr. a corr. ex s in scrib. D. 8.
SHUTSQCCV D. 9. oiovg] -4- e corr. C, ittovg Kvuhovs D.
10. 7td(X[Lpdvl CD. 12. 7lQ03TriV~\ TtQOTSQCCV D. 14. T7^(alt.)]om. D. 15. 7tsiHr](pd>s]
-- ins. A 1
,-si- in ras. D 2
,-I- corr.
ex d D 2. 16. /.'I v.cu ~L MI D. 19. Ttr\teiyhai D. 20.
iv] corr. ex CCSL D 2. 22. avrov] corr. ex ccvr&v D.
Ptolemaeus, ed. Heiberg. 18
274 KAATAIOT HTOAEMAIOT
xarQG)d'v r/tot XQV aitoyeiov r)rov 7tQi-
yeiov Kara re ri\v itgoregav eK^eityiv rrjg eregag dia-
6rd6&g xal Kara rr\v devregav ri\g eregag. ovrog
yaQ av [lov&g rjovdsv
T}rb avrb yCyvoiro diacpogov
5 Ttaga xr\v av&naMav avrov KCL& sxarsgav r&v dict-
,(Stirs xal I'ticcg rag Jtikcc[i/3ttvonsvag yivsG&ai
ijroi dA,htjA,ccig 7)ual aMtfAaLg xal rcclg
opahcctg.
dsvrsQov ds fiyovpefta, detv xai itsgl rovg dgopovg10 ryg Gshtfvrjg rr\v d{ioiccv iitfara6'iv TtQiEiG&ui. rovrov
yap adiaxQirov pe'vovrog vds%6^vov it&Kiv (pav
rb ncci rqv (jfhtjvrjv jtoMdxig faag 3tQicpQiag
prjxog v rolg fooig %Q6voig zitikaiifiavsiv dvva<5&ai
{irj Ttdvrcog Hal ri\g avo^a^iag avrfjg d7toxa&i,6ra[ivr]g.
15 <?t>ft/fy'<?r<u $ rb rouovrov, iav re Ka& SKarzQav r&v
dia6rd6G)v dnb rov avrov Kara 7tQ6(5d'6ivfyrov av-
rov Kara d(paio6i,v daopov TtOL^rirai rrjv dQ%rjv xal
^ 7tl rov avrov xara^yrj^ edv re Kara [ilv rr\v
rf
oav aitb rov [i^farov doopov aQ%o[ivr] Hxl rov
20 sA.dftio'rov doopov Karakriyri, Kara d rr\v ersQav dnb
rov eka%i<5rov doopov 7tl rbv iisyiGrov, edv re rb
i'Gov aitB^Gt^iv xarQcod'v aito rov avrov &a%i6rov
daopov o re ryg eregag di,a6rd<5(og jto&rog
xai 6 ri]g ere'aag e6%arog. xa6rov ydo rovrav,25 eav Gvyipaivri, 7}
ovSev rtdfovrjrb avrb noi^ei Ttaod ri]v
4. yivoiro D. 5. r&v] bis D, corr. D 2. 9. d^] 8' D.
10. opoiav] 6- ins. A. 11. 7^9] seq. ras. 3 -j- 2 litt. A.
]a- in ras. A. 16. KCCTO] corr. ex nctl rd D 2
. 17.
nonfi6i]-tai~] TtQir\ta.i corr. ex aoteiVcu D 2. 18. xaraArjyft D.
20. dQO[Lov~\ om. D. 21. dgofiov] om. D. TOV] TO D. 22.
UFOV] i6- e corr. A 1. ib^fwrm] -we- in ras. A. 25. r\ (pr.)]
om. D. avro] bis C.
MA0HMATIKHS STNTAEESS A'. 275
v avryg didtpooov xal dia rovro rag per Kara
MpfaiQ faces aTtfoyd&rai, , r^v ds av&yiaMav
dxoxaraGrrjfai. ovdsv aoa ovds rovrov r&v
%iv dsl tag 7taQaha[ij$avo[ivag dia-
el iifMrjGovG'iv avro&fv rbv K7toxctTcc6taTt,xbv 5
. rovvccvrCov d' av
dwccpevccs ,sav py oAat neQify&vrai rrjs avo-
K7toxccT(x,6rK6Ei<3 ,iQvrititiv orav ^ ^6vov anb
dgopcov rag KQ%K$ f^to^v, AAo: xal 6(p6dga 10
rjKara ps^d'os r\
Kara dvvaniv, xara ft-
&$ orav xara ^ev tv\v srsgav didtiraGiv
anb rov sA,a%i6rov dgopov aQ%r}rai, KKLp/ty
siti rbv
lifyiGrov Karakriyri, xara ds rqv ersgav, orav anb rov
psyfarov &Q%Yirai xal ^ Bid rbv hd%i6rov xaraAtfyy 15
ovr&s 6rai, rrjs xara
oAeov xvxAcov artaQri&iiwcov ryg
orav [idhitira reraQr^o^Lov fvrj
KKI ryia
Kapftaviiitai, dvtil ror rotg Jtaoa
avG}[iaMav diayogoLg aviG&v r&v dia6rd6G)v iftopt- 20
vov xara dvva^iiv (Jf, o>g orav
r&v dia6rd6&v aitb rov {i6o
anb rov avrov df ftftfov, AA xara {isv ryv
cuto rov nark 7tQ06d'6iV) Kara d rr^v roav aitb rov
dcpaiQ6iv' xal ovro yao rb nfalGrov diofaov- 25
2. aitEQydasrui D. Si] 8' D. 4. TtaQc
-fta- ins. in extr. lin. A 4. 5. fifyUrjtfovffn'] mut. in
C 2, pr. I del. D 2
. <broxcmK<mx6v D. 7. ocpsttopev BC.
(fccvf]6ca B C. 9. ci7tov.oiTa6ra,6r\g D, corr. D 2(comp.). fiovcov C.
10. dgoiicov 11. diacpOQoov] mg. D 2(netiitvov). 12. V.KTK
ju-f'r]corr. ex psv xara D 2
. 16. itteiGTov C. y#(>] y- corr.
ex G in scrib. D. 23. ftsV] ft'vA, om. D. 25. OVTCQS D.
18*
276 KAATAIOT IITOAEMAIOT
6iv akkrikozv aC rov ntfxovs facovtffai [idhtira [ITJ aito-
r}s avGjpakiag reraQr^oQiov pev vbg
i}xal rgifbv BTtiKa^avo^vov [nag dvG)[iaMag
dv6l rots Jtaga ri]v av&tiaMav d(,atp6()oig,
5 de TrraQ6i. dia ravrcc dy KOI tbvff
Iit7iccQ%ov
rcbv rtccQt,A,r)ii[isvG)v SLS xty roiavtrjv
sxhoyf} ual GwyxsxQqiisvov [isv r& rrjv
Kara fifi/ ti]v snlgav diccGraGiv CCTCO rov (is-
10 yfarov dpopov 7t7toirj6&ai, rrjv CCQ^V xal (i^ exl TOV
ekdftiGrov xaTa7t7tav<5&a^ Kara df xi]v TQav ccnb rov
A.a%i6rov dgopov TtsnoiriG&ai rrjv OCQ^YIV KKI[irj
7tl
rbv insyi^rov xaraTtfTtavG&ai,) dioQft&Gavra de ual rb
Ttaga, rriv rov riMov av&naMav yv6(ivov15 xatroi, PQCC%V ov dt,a rb d' fyyitira vb
QLOV xal pr} rov avrov7}
rov rb i6ov Jtoiovvrog
yoQOV rijs civo^ia^Cag KK& xarQav r&v
ig 6'Aovg uvxAovg a'AAeAowreWt TYJV rov fjMov aitoxa-
20 ravrcc elitopEV ov
rijs r&v ttQiodix&v a7toKara6rd6G)v
aQitiravrfQ^ on pera ^iv ri\g 7too6-
7tt,6rd6G)g xal rov xara rb axohov&ov iiti-
xarog&ovv dvvarai, rb
25 si $ nva xal rb rv%bv r&v xr&i,iiVG)v
3. ciVfopaUag] -pec- ins. in extr. lin. A 4, -s corr. ex -v D 4
.
4. 8vci~\ supra scr. D 4. rots TIUQK rr\v KvcopuUav] om. D.
5.Si~\ supra scr. D 2
. rsrccQGi AC. 6. evopi& D. 7. sni-
D. 8. xca] corr. ex i in scrib. D. 10. %ca] suprascr. D 2
. 12. dgofiov] om. D. 13. xov\ corr. ex TO D 2. Y.UXCC-
Q'ai B. di.oQ&a>6uvTa] -v- in ras. D 2. 15. d']
D. 18. ivteloutivai CD, corr. D 2. 20. $i~\ d' D.
MA0HMATIKHS STNTAEE&S A'. 277
pdrcov TtKQBk&oi, dia^V(3&i^6Tat JtavTanatiiv T^g Irti-
rjTOV[ivrjg xaraAitjfa&g, xal on dvGTtooiGTog 6Tiv
rots 8ioQttrixG)<3 3toiov[ivoi,g rrjv rcbv TOLOVT&V rrjQij-
6G)v xA,oyrjv r\ ttobg TO dxgi,($g jtdvTov rcov ocpsi-
ccvralg vitd()%si,v avrcatodoGig. 5
*yovv XT&i,iiVG)v 3tQiodtKGbv Kitoxccrccdrcc-
XCCTK rovg vjtb rov(
l7t7tKQ%ov yfywrjiiwovs iiti-
ovdfvl
vtrai, dityv6yiBVYi r^ cd.y&iccg, i\df ryg av&iicdtccg 10
xccl rov itAdrovg aZiohoyq) nvl dirjiiccorrjuwr], &6T xal
XCCT<X TO <X7tA.OV6TQOV XCCl V7tOQt,6TOTQOV
od&v, ccg vftvg K7todL^o^iv apa Tfi
xrig avG)[iakiccg nooXT&i,[jLvoi, 15
TCQ&TOV dt,d TO Jtgbg TU Qiig v%QT}6Tov TK Kara
xwtJuciTcc iiijxovg r
ccg xal n^drovg dxoAov&cog Totg
xal ra X rife artodL%&r}6oiivr}g avrcov diooftcbfaog 20
2. KccTcdriiiipfoos C, corr. C 2. tan D, comp. B. 4.
97]
ins. D 2. 5. atccnodoGig D. 7. ysytwrjusvovs AC, pr. v
eras. A. 8. vytw?] C 2D, vyftwg ABC. 10. SLS^VG^VJ]
mut. in distysv^iLivT] A 1. rj]
corr. ex si D 2. 12. yeyovevcci]
corr. ex yeyovev D 2. 15. itQ06K&[jivoL D, -6- del. D 2
. 16.
rd (pr.)] corr. ex TKS C 2,TO D. 18. &Y.olovft(os\ pr. o in ras. A.
19. (knoKCLrciGrwoig D. 20. cc7toSi%d'r}6opvi$ A, corr. A 1.
D.
278 KAATAIOT UTOAEMAIOT
y. Ilfol rcbv Kara, psgos bpah&v
'Eav roCvvv rb artodsdeiyiisvov peGov rov
o v&rj i% ~i
rag rov vbs
x xal rotg ywof&otg Jtao6&&[iev svbg xvxhov uot-
,
r
&>opev, as sv rtp svl pyvl iisti&s % Gshrfvy
xara ^TCOS MOIQCCS md- i xy a xdJ3
A v't,
ravras sitiiieofaavrss sis
10 rov [irjvbs VJIISQCCS %o(iev fftisariGLOV psGov Xivrj[ia
[loiaas Ty 1 A^ v^ Ay A A syyitfra.
rovs <?# KVK^OVS vfjs
itl ras rov evbs xvxhov {lotoccs
poio&v 11 ygo|Lt. ravras [isofaavrss sl>$
15 yivopEvas f){iQKS rcw <5vcc [irjvcov gvift I ^d va jif
lisv xal avG)[iccMas rifieotj^iov [istiov xtwj[ia [loioas
y vy V$ xfr faq faq.
t&S f^KY rov ftAdrovs aitoxarccGraGeis
ra rov
1. y'] mg. AB, recisum C, om. D, xecpdlcciov y' B 3. 3.
rot) rjMov H&GOV r^iEQ^Giov mvrjfioc D. 4. o] om. D. ty]
supra scr. A 1. ^yy>ra] om. D. 5. v ^] vj\ D, diremit D 2
.
6. yfvoftfvot?] -e- corr. ex t in scrib. D. nvnlov] -v in
ras. A 1. 7. ^|o;fv] seq. ras. 2 litt. A, supra e- ras. W]
f C, om. D. 8. xy] x y D. 9. Tr^oHftft^as] -sV- corr. ex
?]v D. 12. fff^] Igijxoftff D, dmx/ ins. D 2, mg. c^ D 2
.
TroivTrZactaaavres D. 13. xvxZovg C. 14. (JLOLQMV] ftA CD.
ft C et supra scr. A 1
,om. AB, f @ e corr. D. 15. yivo-
corr. ex ysvo^vag A. t>va] ~G seq. ras. 2 litt. D, vcc
supra scr. D 4.
/~^jj] ^y tp BC. 16. xa] g C, del. C 2.
18. 6/iotcog] supra -ft- ras. A. Deinde xat add. B 3
.
O supra scr. D, r D 2. ^xy] -y in ras. D 2
.
MA0HMATIKHS STNTAEE&S A'. 279
aty
(lOiocbv ft JpGTt. rccvras ^iQi6avrss sis
t tg
ras t&v jvvr] [irjvcov yivo^Bvag rjpzoas ft- ,aoo vr\ vr]
y x '|oftv xal nkdrovs fi[iatf6iov [i6ov1 <x ^ a.At/
1
ftt ttr.
Ttdhiv dnb rov rijs 6A,tjvr]s xara
rb rov iiUov
if} LCC K% fta K L v&. dice [isvTOi rcbv etps^fig, as
ftiiv TtccQahrjcpd'rjGoiiev&v sis rfv roiccvrrjv
scpod&v [cap. YII] TO {isv rov ^KOVQ f}[iQrj- 10
%s8bv ccTtaodAhaxrov VQi6xo[iv red itoo-
xccl rb Tys <x7to%fis drjAovori) rb $ rijs
gkarrov poiQcas oooo lajilg A^, ess
v 1/y y ~vy v^ it, va v&, rb $ rov ithdrovs ntetov
oooo ^ A-9- 7^, cos xccl ccvrb yCv^&ai [lOiQ&v 15
xara ravra drj ra rftiforjcJia Aafiovrss ftfv Zxdtfrov
rb flxoGTorsraorov efcofisv aoiatov ii6ov
xovs ft^v {lOiocbv o A/3 v x xz x/y ft? tf,
ds poiQ&v o AjS AO- ftd v ftd A^- vj A, TrAarovg df ftot- 20
o Aj> <? >cd # A/3 sea A/3 A, cbro^g df [lOiQ&v o A
1. ji
y] ^
c<rB, pvgiddas supra add. B 8
.
y^<] - e corr. A._y |3(73r mg. D 2
. 2. apo^ C. HVQL tg ^90^ mg. D f.
3. x] om. B, xf supra scr. B 3. 4. ty (alt.)] i- ins. D. t] nrj
D.
8. J\\LIV wg Zcpaptv D. 13. ju-ot(>atff] comp. ABCD. oo(pr.)]
in ras. A; pr. et tert. o e corr. D 2. ytVccrihu] -t-inras. A. 14.
LQ&v] comp. ABC, [ioiQa$D. 15. ju-ot^atg] comp. ABC, poiQasD.o(pr. et tert.)] e corr. D 2
. yiyvsc&cci D. 17. ncc-co] KKI A.
18. SLKOGTOxeTUQTOv] K j D. wQcciov D, corr. D 2. 19. ftot-
D, comp. ABC, ut etiam in seqq. 20. Ifi] -fte corr. D*.
21. <?] ins. D 2. I (alt.)] seq. ras. 1 litt. D.
280 KAATAIOT HTOAEMAIOT
JM? AS jityx /Ltd vf A, tgiaxovtaxis ds Tt
a, xal acpshovrsg xvxkovg f^opev pqvwfav [i-
ds iioigibv Aa vZ vrj rjvs v& A, 7cldrov
AS" v/3 ft-O1 vd wrj Irj Aa, jco^i5? ^ IIOIQ&V
rjv& A.
TCC fip,Qri6ia TtokvTtkaGiKtiavrsg exl rag vov
Eviuvtov fjiispas T%e xal c
viav6i,ov istivv 7tov6iav
10 yioiQfbv $%& Kfi jitg ~iy v A/3 A, d
ytrj w \ xij fia ly v, ithdrovs
?toi,tf<5ccvrs ra wiavtiicc dia TO
<bg
15 r$ o'Aovg xvxlovs
gvz ~v% id Ag xft I A,
Qvg v & ft-91 tO1 A A, asropjg de yioigwv goy
t/3 5cg A^ ^ 7 A.
20 diaygatyoium ovv, &6itg xal inl rov ^Atov, xccvo-
1. fty] |x- in ras. D 2. 2. xvxXovg] x D, x D 2
. 4. ^a]
-a in ras. D 2. 5. \d\ \ seq. ras. 1 litt. D. 6. fZ rj] /Trj
BCD, corr. D. v-fr] corr. ex vp D. 7. TroUajr/lactaffavrfs B.
8. xat] om. D. 10. [IOLQ&V (utrumque)] comp. ABCD. 11.
TTTf] pTtT] BC, 9- eras. C. ^] fzj BC. nlarovs] -e ins. in
scrib. D. ju-ot()wv] comp. ABCD. 12. xs] x- in ras. D.
K7to%f)s~\ corr. ex no%f)s D. /^(H9<m>] comp. ABCD. 13.
TO] om. C. 15. oxtrooxatdxafTTj^i^og D. 16. fisv] om. D.
jtt^] seq. ras. 2 litt. A. 17. ^OIQ&V} comp. ABCD. K?]
seq. ras. 2 litt. A. x(3] -|3 e corr. D 2. 18. jnot^wv] comp.
ABCD. p?s] corr. ex g^ D 2. v ^] r^ ABC. 19. tp]
-|3e corr. D 2
.ZJjf] -(3
e corr. D 2. 20. dictyQatpcoiifv CD 3
.
MA0HMATIKHS STNTASE&S A'. 281
vag y ml tirfyovg pv itdfav ^s^ GeMdia ds xaO-' exa-
tirov 8' rtiv tie <58hidi&v ra pv itQCbra itSQiQei, rovg
%QOVOVS snl [isv rov ngcorov xccvovog rag
ccs, iitl de rov dsvregov ra err} xccl
rag coQCig, enl ds rov y' rovg [i^vccs xal 5
Jtdfav rag r\yiQag, ra ds houta rstftiaga rag
oiKSiag rcbv {loiocbv Tcagad'^sig^ ra {isv dsvrsoa rag
rov iiijxovg) ra ds rgira rag r^g avonaMag, ra ds
reraora rag rov Jthdrovg, ra dl Tte^iira rag rr^g
axo%rjg. xaC etinvfj sx&sGig rcbv xavoviwv roiavrrj' 10
1.p8]ji,ev
C. 2. t&v~] TOO C. 3. TtQmrov] a. B. 4.
B. 5. Tovg] rdg C. 6. tsGGu^ci] // corr. exA D 2
. 10. &nowe] corr. ex footfe B 3.
282 KAATAIOT HTOAEMAIOT
It
O oJ O oj O
I* 7|
13
oooooo
20*
-s-g
x* -"<fc a> *
^ U> u>
Is? 8 I-
MA0HMATIKHS 2TNTA3E&2 A' 283
O *I O *< O O"<0XO,o!Oxio>JO
*o 'o * V **51 "<*> *>^ X cJ* >
m- ot^co =L
O "< I* O * ^jo
2 *
<*>
.
QO
.
3 a
Q^T-rt 3 ?> 5> Or
284 KAATAIOT IITOAEMAIOT
s s
o oe o \<*e o r>e
10 wJ.
"S
.
!/><*>
^0 Jk-^
(jf-4
0"<JO ojootf.Or^o
55 a. 3.
4"& e,5
o < o x o >; o
ff 55il^^!
tit
411-
MA0HMATIKH2 STNTASESS A'. 285
JU>->-r s=-
ir
ox o x o
Ooj O<^ O O "J I O ^ O
<*'*'*
813 55 2 U> l/>
286 KAATAIOT nTOAEMAIOT
x *
<*> g~
<*!. U>
5L *
1l-l| r
3
8
tOi
5V"4
S 5
1-rs
s? ?
a 8 :*.
US- ?
|
I
o
i
MA0HMATIKH2 2TNTABE&S A 287
o it x o :*. x o
2 5
a3^ 06*
U1 ^ VS S
X* ~
a qe_ x.'o *
<*> <J>
* x a
_ .
ls afl M ^3
^'
288 KAATAIOT IITOAEMAIOT
I1 -
x *
*\**
a x
1/> <v w
sg-s,
r
o a
\ \
*\X
3 3
t-t?
X Uxfc
MA0HMATIKH2 A'. 289
>.u,
20 .
J.J. X
* =0 <*5 "0
xx ! -Vo ** rhr
??*'
22
x05
~I l
-^ >..
Ptolemaeus, ed. Heiberg. 19
290 KAATAIOT nTOAEMAIOT
1-
rvv stt
<J> 5 2
t rv
$ 2
*$
OOOjOOOOOO'OOO
9.W
1
1-en
*I a i/> a
8J 1 fc S
1
o 2
o <>: o .^ o i <J o
rv fS-l
MA0HMATIKH2 STNTASE&S A'.
$ S g 3 3
^3.
^ 2
HI
O X|5.
291
g.2.S d d g ^i5
jf * X6 *
O oi O >S O
ill:
2^-
O'XOl'XO'XlO'XO
^/> ^ O
tt
^ x^
*^^
*?
o ^rW >. <
292 KAATAIOT IITOAEMAIOT
<S-
Q
.
-<y 0.
3, X 5L X
x a oc.
O << I O <X O
RTt
g ga
*
S-H
rv
x 3.0
* x ax 3.
5.*'*"}V
oiOoilOoiO oJO<X;O<XO
S"x*
*2 ^-
g-
JJJt ij*
S
<*><*>
aLx<*><*><*>
x6} K- ss-
MA0HMATIKHS STNTASE&S A'. 293
9
U- I*I
It 4" 13<= to to to 1
294 KAATAIOT HTOAEMAIOT
s'. "On xal Bitl rtfg aithfig vrtofteGscog ri\g
vrjg tft avrd (paiv6^iva vtoiovGivr\
rs xar*
xai
(
EjtO[lVOV $8 rovroig rOV dsl^KL rOV T6 TQOTtOV KOI
5 rqv ityfoxorrjra ryg GfAyviaxiig dvcopaMag vvv
rbv Jtsgl rovrov hoyxccl itdvrss 6%sdbv oi TCQO f][i(bv
$ xr\ xccra rbv
%gvov aTt
10 rccvrcc dt|o^v, ort noilra,i nvcc xcci dfvrfyav avco-
fj (5^vri itaQa rag Jtgbg rbv
rag
dig v
avrdg r rag Gvvodovg xal rag
15 Ovro $ rr\ ra^ei rrjg artodi%G)g %()r]66ii&a dt,a
rb ravryv [iV avv rijg Ttgcbryg 6v^i7C7C^'y}ivrjg ye
avrfl 3idvror [lydap&g VQ&i]VKi, dvvaG&at,,
$ xal avv ryg dvrQag, 7iidtJ7tQ aitb r&v
x&v xA,fyG)v ^a^i^dvfrai^ natf ag ovdfv
-10 ytvrai didtpogov x rqg naga. rbv ijhiov
iitl d rqg 3t^orjyov^v^g dnodL^oraig rov &G)Qri[iarog cqpddotg, alg xal rbv
1. f'] om. AD. 2. ij] ri]v ij D, sed r^v del. 3.
AC, HUT' BD. 4. TOV] TO B. 6. TKvtr\g\ ncti T?)g ccvrfjg BD.7. J] ins. B 8D 2
. G%86v\ 6%ov C. 8. enifapri^res D,corr. D 2
. 9. &nov.ct6t(xri,Y.6v A, sed corr.; ccrtOKccTKCziKov D.
10. SfvT^occ C. 11. &TtOY.KTK6Ta.6is D, corr. D 2. 14. TS
Tag Tf D. Mg. rd$ T Tag ([^ (h. e. cvvodovg) D 2. 15.
g D. unodei&cos] anodet'^ecog r^v dwrtgav BC. 18. ccno]
s' ccno D. 19. ag] seq. ras. parua C. 21. sni] -C in ras. 2
litt. D. Ss] -i e corr. D. 23. IK^OVTS? D.
MA0HMATIKHS STNTASE&S A'. 295
xal avTol rgstg sxhsfyeis Gfhrjviccxdg ds^o^isv^ OGOV rs
TO itkstGTov didcpoQOV yivzrai nagd Tr\v ^e'tf^v %ivv\6iv
xal Trjv XCCTK TO ditoySLOTCUTov iitoyr\v, d)g Tfjg TOKXV-
Trjg dvcopaMccg xa& avTr)v ^soQOv^svrjg xal did Trg
XKT iltlKV^QV V7tO&S6G)S fbrOTfAoV^fV^ff, TG)V
avTcov rtdkiv 6o{iVG)v (pciivo^iBvcov xal did Ti]<3
XXVT()6Tr]TCC V7CO&0G)S> OiXlOTQOV d' CIV
dvG)(JLCifaG)V Tfl dVTQ$ Xttl JCCC^d TOV ijkiOV 6V{lflcCl-
OTt, [lVTOl TO. KVTK Ttdfav KCCi IvTKV^a yiVTCCl, 10
VCC di XdT()CCg T&V XXt,{lVG)V V7tO&0G)Vixav arf 1601 cbtfiv ^AA^'Aotg, &67tQ itl TOV rjhtov $-
oi %Q6voi T&V ditoxaTaGTaGfCdv d[icpoTQG)i'
T KCCTK rr\v dvco^ia^iccv xal Ti]g ngbg TOV did fte-
T&V t,G)dlG)V XV%A.OV ^(DOOV(JLVr]g^ dM.(X. XCil &67tQ 15
fill Trig Gf&rjvrjg UVLGOL T&V Aoycov ndfav [lovcov vito-
TCOV ccvTcbv, ovTcog uv xaTavor]6ainv in
Trig xxt,[ivr]g cbrAi} dva)[ittMag Tr^
1tOlOV[lVOl Tr)V Jtl6Xtyl,V. Jtldr) TOiVVV
6M\vri TtoifiTca Trjv itgbg TOV did [isGcov T&V tydicov 20
xvxkov dTtoxaTdGTKGiv Trig agog Tr]v V7toxi[ivr]v dvo-
v, v Totg Itioig %Q6voig dyhovoTi, xciTa plv Trjv
sitixvxkov VTtQfttGiv pti'tpva. r}XCCTK TO opoiov
7tQKpQt,av 6 7tixvxhog dd xivrjd-rJGMai, nl TOV
1. rt TO] corr. ex TO xe D 2. 3. fno^v} AD 2
,
BCD. 6. cpcctvo^evcov] om. C. 7. o6ca6r(>oi'] corr. ex
oixiOTjTa D, mg. yp. otxftoTfpov. 9. T$] bv ry D. ini-
Gv[iaivov6r] D. 10. ftf'i/TOt tec ccvra] (JLSV TQIKVTU C. 12.
Y.&V} post r'as. 1 litt. C. 14. TOV] T&V C. 16. povov ndhv D.
18. a7tU]$] corr. ex aitliog D 2. 19. tniidri] corr. ex faei D.
Ta^ior] A, Tcc%iov BCD. 20. TOV] T&V C. 23. opoiov]corr. ex O^IOLKV D 2
. 24. ini} supra scr. D 2.
296 KAATAIOT IITOAEMAIOT
KvrQOV x& ^cpdianti KVK&OV Tvjs vjtb tfjs
rbv BTtiKVK^ov ajto^a^avo^vrjg ,iitl $ rife Kar K-
Kvroor^ra % plv as^vrj rrjv bpoiav rf\ Bid rov Biti-
KVK^OV Kal 7tl rov iKKevrgov xivrj&tJGsrai, 7tQi(pe-
5 $iav, b ds KKvrQOs 7tl ra avra rr\ 6^tjvri iteQi ro
usvrQov rov ^codianov rrjkixavrrjV) fiMxrj /itov 6rlv
'fjKara (ifjuos itaQodog rijs Kara rr^v avG)[iaMav, rovr-
i6nvfj yi,vo[ivr] rov 6[ioxvrQOv 7tQi(pQi,a rijg rov
itiKVKkov' ovrcog yag av ov [i6vov at r&v Adycov,
10 AA xal ai rcbv %oovcov xaroas r&v xivrjGfav b{ioi6-
V apcporeQais ralg VTto&faeGiv diatic
rovrcov dfj Kara rb aKokovftov avro&w
6 [iv b[i6Kvroos r<3 dia {istiav rav
b 4BF 7Col KtvrQov ro A Kal 8id-
15 ILMQOV rrjv Ad, b $ TCLKVK^OS b EZ 7Col Ksvrgov
rb P. vitoKfiG&G) dS) or {t,v rjv b TCLKVK^OS Kara rb
A, Kalv\ 6A,ijvr] Kara rb E anoyfiov rov TCIKVKA,OV
yzyzvriiiitvri, iv r& facp dl %o.6v<p b [iv 7cCxvKho$ rr\v
AT 7tQi(pQiav dtfA^At>0'c6g, rjd 0^,tjvrj rr\v J5JZ,
20 Kal 7t&v%&G)6av ai J5Jz/, FZ. Kal jcd {iia)v <5rlv
TIKara rb QIIOIOV fj
AT 7CQt,(pOia ri\ EZ, aiti-
Aij<p&G) fjBF bpoia ry EZ, Kal tt&v%&G) f]
B z/.
on [iv ovv v r& facj %QOVG) Kal b KKvroos ryv
1. xvnAov] om. D. t% (pr.)] corr. ex x& D 9. 3. ini-
v.vv.lov] y.vy.1.ov C. 5. W] 8' D. 9. T&V] r- e corr. D 2.
11. vno&sGBGi D. Sicc6woivro] -01- e corr. D. 13. TW]corr. ex r&v D. tcav] corr. ex TOV A. 14. 6] om. D. 15.
AJ] -A e corr. D. 8t\ d' D. 17. V.CCTO. TO] snl rov D.18. Vsvr][ivri C. tv\ h 6s D. ds~\ om. D. 19. 8if-lrr
-9-cbg D, con*. D 2. 20. iiti&v%Q-(o<>civ BC. at Ez/] ij
rs
EFJ KCU i] D. 21. Tfjg] corr. ex TIJV C 2. a7cedr}(p&ca
-
22. EZ] supra scr. D. 22. rf?] rrjs BC. EZ] EZ 1 D.
tae&vlfaoi A, lTtisv%fro BC, corr. C 2. 23. ort] post ras. 1
litt. C. fynsvTQOs D, corr. D 2. TTJ'V] rj] seq. ras. C.
MAOHMATIKHS STNTASE&S A'. 297
vjtb A4B y&vCav Tijs TGJV rtccgodov a[KporeQ(X)v VXSQ-xccl ydyovsv CCVTOV r6 rs XSVTQOV KOI
TO aitoyeiov iitl Tijs
J3z/, (pavsQov. TOV-
rov d' OVTC3Q %ov- 5
rog xffa&G) tr\ TZfay fj AH, xal 7t-
ZH, xal
H, dia-
T& HZ, 10
6 Zxxsv-
6 Z.on xccl 6
f)
6 CIVTOS 0Tcci, r<p
ds iv\v V7t6&6i,
f'GTCU, TOVTBGTW 6{lOia KOIJ)
TV EZ.iti yap i'0rj itiriv
fyvjtb
EFZ, TtccQccUyMs ten
*ai e<5TW far] r]FZ TTJ
far] T i<5xi
ZH
agogxal KCCT& 15
TO Z 6rnislov
Z 3tQl,<pQlCC 0Tat,
B^JF y&vicc rfj vito
rZ-Tfj AH [Eucl. I, 28]. 20
xccl r]ZH a$cc TTJ
[Eucl. I, 33], xal 6
Hd Adyog 6 ambs T& Tr]s 4F ngbs FZ.
1. AJB~] corr. ex ABJ D 2. ycoviav] yavicc seq. ras. C.
2. ti\ om. D. 6. E*v.Ei6&(o D. rfj] rfji, corr. ex tf\ A,
Tfj C. 7. JH] in ras. A 4,HJ D. xat 8. ZH] om. D.
7. 3*tge^g4to BC. 9. SiuGTriiLctTi ]xal diccGrijficcri, D. 11.
6] om. D. 12. Z] Z wi bteevx(o 17 ZH ktffprfrta$e f] ZB (mut. in 4B] snl TO & D. 16. TUVT^V] corr. ex
Tciv-tarriv D. 17. OT<U nsQiysQi-Ltt D. 20. ETZ] ZTE D.
i] AH rfj rZ D. 21. xat (pr.)] ras. 1 litt. D. <mv]sWtv ^g xa/ D, -v del. D 2
. r) TZ T7j JH] om. D. ZH]HZ D. 23. Tr^dg (pr.)] nqbs rtjv D.
'
TW] SGTL xti D.
298 KAATAIOT HTOAEMAIOT
7cd TtaQccMrjkos 6nvfj4F TTJ HZ, fay i<5x\v
J)vnb F4B y&vCa, rf? vnb ZH [Eucl. I, 29]. vxe-
XLTO ds xal rj vnb FJB rfj vnb EFZ fay tiers xal
fjZ 7tQt,(pQl,a T\\ EZ O^lOiCC 0TW. V Ttt fa& CCQO.
5 %QOVG) xa&' SXKTSQCCV rcov vjto&fas&v Kara TO Z
6r][iiov yfyovw ^ (?fA^V^, 7ti8tf7t() avrrj ply xv\v rs
EZ rov IniKVKkov xccl ri]v Z rov IKKBVXQOV itQi-
TO d TOV iiti-
XVX&OV XVTQOV TJJV AF, TO dl TOV XXVTQOV Tr}V
10 AB v7tQO%i}v T^g AFn^bg Tijv EZ' oitfp $i
OTL de, KKV opoioi ftd-
vov (btiiv 01 Adyoi ncd[ir]
faOi [irJTS KVTOi ^T 6 X-
XVTQOS TG> 6[IOXVTQG}, TO
15 CCVTO Tt&klV 6VlLfittCvi, Xttl
OVTK>S
XCCTQCC TK)V
Xttl <JTG) 6(A
20 T& dltt HB6G)V TG)V
6 ABF vital XSVTQOV TO z/ y.al dicc^TQov Trjv
,b $ enfavxhoz b EZ nsQi XBVTQOV TO F, ^ ^
TO Z, xal ndkiv b [iev f'xxfVTQog xvxkog b
H&K 7tol XSVTQOV TO A XCCi
1. s'jm] corr. ex inC A. 4 F] FJ D. 2. vnintiTO 6s
v.a.1 i] vnb PzlB] CCQCC D, corr. mg. D a deleto KQK. 3.i'cri]
seq. ras. 3 litt. D. 4. Z@] f)Z D. tW A. 6. avrr^v D.9. fyxtvTQov D, corr. D 2
. 11. Ss, v.av\ COIT. ex dev A. 12.
firy] ins. D 8. 13. fyv,evrgog D, corr. D 2
. 14. TO ccvro] mut.in to. ccvrd D 2
. 16. r](iLv] post ras. 1 litt. A. 22. r) ds
c&r\vri rb Z] oin. D. 23. ce^vi A. 24. H&K1 corr. exHK& D 5
. 0AM] @A D.
MA0HMATIKHS STNTASE&S A'. 299
(p
iv rc3
TO tov <pdiaxov xevtQOv fatco to M, to de K'
17 6hrivrj, xal nv%&G)6av xst plv aC A TE,
z/Z, v&dd d a[ HM, KM, KA,d b tils AT ngbs TE6 avtbs v& tils A ngbs AM, 5
xal XXt,vrJ6d'a
vnb AAT ywviav xalf]
<S-
^vri ndhv t^v vnb ETZ, 6
df xxvtQos vyv vnb HM0 10
y&viccv xalfj 0^vrj ndhv
trjv vnb AK.I'Grj aga 6tl
tovs vnoxi[ivovs i&v xivi]0G)V Aoyovg ^ y&v
ETZ y&vCtt ty vnb AK, r)dl vnb AAT <5vv-
rri t vnb HM& xal rr\ vnb &AK. 15
tovtov d ovt&s %ovto$ Kiy<a, oti nakw xa&
XatQaV t&V Vnod"6G)V V tG) l'<303 XQOVG) tfjV I'GrjV
6A.rjvr] (pavri<5tai di&r]A.vd'via, tovt-
6tiv oti itiri titlv rjvnb AA 2, ycovCa tfj vnb HMK,
Infidrj xata [ilv xv\v aQiffiv tils dia6td0G)s sxt t&v 20
anoysi&v ovtia17 ^^nvrl xata t&v AA xal MH v-
&iG)v <pawto, xata dl to t&os snl t&v Z xal Kov6a dia t&v Zz/, MK.
2. WML C, corr. C 2. 3. TZ, z^Z] *ca FZ xai JZ
D. de] BCD 2,om. AD. KM] xal KM D. KA]
KA C, xat KA D. 4. SE] ZE D. 6. XSVLG&COGUV C, corr. C 8.
8. AJF] in ras. A 4. 9. nctiiv] om. D. 10. ^8 SKKEVTQOS]
8' fMevrgos D J,8s XEVTQOS D. HM&] H- e corr. D. 12.
WD. 14. rjj] rjv C. 15. HM@])
&AK D. AK]HM& D. 19. OTI] supra scr. D 2. latv\ D, supra scr.
at D 2. AJZ] AJ- renouat. A 4
(oorr. ex AJ?]. 20. $ni~\
cog inC D. 21. ttpccwf-To tt&ei&v D. 23. OVGK MK]om. D.
300 KAATAIOT HTOAEMAIOT
df] xarQa rcbv &K xal EZxdfav r] BF, xai 3tesv%d'G) j] BJ. ensl rot-
vvv 6riv, ag f]4F agog FZ, r\
KA ngbg AM^ xccl
itQi foag y&viag rag agog rotg F, A Grjiisioig ccC
5 rtfavQal ccvdAoyoV) faoy&viov 0ri, to F4Z rgiycavov
i& KAM tQiy&VG)) nal VTIO rag dvahoyov nfovgag ai
ywviai facet [Eucl. VI, 6]' 017 KQCC farlv % vnb FZ4ycovta if) VTib AMK. aAAa xal % vnbBzIZ rr) vnb FZ4fay [Eucl. I
? 29] dta rb yta^K^yj^ovg slvcci, rag FZ,10 BJ [Eucl. I, 27] foav VTCOXS^EVCOV r&v VTtb ZFE>B4F y&vicbv for] KQCC xal
r]vnb Z4B ycovicc rf] vitb
AMK. vnoKSiTKi ds nolr]vnb A4B Tr]g v
TG)V M,Vr\6G3V XT} VTtb HM TOV XXVtQOV
for]' Kal ohrj ago, r]vitb A4Z for] 6rlv o'A?; T\\ vnb
15 KMH' OTtEQ 7tQOXlTO
g'. 'A7todi%i,g rrjg TCQ&rrig xal aithr}g
rrjg 6Arjvr]g.
Tavxcc ILEV ovv ft%^t TOGOVT&V r][iiv
^ij^O-co, 3toir]66iiE&a d rr]v aTtodf^v rrjg
20 Gfkrjviaxrjg av&iiaMag itl rrjg KU.T titiKVKkov VTCO&E-
2. EF] TE D. BJ] corr. ex BTzf D 2. 3. r] KA]
jtat r) KA D. 4. T, A] A xai T D. at ntevQctl ccvcttoyov]om. D. 5. ianv D, corr. D 2
. 6. KAM] AKM D. vno]ai VTCO D. at] om. D. 8. ycoviu] ycoiviK C. Suprapr. vno ras. D. TZz/] corr. ex FJZ B 3
,FZ4 >IV D.
9. rag'] corr. ex zd D 2. TZ] post ras. 1 litt. D. 10.
B4] v.cii BJ D. 11. BJT] %al vno B4T D. KQK] torlv
KQU D. Z^/B] Z et B in ras. D 2. TJJ] supra scr. D 2
.
12. vntneno D. AJB] corr. ex ABJ D 2. 14. ftrrj
D. %] ol- in ras. D 2. 15. KMH] -H e corr. C 2
,HMK IGTLV tVrj D. 16. 5'] mg. AB, om. CD. 18. ngo-A, corr. A 1
.
MA0HMATIKHS STNTAEE&2 A'. 301
til 7JV iTtO^LV KITIKV,TO JiV JtQ&TOV Ktp' G)V
ccQ%caoTttTcov sxtefysav TQitii Tatg
doxovGcug avu'ys'yQdcp&ai, 0vy%Qri6a^vo^ (p%ijg ds xal
ccTtb T&V v T& vvv fflovG) TQitil itA^iv tcclg vy' fin&v
avt&v axQi,p6tara tSTrjQrjiisvcus' ovt&s yaQ rjts 5
,dt' o0ov ye [idfaGtct dvvcttbv
xal aM&s (pavsgbv eGtcu, diori, TO
re TtKQct r^v KV&pccMccv didyoQOv TO CCVTO % a[iq)OT-
QGJV T&V dl%0)V fyytfTCt K7(0^6TCC^ KKlf}
TG)V [l6G)V
KKTO, 10
TQCCV dioQ&otiw 7ti,6vva'yo[ivr]. Jtobg drj TJJV
xctl cog %&&' avTrjv &G)QOV[ivr)g
TOV TQOTtOV TOVTOV. 15
T Xttl V TK> KVTGJ 7tt,7lda} Xi[lVOS TG)
dia [i6G)v r&v gcodttov, jrpog dl TOVTOV TQOS tynrnki-
[ivos avccho'y&s TTJ rty&MOT'rjTi, rijg KCCTK TC^KTOS xccoo-
dov Trig 6A,ijvrjs jtoi,q)Q6[ivos oftaAwg ig TCC xoo- 20
7Col TO KSVTQOV TOV dia [ifawv T&V Jcodtov
T06QVTOV, O00V i\XCCTCC TC^KTOg XLWTjGig VTtSQ-
Trig XCCTK iiijxog. iitl \LBV ovv TOV Ao|oi) TOVTOV
{lVOV VTtOTi&yi&a TOV XCCA,OVILVOV Tti-
xvxhov o^ia^&g itdAiv fig Ta itoiiva, TOV xotipov axo- 25
T?I xccTa xAuTog aitoxaTa<5TK6i, rJTig
corr. ex SLTIOL^V D. 2. l>t|^ti/>fa)v corr. exA 1
. 5. yap] D, yug &v ABC. 6. ys] D, corr. exrs B, re AC. 10. &el] om. D. 12. Sri] Ss D. 13. eavvyv D.
17. xftftfvoff] om. D. 18. f'yxfx^t^vog] AC 2D 2, ifHtnlutf^vos
BC (-G- del. B), %SV.UIIEVOS D. 19. ccvcclioyos C. 23. rovtovrov loov D. 25. snofisvcc] -ofiev- e corr. D 2
.
302 KAATAIOT nTOAEMAIOT
avrbv rbv dia {isG&v r&v Jepdtcav
xarcc [lijxog itoislrai xwriGiv, sitl ds avrov rov
jv &g xccra rr^v ciitoysi
Qi,av fig ra TtQorjyov^isva rov xoGpov rr\v
5 noioviisvriv axohovd'&s rfj rijg av
0t. TtQOS ptVTOi TY}V VTtOKEi^BVTflV dsl&V OvdfV CCV
atjrs rijc;dice rb
rov Gshyviax
ovdspiag cc^io^oyov diaytooas rfj xara
10 firJKog jtaoodG) jtoo6>
yLvo[ivr]s BK r^g sitl rotiovrov
G3v roivvv slkrppKiLSv ttahcucbv roicov exhsfye&v fa
r&v iv BccpvA&vi, rsryorjiisvav, j] per Tto&rr) avays-
yoaTtrca ysyovvla rep Ttocora) srsi Maodoxs^iTtddov
15 Alyvitriovs (&&& x&' stg rqv X'. riQ^
psra ryv dvaroArjv fttag ftoccg Cxav&s TCKQ-
KOI s&tei'Jtsv oAr]. sxsidrj ovv 6 r
rcc 6%ara r&v 'Ift&vcov r\v ,KOI y vvt, tbo&v
vCbv i{$ k'yyiGra, f] {isv CCQI^I rijg fafafyscoc; eysvsro
20 d^Aovdrt nob d /_' cao&v i6y[iQi,vG)v rov
6 $ [isGog %o6vog, jtidiJ7tso rfteia i\v y
nob/3 /.' mo&v. iv 'j4A.,KvdQia (), 7tidnJ7CQ nobg
rbv di ccvrr}g iieGrnifiQivbv rag ctiaiaLag 7to%ag 6vvi-
i df b dt avrrjg ^0rj^iftoi,vbg rov
1. rov] ins. D 2. ^stogov^v^v C. 2. noift D.
om. D. 5, itoioviisvr) B. 7. dia] v.ccrd D. 8.
^o|cb(jfoos] supra scr. D 2. 11. {^xJUtocK D. Deinde add.
ccQ%ri :<^> D, : &Q%ij '.^ D 2. 14. ysyovviui D. MagSo-
vevTrddov D, corr. D 2. 15. ob^] e corr. D 2
. x^'] -&' in
ras. D 3. 17. l&Uitiv A. 18. fy&vm C. 19. tyivsTo]
ytyovtv D, -v del. D 2. 20. //] corr. ex g D 2
; mg. (H D.
21. whipis A, corr. A 1. 22.
/_'] dvo ijfiicv D. 23. tag]-dg e corr. D 2
. lno%dg] mg. D 2.
MA0HMATIKHS ZTNTASE&S A'. 303
did BafivA&vog i\^iiGi xal TQITG) syyitira {lias cooccg
,6 ptGos %aovog yyovv Tf}
nob y xal y' cogfbv faiHUQW&v TOV
vvxTiov, na& tjv &QCCV 6 ijhos xara TOVQ
vovg r^ilv rti,A.oyi6nov$ snsfysv aKQifiCbs t&v 'I%&vcov 5
floras nd L' syyiGta.
r\ds dsvTsga rav ixkefyenv dvctysyQanrai, ysyo-
vvia TGI dfvrsQG) ereu TOV avrov MaQdox[Middov xax
Alyvnriovs (dcafr ir[ els rrjv i&. e&teute de, cpqeiv,
dnb v6rov daxtvAovs y avrov TOV ILZGOVVXTIOV. ens! 10
ovv 6 psGog XQOVOS iv BccflvA&vi (pawsTcci, ysyovfog
HUX ccvrb rb [teGovvxTiov, iv 'Ate^avdQGiK oysttsi ys-
yovtvcci, nob /.' nctl y' peoovs pices woas TOV [tsGo-
vvKTiov, xa&>
r^v CVQCCV 6 fjAtog dxetysv dxoiflcbs T&V
'I%d"vcc)v iioioas ly /_' 6'. 15
f)ds y' Tfbv sxfafys&v avaysyQttiiTai ysyovvla rc5
avT& dfVTeQG) Tt, TOV Mccodoxs^iTtddov XUT'
TLOVS (&a[iLVG)d' t,
f
fig rfv tg'. yo&TO df,
TOV f\iifaov<s. 7tidri ovv 6 ijAios ^^ rfv 20
v t nctQ&tVQV, TO
Tec'
2. ytyoviv] -v del. D 2. 3. y] mut. in r* A 4
. y'] jf
mut. in r A 4
, TQLTOV D, rgfaov D 2; TCQO rgitov v.a.1 rqi&v WQ&V
mg. A 4. 5. Inefysv] corr. ex in/l%ov D 2
. 8. Post tov del.
SfvT^Qov D. MccQtioKeiiTtddov'l -do- in ras. A, -p- corr. ex
v D 2. 9. i&lfinev D, feline D 2
. 10. avrov] TIQO D. 11.
(fctivtrcii ysyovcbg] yiyovEv cbg cpccivercci seq. ras. 2 litt. D.
12. oqpalft] ncchv dgjft'Aft D. 14. 7tet%v ccKQip&g 6 ijliog D.
17. dsvTSQOj] B B, a post ras. 1 litt. D. MccgSo-ufvndSov D.
19. I^AtMMv] mut. in st-sUnsv D 8. 20. TJ^LGOVS] corr. ex
A 1. 21. IIctQ&evov] TICXQVOV C, ut saepius. 22. BKV-
-i add. D 2. IK] i- renouat. D 2
.
304 KAATAIOT UTOAEMAIOT
TO ds ijiit,6v 1% vvxrbs s L' &Q&V xccl
CCQCC rijs sxAsfysas ysyovs ago Jtsvre
v rov [isGovvxriov did TO para rrjv dvaro-
,6 ds psGos XQOVOS itgb y L' cbp&v, sjtei-
5 dijrtSQ 6 nag XQOVOS rov TrjfaxovTov psyd&ovq rijg
yti6xorij<S6G)s tQicbv syyi^rcc COQCDV ocpsttsi, ysyovevai.
sv 'j4A.t>ccvdQi(x nakiv KQK 6 [isGog %()6vos r^g exfai-
il>SG)g aTtstskeG&ri ICQO d KKL y' G)QK>V itirnLEQiv&v rov
IIE60VVXTIOV, KK& 1JV &QKV 6 ^AfcO SttSfySV O.KQifiG)<S
10 rrjg nag&svov [ioiQcc$ y d' syyitircc.
v ovv, ort dnb [isv rov fif'tfov %QOVOV rrjs
ni' vbv rrlg devrfyKS neKCvritai 6
xalv\ ^e^tjvrj^ {letf ohovg xvxkovg [io-
TII& 7?, ccTtb ds rov rijs dsvrsgccs
15 %QOVOV 7tl rov ri]s rqirriQ [IOLQUS Q%& A. AAa xal
j]rtibv [isra^v ^QOVGOV did<5ra,6i KTCO psv rov
snl rov dsvrsQOv ftfiSQas it^d%Bi rvd xal CDQCCS
USQivag ccTthcos psv ovr&g &sa)DOv<5i,v dvo iJiuGv,
ds rov rcbv 6[iccA.G)v vv^d"rj^iso(DV STtihoyiGiibv dvo
20 ij[it,6v Ttsvrsxcudsxarov., dnb 3s rov dsvrsgov snl rbv
rgi'rov fftiBQCcs QOZ xccl COQCCS farjpSQivas aitAwg [isv
x/_', dxQifl&s ds x Tts^itrov. xivslrca ds 6ft-
agog yaQ rbv roGovrov %QOVOV ovdsvl
dtot(?ft, xav rats tivvsyyvg rcov
2. nivts\ s BD. 4. r)g%&ai] corr. ex dai D 2. 6 -
C.^
mg. A 1. 8. Kitors'keGft'Ji C. 9. S7ti%v 6 ijkios D.
11. rov] ins. D 2. 15. I] ins. D 2
. Post xcu del. fast D 2.
16. Sid<5tKGi<s\ ante GT ras. 1 litt. D. Ttgrnrov] a B,,
TOV C. 17. TOV] corr. ex TO A 1
, rrjv D. dsvrsQccv D. 18.
dvoijfiicv'] ft [_' BD. 20. ij[LL6v] om. D, /.' BD 2
. m-vrs-
is D, is" D 8;a {_ Is supra scr. D 3
. 24.
D, corr. D 8. Gvv\syyvg A, Gv\veyyvs A 1
.
MA0HMATIKHS 2TNTABE&S A'.
V tth
305
l cbgcug i6rnLQi,vaig /3 /_' IB' ccvco^ia^ag [isv
okovg xvxAovg
v $ ralg $o<5
r? x, prpiovg d [toiQccg rjie
K
,ai df rr^g dvrQag 10
# xcctii, rr\g [iforjg
- 5
fitfavxhog 6 ABF^ 15
rijg
OV fV V
rijg 6^tjvrjg inl
rov ETtiKVKkov yLt<x,fiK6ig &g onto rov B iitl rb A xal
b rov A 7tl rb JT ivoifvr &6r riv iv ATB
rb 20
7tl
rr\g rtQGyrrjg sxfafyf&g 25
V ov6av rg KB 7tQO<5n%'8vat, rfj
1. &KoJtt*0ifari D a, &*olov&j*n ABCD. 3. olovg] -I- in
ras. C. vu\ v$? D. 5. (JLOLQCCS (pr.)] om. BC. 8e]ins. D 2
. fioiQag (alt.)] om. D. 14. TOVTOV] xovzcov ovv D.
16. 86T(o] vitOKi-iG&aj D. xa#'] e corr. D 2. 22. aeMvrig A.
23. xai a^ro rov A] supra scr. C 2. 24. T] corr. ex r^trco C 2
.
26. x?] mut. in nd C 2,%^ D. Tr^offtrtO'fWt] post -- ras. 3 litt. D.
Ptolemaeus, ed. Heiberg. 20
306 KAATAIOT IITOAEMAIOT
[toioag y xd, rqv $ BAT, r^v XEXivqrcci, axb
rr\g dsvtSQccs exfafys&s iril rqv rgirrjv,
~gv xs K(paiQlv tils iisGys poioag o AJ, SIK rovro
xal ryv plv onto rov B sitl rb A ndgodov5 ovtiav vy Af cupaigslv r^g peGris VMS ccvras
xd r^v de aitb rov A 7tl rb Fori, ovv ov
dvvarbv eitl rijg BATQiccg rb itegiyewrarov elvau rov
10 eTtixvxkoV) (pavegbv ex rov dcp-
\v re avrqv vTtd^eiv xal
flliixvxhiov rijg
xara rb
enel $ TtKvr&g eitl rijg
15 BET, iA,rj(p&a) rb xtvrQov rov re
dia p6G)v r&v fcodttoz/ xvxkov xal
rov yegovrog rb xwroov rov eitixvxhov xal eGrct rb 4,xal jt^v%d'C()6av an' avrov 7tl ra rcbv y exkefye&v
Gripeta ev&elai at 4 A, 4EB, 4 JT. xa&okov roCvvv,r
iva
20 xal Jtobg rag bpoiag deC^eug evEitifiokov rty peray&yriv
rov frfcoorifiarog itoico^eQ'a^ edv re dia rijg xar eitCxvxkov
vjto&<jG)g avrag cog vvv deixvvcopev edv re 8ia rijg xar7
exxevrooryra rov 4 Xvroov rore evrbg
\iia \Jiev rcov
25
2. r^trrji;] supra scr. D 2. 3. QV] seq. ras. 1 litt. D. 6.
ds~\ re D. 7. ^] jit-e corr. D 2
, pfl BC, corr. C 2. 11. rs
Ss D, sed eras. 14. tnef] corr. ex Ini C 2, InsiS^ D. 15.
BET] corr. ex BT A 1,PEE D. 19. JEB] wl JEB wi
seq. ras. 1 litt. D. 20. evi-nipolov] mut. in fvBit^olov D 2.
21. noica^Q'ci] A, corr. ex noiovpE&a D 2,
7tOi/
r]6co^Q'ci BC.22. 8siv.vv(o^fv cog vvv D. 24. ft/a] corr. ex (iLccg D.
MA0HMATIKHS STNTASE&2 A'. 307
it\ rb Edjtb rov B rijs dsvrsoccs fafatifjecog, rd ds koma dvo
6r][ita r&v extefys&v srti&vyvma) svd-sla CDS v&dds
t\ AT, xal ditb tils ywopwys ropijs vnb rijs s^ftsft^-
fisvrjS) olov rov E, e7ti&vyvv6d'G)6ccv psv snl rd koiitct 5
dvo Gypsta ev&eiai, cog sv&dds at EA, ET,ds ayfa&Mdccv sal rag onto rcov kont&v dvo
7tl rb rov ^codiaxov usvraov smfevyvviisvccsM plv tyy AA ri EZ, M ds ryv F4 % EH, xai
srt anb rov srsoov r&v sior][isvK)v dvo Grjiisicov, cbg 10
sv&dds catb rov F, xd&sros a'yeGd'G) STtl rqv dab rov
srsoov avr&V) olov rov A, STtl rqv ysvopsvrjv VTCO rijs
disxfiohiis 7csoi,66^v ro^v, olov rb E, smfevx&stGav
sv&stav, &s sv&dds iril rrp AE i\F' drto&sv yaa
av %or)6G)[isd'cc rr\ ri}s xctra /
yQcc(pijs ctywyfi, rovs ccvrovs 15
fxflccivovrccs Aoyovs dux rcov rijs dst&cos
rijs Mhoyijs nobs rb v%or]6rov p6vov xarcc-
7tl roivvvfjBA jtsaicpsosia vitorsivovGcc
rov did ii6&v r&v fydiov nvukov poious y xd, sty 20
av xcdi\ vitb B4A y&viK nabs t& xsvraa avrov
ovtia, of
i(Qv [iv i6iv CCL d ood'al r, roiovrov y ^d,
OLCOV ds at dvo oafral r^ roiovr&v ? prj. &<3rs nut
1. diKpaM.oii8vr}v (post ras. paruam) s'^o/ifv (post o ras. 1
litt.) avTO&fv D. 5. olov] tv&stces olov D. ra, konta\ -a fol-
ia ras. minore D 3. 6. sv&sfai] -stcti e corr. D 2
. at] ^ rs D.
EA] AE C, EA*ctiri D. 9. ini (pr.)] post ras. 3 litt. D.
jitsV] supra scr. D 2. 8fr] ins. D 2
. 12. A~] e corr. D 2seq.
ras. 1 litt. 13. rb E] supra scr. D 2. 7te&v%d'i6av D,
corr. D 2. 14. r<9] e corr. D 2
. 16. BV^GCO^BV BC. Myovs]-ov<; in ras. 2 litt. D 2
. 21. ctvrov] om. D, rov avrov suprascr. D 2
. 22. OIG>V\ olov CD, corr. D 2. at] om. A. 23.
ol'(ov] corr. ex olov I)2
. dvo] B B.
20*
308 KAATAIOT HTOAEMAIOT
ij fti> itl rr}g EZ sv&stag TteQiysQEia TQIOVT&V i jitiy,
olov 6 itol TO 4EZ oo&o'y&viov yoa<p6[ivos xvx^og
f)EZ v&ia TOIOVTCW o,
X. 6^oto>, f'jtfl$\BA
v 6Ttv vy As, sft? v xat17
#6 5?^ yewCo,
OV0K
d avrcbv i\v xalfj
iiitb B4A[Eucl. I, 32] CCQCC r\
i)7tb EAZ[i. &6r Kal
i] pv itl
10 Trig EZ itQLCpBQia TOLOVTCOV faxlv ^ ftf, oicov 6 Jt$l
TO AEZ QQ&o'ycaviov xvuhog T|, ufai] dfjEZ v-
TQIOVTCDV[l Kf\ A, OtW <3TLV % EA V7tOTlVOV<3CC
' xal OLCOV 6Tlv CCQCC i\ plv EZ eti&fia 5 ^ o, 17tie
TOIOVT&V 6T<u xalf)AE v&ta 1% v A/3.
15 TtK&lV) 7tLr\ BAT 7tQi(pQia VltOTLVL TOV
lioiQccg o AJ, i'rjav xal
v\ VTCO BAT y&vicx, it
XVTQGJ TOV CCVTOV OV6d^ olov [lV l6iV CCi d
T|, TOLOVT&V O Af, OIG)V $ Kl SvO OQ&al T%, TOLOV-
TOV a id. &6T xalf\ fisv iitl r^g EH 7tQi,<pQi,a
20 TOIOVTCOV 6TW a fcd, OiCDV 6 TtQi TO AEH1. g] iarlv s D. 2. oi<av] corr. ex olov D 2
. 3. o] 6
ABC, om. D. 5. tcriv} comp. B, -v eras. D. sir] 6. fa]
mg. D 2. 6. oi'a>v] corr. ex olov D 2
. 8. EAZ] EAJ D.
9. sanv] comp. B, -v del. D 2. siti] corr. ex vno C 2
. 10.
EZ] EZ fu-9-fiag D. sartV] comp. B, -v del. D 2. oioov]
corr. ex ofov D 2. 11. ^EZ] A, E^Z BCD 2
,AZ D. _12.
corr. ex olov D 2. E-4] -^ in ras. A 4
. 13. f o] o A,
o BC, g D. 14. Ez/] zfE Idthfrri D. fdt<*] |r^ D,-v eras. ^E] E^4 D. t-v&siai D, corr. D 2
. 16. o] seq.ras. 34 litt. D.
17] supra scr. D 2. Bz/T] corr. ex EA D 2
.
ycovicc] -i- ins. A 4. TOJ] TO D, corr. D 2
. 17. Y.EVTQOV D,corr. D 2
. TOV avrov] supra scr. D 8. OVGUV D, sed -v eras.
18. o] in ras. D. 19. a id] corr. ex cci 8' D 2.
D, -g eras. 20. tQiycovov] oQ&oymviov D.
MA0HMATIKHS STNTAgESiS A'. 309
avrri de fjEH sv&eta roiovrcov a it, A,
titlv
BAT 7tQi(p^ia {lOlQWV 0TIV ^V X5, sify aV XalJ]
vnb BET y&via, jroog t$ itQi<pQia ov6a roiovr&v
~QV xg, 0603V sfalv at dvo oo&al v%. rcov d% avr&v 5
^v xalr\vxb EAT ynvtcc a ~id' xccl lom^ [Eucl. \ 32]
ccga j]vitb ETA rcov avtav stitiv QH& ip. coGre xai
?l iilv sill rijs EH itQiq>SQicc roiovr&v tirlv QII& ij8,
otcov 6 TtfQl to FEH dgftoyaviov KVK^OS r|, avri\ de
fjEH v&ia rocovTfov ^n jUa xa, oicov 6rlv 17
TE 10
vitorivov6a QK' xal oicsv sGtlv agct ^ ^ V EH v-
&ia a 1% A, ^ dl AE ^x, roiovrcov i&xlv rjFE v-
K x wy. r&v $ ctvr&v dt%&rj xal i\EA sv-
fj AT jtQi(pQia poiQcbv fdffy&r] gg 15
i/, elrj av xali]vnb AEF y&via rtgbg rr\ 7tQi<pQSia
g ^VK, olcov sfalv at dvo ogftal T%.
fj [lV 7tl tr\$ r 7CQL(fQia TOIOVTCOV
6rlv gg va^ ol'eov 6 7C^l rb PE& rgCyczvov r|, ^ ^iitl rij$ E 7tQHpQia t&v AoiJt&v [Eucl. III
7 31] tg 20
TO rjiiixvxfaov ity ft' xal ai v7tOTivov6ai aga avrag
v&lai, ftiovraii\ plv F TOLOVTCOV 7t& jiig td,
3. 86TLv] comp. B, -v eras. D. 4. ovocu D. 5. tie] 8' D.
7. EFJ] ETJ yatvta D. eGTiv] comp. B, -v eras. D. 8.
TCfQicpsQsLas D, -s eras. 9. 6] supra scr. D 2. 10. EH] E-
e corr. in scrib. C. xa] -a e corr. D 2. 11. ^x] -x e
corr. D 2. xat] corr. ex xot C 2
. 12.if] D, seq. ras. 1 litt. A,
Iri BC. Post z/E del. iSti^j] D 2. IdrtV] comp. B, mut.
in icxi xat D 2. 13. x] supra scr. D 2
. de] om. D, <?MD 2.
15. Ante Tra^tv eras, s D. 16. 17]om. A. 17. dvo] ]? B.
19. Qg] corr. ex 9 D 2. r^tycovoo'] d^oycbvioi' xvxAog D.
8s] d' D. 20. ni-QKpsQeiK] om. D. 21. jty F] con*, ex
ny o A 1
, ny& CD.
310 KAATAIOT IITOAEMAIOT
TE V7tOTlVOV6CC 03C , f]^ E r^v CCVTG)V
oO* A vs. xal oicov CCQK 6T\vfjTE ev&ela a % xy,
TOIOVTOV h'tixai xcclf] psv T sv&EZa a o 77, f]
d
E OIIOL&S o ~vy me. T&V ds CCVT&V f}v % EA oArj
5 tj v? A/3' xal koLTtri KQK t\A roiovrov etitlv i^ /3 ta,
OLG3Vf\F di%%"Yl a O ^. KKi 0TiV TO {llv KTtO Trjs
AS tttQdy&vov 6$ id t#, rb d coco r^ F0. O ij, a 6VVT&VTCC 7tOLi TO KTtO T% ATvov [Eucl. I, 47] <5c,cc id Ag* p,rpii aga 6Tiv
r\AT
10 TOIOVTCOV l 7 V%) OICOV 0TiV fj [lV 4E VfriaJ33C,
j]d TE T&V KVT&V a % wy. S'GTI d\ KCCI, o
r
i(QV fi TOV
7CLKVXA.OV diK[lTQOg ^5C, TOLOVTC3V f\AT
jUg id' VTtoTivi, yag Tr\v AT nQi,(pQiavovtiav gg vcc. xccl olcov aga 6T\v r\ [iv AT v&la
15 7t& ^ig td, i]$ TOV 7tt,XVX&OV 8iK^LTQOS ^3C, TOiOV-
TO)V 6Tttl KOl % plv /IE V&tCC %A.tt 1/y ft^, f]d TE
T&V CCVT&V P V' K)(3T KCclf] [LV rf CiVT^ XQl,(p-
Qia f\TE TOIOVT&V g (id a, otov fVrtv 6 7tfavxA,os
T%. TO)V d aVTG)V VTCOKfiTKi XCci BAT 7tQl,q)Qltt
20 ~QV X?' X(d 8A^ [lV CCQK fl B TE 7tQl(pQia pOLQ&V<3Tiv Qvt, la, fi
d vit avTqv v&laf]BE TOIOV-
2. ^] I- ins. D 2. 3. xat] om. D. 4. 8s] S' supra
scr. D. 6. 17] %al r) D. o] e corr. D 2. SGTW] comp. B,
icn D. 7. A] -& e corr. D 2. 8. a] e corr. A. o] corr.
'ex ft D. a] corr. ex a D. TO] corr. ex TOO D seq. ras. 3
litt. 9. o9a] c9 D. Is] e corr. D 2. 10. sv&f-icc] ev&ficc
vnotsivovca D, vnoreivovocc supra scr. B 3. 12. Totovrov -
15. ^x] mg. D 2. 13. [loiQ&v] om. BCD. 17. ph~\ om. D.
18. roiovTcov] roiovrcov icriv D, -v eras. % pd a] ^L doc D.
oi(ov]_oiov D, corr. D 2. s<ntv] om. D. 19. ^] S' D.
20. pv negicp^QBLcc] bis C, corr. C 2. xca
']. (pi'iore loco)
comp. ins. C. 21. r oj Tec ABCD. 8] d' D.
MA0HMATIKHS 2TNTAEE&2 A'. 311
TG)V A/3, olov 6rlv % plv rov BitMvxkov did-
t pw ovv j]BE v&ta l'6r] r)v BVQ^BVVI rrj
rov fitixvxhov,id avrfjs av
on rb xvroov ocvrov, xccl ccvro- 5
&V av cpaivro r&v
avrijSi &&66nv o\ noliiBTE
7CQifpQia rilLMVxMQV, d^Aoi/, OTt
TO Kvroov rov IrtMVKkov Krbg 10
7t(3sirai rov BATE rpijuaros.
vjtoxstctd'G) dy rb K 6r][ilov,
KOI BTte&vi&G) KTCO rov z/ %vroov
rov dia {ifa&v r&v ^coduov uvxhov
dice rov K v&Zct ^ z/MKA, co6r 15
TO [iv A 6r][iZov yivsG&ui rb aito-
yBiorarov rov fjrwruxAov, TO $ Mrb TtSQiyBiorarov. 7ti ovv rb VTCO
faov 0rlv rc5 vitb r&v 20.
Ad XCtl Z/M JtQl%OllVG) OQ&O-
[Eucl.111,36], dedeiKrui d'
on,, O'LCOV 6rlv rov eiti-
r\ didiittoos, rovrfanv
) ^5c, roiovr&v farlv ^ f*^ BE v- 25
fjd Ed r&v avrcbv %la ly prj, rj
r\ARM
&tcc it
3. BE] corr. ex KE C 2. 4. Irvy^ccvB A. 7. d'] 8s D.
8. Ante SB del. i<n D 2. j]\
ins. D 2. 11. Post BAFE rep.
9. TtSQifpfyzict 10. iniy.vY.lov D, corr. D 2. 13. KEVTQOV] e
corr. D 2. 15. K] a e corr. D 2
. 4MKA] AK, M4 D. 16.
yiyvso&ccL D. 20. iotlv] comp. B, scrL D. 21. JM] corr. exAM D 2
. 23. rov] rj rov D. 24. rf]om. D.
312 KAATAIOT HTOAEMAIOT
ds B4 oAr] dyhovort, typy va K, yivzxai rb vnb rcov
xal 4E, rovrfarw TO vitb r&v A z/ xal AM,n _
OQ&o'ycbviov r&v avr&v M fify xal
s A/3. rtdhv ds, ejtsl KOI rb vnb A45 xal AM [ira rov dnb rijs KM Ttoist rb ditb JKrergdyovov [Eucl. II, 6], 17
^ KM sx rov xsv-
rpov ov0cc rov eTCLXvx^ov r&v avrcbv i<5nv %, lav ra_2% rov an' avrijs rsrgay&vov 7tQ00d"S)^v rats M fity
A3 %oiv rb CCTCO AK rfrdovov r&v avr&v_
10 My gr A/3* xal pyxM aga b'tirat,
rjx rov
rQov oi)6a rov (pfyovros rbv sitiKvxkov O{IOXVTQOVx& dice [isG&v r&v ^G)dic3v xvxAov roiovr&v yc, xal
%r)xo6r&v y /Lt/3,oicov 6rlv % KM x rov xwrgov
ov0a rov Ijtixvx&ov ,ijxovra. &6rs xa^ OICQV 6rlv i]
15 X rov Xvrgov rov cpfyovrog rbv fitixvxhov bpoxw-
1. x] xy BC. TO] agcc TO D. 2. rovrsGnv'] comp. BT
tovrion D. Ad~\ dA C. 3. r&v ctvr&v] -&v avr&v in_ _ _ _ms. A 4
. M flip] BC, p By D, pvQidStov p $ty D 2,
p 8%cnuiAia>v (postea del.) TQIKKOGICOV (sire- supra scr. postea)in ras. A 4
, ty postea add. mg. xal ?]-]in ras. A 4
. 4.
end v.ai\ om. D. AJ~] T&V AA D; seq. ras. 1 litt. B; AJK A,K del. A 4
, ylz/xj, in fine lineae C. 5. xat dM~\ corr. exxa ijp D. XM] KM xBXQKymvov D, Tfrguymvov supra scr. B 3
.
4K] rfjs 4K D. 7. I"]corr. ex I D 2
. 8. ,y| ri D,jU? _ ^f/1
/r5J D 2. rats] om - C, irarg ngoy,i^vccig D. M ^i/Tj ft |3t/; D,
^t ,(J_^_D*.9. 4K]rfe JK~D. 10. M] mut. in ^ uvf D 2
.
75r ^] mut. in
ys r F D 2
. z/A^] -X supra scr. D. ex 12.
xwxiov] mg. D 2(yp.), ^x roi) KVTQOV et TW ^ia (JLSCCOV r&v ^w-
xvxlov etiam in textu. 12. TW] 'scripsi, TOV ABCD.
r e corr. D 2. 13. 77] i\ CD, corr. D 2
. Post ^supra scr. MOTS xca' D 2
. KM] del. D 2. 14. OVGCC 15.
om. D.
MA0HMATIKHS 2TNTASE&S A'. 313
B
toov tri o^i xvxAov Qtjxovta, toiovt&v 6tai xalj]
ex tov xvtoov tov tmnvxhov ~iy gyyitita.
%%&& dr) 7il tijs dpoias xataygayils aito rov Kxvtaoy xd&tos itl tyv BE fj KN&, xal im&vyftG)
f)BK. siisl roivvv, otW 6xlv
r\4K jfc rj ^/3, roi- 5
ovtcov i\v xalf] [isv /IE sv&sia
%&cc ly jZ^, f)ds NE fftifasia ovtia
rrls BE [Eucl. IE, 3] T&V ccvr&v
vrj ^/Y] fig, >S xal oAyv TYJV
4EN r&v ccvrcbv yivsGftui yfi xal 10
Ad, xal oi&v aga rj
6rw ^x, roi-
OVTG)V xali\ [isv 4N 0tai,
vr\ v, i]d 7i avail
QOTJ ft fyyitira, O'LOV 15
tcbv
<3tlv 6 7Col tb
viov xvxAos T|. co6t xal % vno
dKN yavi'a, oi&v [iv sfaiv at
dvo OQ&al T|, toLovtcov i&xlv
Qoy /3, oicov $ aC d OQ^al rj, 20
toiovtav nd1 a. xalfj [iv &J\
ago, tov 3tixvxA.ov
pOiQCOV 6tlV ltd1
,
iS tb fjiuxvxAiov 9 v&. tcov ds avt&v
Jtai,(paia inii6ia ov6a tils B&E pot,- 25
4. BE] EB D._ 5. Wv] om. D. JK] JK sSttz&T] D.
r[\ ins. D 2. 7. J^a] -K e corr. D 2
. 12. JK] J- e corr. in
scrib. C. 14. ^] S' D. in3
} corr. ex bn D 2. 16. JNK]
corr. ex JHK D 2. 17. acre 19. T|] om. C. 19. EGTLV]
om. D. 20. at] in ras. 1 litt. D 2,om. ABC. 21. K] [ii&s D.
23. SGTIV] comp. B, -v eras. D. 24. loina>v~] bis D, corr. D 2.
Ss] om. D, 6' D 2. 25. B] B3 D.
314 KAATAIOT HTOAEMAIOT
orj Aa, ^sidr^TtSQ % BE~i eyyidra' xul koutri agcc i\
AB rov
r^v anefysv f} (Ss^tjvri rov anoysiordrov
xara rbv xxi[ivov pitiov %oovov rijs devTSQag x-
5 Aefyscog, poiQ&v fativ ij$ xd. b[ioicos df, endfj VTCO
4KN y&viK sdei'xftri TOIOVTGOV 7t& a, ottov sfalv ai
d OQ&ccl T|, xal koiTtfi stirou,17vnb K4N y&vtcc, ij
rrjv a(pKLQOv^ev^v rijs {ifays xara
7teQ(,(pQi,av sx rfi TtccQcc TTJV AB rov
10 xvxhov ywoiisvrjs avKt^K^ia,^ r&v tontfbv sis ^nv
do&riv [Eucl. I, 32] ^LOLQ&V o v&. nctl Kara, pijxog
UQCC yiB6G)$ STtstyev fj GsAyvr] xara rbv psGov %QOVOV
rils dsvreoag sxfafye&s IJaodsvov poious id ^d,
dijrteo axgifl&s exsfye [IOIQKS 1/y jiZf, o6ag xal 6
15 Iv rots 'I%&v(5i.
,(bv siA.ri<pcc[iv roi&v exksfyscov sx r&v 7ti-
v\\iiv iv 'Ake^otvSQsia rfrrj^^
yfyovs rat 1% k'rei 'AdQiuvov xccr'
Ilcivvl K SLS rijv xa', rbv d yidGov %QOVOV20 7tA.o'yi6diid-a ysyovivai itg/Q yjifaovs xccl rsrccgrov
ifS^BQlV^S fOV [ISGOVVXriOV XCtl %A.l,rtV
JV COQCCV axoiflcbs yfl%v 6 rikio<s rov Tccv-
oov {lotoccs ^y ^' ZyyiGrcc.
fjd dvrocc yzyovs rw id"' srei, 'AdQiuvov xccr'
1. Ifo^tfr] D. 2. A B] BAD. 5. icxiv] comp. B, eon D. 6
AKTL D, corr. D 2. 7. \ontr\\ IQIUJ\ &QO. D. 8. ag>-
D, corr. D 2. 9. A E] -E e corr. D 2
,corr. ex AAB A
11. o] corr. ex ov B 3. 15. I%&VGIV D. 20.
-Q-cc BC. 21. f<5s]~
g J' D. 21. |&eurermut. in B'gilmsv D 2
. 22. sitsfysv cMQifias D. 24. dsvrsga~B B. ys'yove] yiyovsv sv D, iv del. D 2
.
MA0HMATIKH2 STNTASE&S A'. 315
AfyvTtriovs Xo'Cax ft' slg rfjv y', rbv de [i6ov %QOVOV
STtshoyrfdiisd'a yeyovBvai ago a &QCCS farj[iQi,vijs rov
H6ovvxriov xccl %Ai,7tv ait ccoxrcov rb L' xul yr
rijs dia[JirQov, xa&' r^v COQCCV itt%v 6 ijfoog axQifi&s
r&v Xrj^cov [IOLQCCS %e %' syyidra. 5
i\ds tQifri r&v exfafyeov yeyovsv rtf x
e
srsi,
rbv de jieGov %QOVOV sitsAoyiGdnsd'cc yeyovsvcci,
d &QCCS faqpSQwas rov peGovvKrCov xccl s&teirte rb
rftiitiv rijs SiuyisrQov cut' ccQxr&v, jtsZ%e $ ucci xaroc 10
rccvryv rrjv &QKV 6 ijfoos r&v 'I%&v(ov [IOIQCCS id i$'
ovv, on xccl
&itb [iv rov [i<5ov %QOVOV rrjs
rbv [i6o
6 TJAtOff, [IOLQCCS OCC V,
CCTtO
rov rrjs dvrQas fti rbv rijs rofarjs [tongas Q^fj vs.
<5uv $ xai b [ircc,v %oovos rrjs (i&v rtgcorrjs diccGrcc-
<?o>g fvtavrov AiyvitnKKov svbs xal f}(iQG)v (>|g xal
wa&v far)[iaivK)V ajth&s pw ny L' <^'? axQisfl&S $ ny 20
/_' j\ , rijs & dmrsQccs diaGraGs&s wiccvrov it&Kiv Ai-
v vbs xccl fj[iQcbv Q^ xal MQ&V fa
1. Xoia. *$ A. 8e] con\ ex did D 2. 2.
lie&cc BC. a] A, (iL&gECD. 3. ttteuc$v] mut. in
Tfsv D. 4. ctKQifi&s 6 jjhos D. 6. T(>mj] F B. yg'
-v eras. D, yeyovs B. 7. Qccqitovd'C] supra -9- adp. A8. 7iJioyriad{ji&(x BCD, corr. D 2
. 9. Qeleine] ABC,DB 3
,itlint D 2
. 10. int-fyf-v D, -v eras. KOCTCC]
V.K C. 11. id] supra scr. D. 15. Ttgrnrrig] & B. (JLSGOV
%QOVOV] om. D. SSVXSQCCS] B B; et similiter saepius. 16.
Kteiipcos~\ om. D. 17. glLy] corr. ex QKTI D. 18.
comp. B, -v eras. D. 20. d' -- 21. /_'] om. C.
316 KAATAIOT IITOAEMAIOT
ply s, axgifl&s ds ~s /.'. xivsltai, ds ndkiv17
o'Aovg xvxAovs iv \L\V t& svl stsi,
xal r)[iSQai,s pi-g xal CQQCUS falftteQW(&$ xy L' y' &VG)-
liaMas [isv [IOLQCCS ~gi MX, nyxovs ds poiyu5 fyyitira, iv ds rc3 svl srsi xal fipSQcus pAJ xal
Ad syyiGra. d^ov ovv, on ncd cci p^v
6G)S tOV STtMVKkoV [IOLQCCI, ^H MX,
a<prj(>ijx(x6i,v tijs xatti pjxog [ifaqs Jtccpodov
10 ft/?,ai SI rrjs dsvTSQag diccGTccGscos potQai, TW, Ag
xccra pijxog peGy Ttaooda) poiQas a xa.
TOVT&V OVV V7tOXSl^eVG)V S0TG) 3t(X,klV 6 SJtlXVXhoS
6 ABF, xal to psv A Grjpstov vno-
ov fjv i\ GsAtfvrj iv rco (idtiq) %$6v(p tys
15 itQcbrys extefyscos, to d% B to tijg devtzgccg
to ds r to tils tgitrjSi VOSLG&G) ds caGavt&s
f}cc6iS tys dshijvrjs &S ^Ttb tov A iiti to 5, sita iitl
to r yivo[Levr], &6te tfjv [isv ABOV&KV ^l xa atpcciQslv, (b? s'(pct^sv^ tys xccta
20 iisGys itKQodov [tongas |tt/3, trjv ds BF poiQCbv ov-
6av act Ag ttQOGti&evcti t<p ^tjxsL [IOIQCCV a xa,
ds tqv PA ILOIQ&V ovGav ^)|^ y TtgoGtiftevm to)
tas hoiTtas ponces S *"*
ovv snl tys AB
1. /.'] ins.J)2
. 3. i' r)'~] lj\" e corr. D 2. 6. is] *e
supra scr. Zg v8 D 2. 9. &yr^r\v.uGi BD. 10. nQOGtsft
KctGi BD. 11. ^iGri\ corr. ex (IEGCO D 2. 12. $GTCO ndliv b
^jrtxvxAog] 6 inUvAlog ndUv SGTCO o D. 13. JBT] AB D.
14. G^lv\vr\\ corr. ex GfJLrjvi A 4. 16. -9-co ds ebff-] in ras. 4
litt. D 2. 17. to?] postea ins. D. slra] om. C, fTmra D.
21. TCQOGzi&evat] post -^- ras. 2 litt. D. 22. PA] AP D.
C, sed corr. 23. raj] in ras. D 2seq. ras. 2 litt.
MA0HMATIKHS A'. 317
TCCTOV slvat, del, (pKVfabv x TOV pyre iitl rife BF el-
fitJT STtl rife FA di& TO sxarsQciv av-
TG)V T iVKl Xttl
cog p
Xl[lSVOV TOVTOV TO XSVTQOV tOV 5
v xal rov xvxlov, eg?'
6 fWxvxAog, xai
S0TG) TO Z/, STtS&VX&OGKV TS
ait' CCVTOV sitl TK T&V y IK-
Ev&etcu at 10
KCCi 7ft-
BF rj%&G)6av
aito TOV E Grjjisiov v&tcci, iitl
lilv rcc B, r at EB, EF, mld rag 5z/, z/F eb&eCus xa&- 15
roi CCL EZ, xal EH, xal Tt,
CMO TOV F 7ti Tty BE Xa&-
T0$ %%&& rjF. 7t\ TOIVVV
fjAB 7tQl,(pQ(,a V7tOTLVi TOV
&V Xtti 20TG)V
i\VTtb A4B y&vicc Ttobg rc5 XWTQG) ovGct TOV
oicov [iv i6w ai d oQ&ccl rj, rotovrovft/3
at dvo oa&ttl r^, TOIOVTCOV H- xd. &6T xccl ^ plv 3ti
T^g EZ 7tQi(pQi,a TOIOVT&V farlv T xti, oicw 6 TCfol
TO 4EZ TQfy&vov xvxhos r|, avr?? $ 17 EZ v&ia 25
1. Set] corr. ex dq D 2. 2. pip D. 4. dt] 8' D.
4EA] corr. ex ^^4 D. 4B, z/T] xai z^B xal z/T D.
^v^fta^g D. 14. B, T] BT B, B *ul F etfotcii, D.
xal EP D. 15. rag BJ] corr. ex ra 27Bz/ D 2.
Tz/ D. sv&8ictis D. 22. ^] fi- in ras. D 2. 23.
(5BD. 24. ^0rtV] comp. B, -v del. D 2
. 25. iQiyavov]ymviov D.
11.
EF]
318 KAATAIOT DTOAEMAIOT
TOLOVTCOV ig d ^/3, oicav 6Tivf}zJE vnoTftvovtict ^rx.
bllOl&S') 7tiI]AB 7tQI,(pQl,a [iOlQG)V 0Tt,V J3>7 %tt, #)?
av xaloj
VTtb AEB y&via Ttobg Tf) jtSQitpsgeiK ov6a
ToiovT&v QI, sea, OLCOV sfalv a[ dvo oo&al T%. rcov d'
5 avr&v r]v xccli\
vjtb AAB Is %d' komri [Eucl. I? 32]
CCQK f]vjtb EB^J ycovicc r&v avrcbv iGtiv d v^. caGxe
XttlJ] pV 7tl tils EZ 3tQl(pQSLCC TOIOVTCOV 6tlv d
vt,, oicw 6 3t$l TO BE2^ xvxto$ T|, avtr} dt- ^ EZ
v&iK roiovrcov ay jcg tf, oiov 6rlvi\BE
10 vovtia ^K. xccl oi&v KQCC itixlvi\ pw EZ v&ia
x TOLOVTCOV &rlv xcil BE
PEA 7tQl(pQl,a V1tOTlVOV6tt
TOV dia ii6a)v r&v Jradtov xvxAov iioigccg & jca, sty
15 av xuifj vitb A^JF y&via JCQOS TG) KEVXQG) ov6a TOV
fydiaxov, oicov piv ffaiv ai d oQ&ccl T, TOIOVTCW ?
3t, oi&v 6* ai dvo OQ&al T%, TOIOVTCOV ifi ft/3.&6re
XCtli\ [lV 7tl TyS EH 3tQl<pQlK TOIOVTCW 0TLV L$
^/3, oi&v b ttQi TO 4EH dgftoytiviov xvx^og T%,
20 O.VTYI $f}EH V&ta TOLOVT&V ~iy tg fc-9
1
,Ol&V 6TLV
V7tOTlVOV6K ~QK. 6^0iG9ff, 7tl ^ ABF 7tQltp-
Gvvdymai, noig&tv Q$a vt, , fy av nal q VTtb AEFycwia agog r^ jtQitp()La ov6a TOIOVTCOV Q$a v^ oicov
dvo ofral r. TMV <5f avT&v iv xai
3. AES] corr. ex AEH D 2. 4. dvo] BD. 5.
E ycoviK D. lQinr\\ otai lomv] D. 8. ot'cov] ol'cov iatCv D.
BEZ] BEZ 6Q&oyot)Vt,ov D. 9. sv^f-fa] om. D. TTTJ] rj
nri C. 10. SGTLV a$a D. 11. ^] tSf-fy&ri ^_D. SGTLV]
comp. B, sGTcci D. 14. TtvxAoi;] om. D. xa] seq. ras. 2
litt. D. 17. ofav T|] mg. D. dvo] {3BD. 18. &>TtV]
comp. B, -v del. D a. 24. dvo] ^ BD. *e] d' postea
ins. D.
MA0HMATIKHS STNTASE&S A'. 319
A/1F ycovCcc i$ fift- xal Aown? [Eucl. I, 32] agcc % vjtb
EF/1 rcbv ccvrcbv i6nv po-fr Is. cotirs xal $ {isv iitl
rrjs EH 7teQicp8QiK roiovrcov 6rlv QO& 7f, otcov 6
itSQi rb FEH r^Cyovov xvxAog T|, avrr] dsrjEH
v&ia roiovr&v 6rlv QL& v& v, oi&v B6tlv % FE 5
vrtOTivov6a 'QK. xal otcov CCQU s6rlv17 pfv EH sv-
fteta ~iy Tg t-fr, f]ds 4E edeix&r] ^sc, roiovr&v e6rm
xcclfjFE sv&slcc 1/y Ig %. rcov ds avr&v sdsi%d"r] uccl
YIBE sv&stcc xa ^ v&.
:r/Uv, srtslrjBF 7tQi<peQSia ILQIQ&V 6nv xa Ag, 10
ty av xal % vjtb BEF y&vta itgbg rgov6a toiovT&v ncc Ag, oi-W ffalv at dvo ogfral
G)6f XalVI [lV 7fl T7JS F 7tQl(pQlCC XOlOVtO
no, Agr, OLCOV 6rlv b TCSQL rb FE tQiy&vov
T%, % ds srtl rr}g E rcbv Aoiitcov ig rb r^iLXVK^LOv 15
[Eucl. Ill, 31] 9^ nd. xccl r&v vn' avras &QK v&i<G)v
r\ iilv F sdrai, roiovrcov 'brj xd Ag, oi&v stirlv ^ EFvnorivov6a ^c, f]
d E r&v avrcbv 9 v xf$' KOI
otW agci farlv % FE Ev&sta 1/y 7g sc, touovrov xal
rj psv F k'&rai17 ji jc, ^ ds E bpoicos T p fid
1
, rcbv 20
ds avrcbv i\v f\EB oAty >ca Jirj v%" xal AotTTiJ CCQCC rj
B roiovr&v street, lajiZg I, o'icov xccl
j]F ijv rj p
K. xai 6nv rb [iv CCTCO rrjs B rfrgdycovov
1. t^j e corr. D. 4. TEH] -H in ras. D 2. TQiycovov]
oQ&oywviov D. 5. SGTIV (pr.)] om. D. v] seq. ras. 5 litt. D.
6. &mV] om. D. 8. ds] d' D. 10. Is] corr. ex L D.
12. dvo] @ BD. 14. IffrtV] om. D. r^tycovov] 6Q&o-ymviov D. 17. rj (alt.)] ins. D 5
. 20. F0] corr._exFE D 2
.
E@] corr. ex HO D. T ~] e corr. D a. ^] corr. ex
^ D. 21. de] ^' ins. D 2.
i] (pr.)] xat i]D. 22. ia] -a
in ras. D 2. T, oi'cav] ins. D 2
. 23. fortv] comp. B, SGTL D.
-?] e corr. D 2.
320 KAATAIOT HTOAEMAIOT
la, rb ds artb rijs F r&v ccvr&v o i$ x, a 6vv-
rs&EVTa noiel to coco rfj$ BF rfrodyovov [Eucl. I, 47]
6iy ~p/y A??'
[HJXt, CCQCC 0rlvi\Br rOlOVr&V id A I, (HOI/
6rlv r] plv /IE zv&eia jpz, ^ ^ ^E o/iotcog Ty 7g jc.
5 foxiv de xat, otcov ^ rov STtMVKkov didpsrQOS ^?c,
TOIOVTCOV % FB sv&sla o^ xd A' vitorewsi, yap r^vBF 7CQt,g)Qiav [lOiQ&v ovtiav act Ag* xal o
f
icov aga0rlv ^ plv BF v&tcc o^ xd Af, ^ df roi) eitMVKhov
dlKllTQOS ^X, TOLOVTGOV 6tttl Xttl V\ [lV 4E V&tCC
10 wy Ag AO1
, ^ $ FE rcov avrcov oa Ta d. &6T nccl
r\7t' ccfaiis itQi><pQitt fi
FE roiovtcw 6rlv o/3 jilg I,
o!W 6 frtixvxhos t%- t&v df afa&v f\ TEA vnoxsi-
rcct, Q%rj y* xccl Aotjr^ plv KQK f)EA ttQt,tp()(,K poi-
Q&V i<5nv 9f 7g v, 17$ i)ri ai>r^v fti&tia ^ AE
15 roiovrcov ;r^ ^ t, otov cVrlv 17 f*^v
^ df Jz/ i)frsia yjpy Ag
aAtV ^ EA 1tQl(pQl,
, dijAov, ort TO XWTQOV rov fjtixvxtov x-
rbs 7t6trai, rov EA rp^arog. Mtjtp&a) di) al Zero
20 ro -K", xal tTte&vffiG) fj4MKA, &6r itaKiv rb ply
A Grftislov yivsG&Ki rb aitoyuorarov ,ro dl M rb
7tQLyt,6rarov. 7ti ovv rb VTtb Ad xccl dE
1. Se]_d'D.
x^]corr. ex x(3
D 2. 3. jiy] A 4B 3
, ^A CD. ^] corr. ex t D 2
. 4. x] corr. ex xf D. 5. SGTLV]
comp. B, <>rt D. 6. FB] EP D. 11. TISQ^QSLU] seq.ras. 1 litt. A, nsQicpsQi-icii C. ^crtV] om. D. 12. fo'J d' ins. D 2
.
13. 0!?;] corr. ex p| D 2. 14. v] corr. ex
rjA 1
. 15. 17]
ins. D 2. 16. EJ] 4E C. 19. EA r^urog] E KT^ZOS D,
EA Tj&rjrog D 2. 20. X] K ar^isiov D. xa/] supra scr. D 2
.
AMKA\ corr. ex 4KA D 2. 21. ^1] corr. ex A D 2
. ytyi/f-aO-at C. rb 8s M xb itSQiysiorccTov] mg. C 2
. 22. Post UJTO
add. T&V C 2. Trfpie^d/tifvoi'] corr. ex nQi%o(iEv D 2
.
MA0HMATIKHS STNTABE&2 A'. 321
%6{isvov ogfroycbviov i'6ov itixiv real vjtb t&v A z/ xal
4M [Eucl. IE, 36], dedeixTat, d' rj^ilv, on, oitov
etirlv AKM TOV btucvxlov
x, ToiovT&v stirlvr\
AE ev&ela nrj p tj, r\de 5
Ed T&V ccvr&v ipy ACT AO-, ^ ds
Ad ohy dri^ovon tykfi 7g vs,
yivsxca ro v
rb vnb Ad xal <dM, r&v
avxcbv M ardjitg tf. ndfav de, iitel 10
ro vnb AdM psrcc rov anb KMjtotsi TO ciTtb rr}s 4K rstQccycdvov
[Eucl. II7 6], ri de KM sx TOV
X8VTQOV OVGCC TOV 7tiXVxA.OV [s^tj-
XOVTO] Ttoist TO KTC ccvTrjs /y%, 15
/* _ _Tats Tcgoxeipevais M p,x jilg tg,
jilg i'
lav Ta /y%
v TO curb 4K TSTQaycwov T&V avTCbvM
1. IffrtV] comp. B, -v eras. D. ro5] corr. ex TO C 2D 2. xca]
om. D. 2. d'] postea ins. D. 3. AKM~] A- postea ins. A,corr. ex AKM D 2
. did[itQOS tov ITCLY.V^OV D. 4. fffriv17]
corr. ex Ivtt D 2. 5. if] t?^ D, corr. D 2
. 6. JWKJ --9- in ras. D 2.
8. ytVfrat] yt- in ras. 3 litt. D 2. 9. XOVTSGTIV] -v eras. D,
rovrsOTL B. VTTO] -UTTO TWV D. Ad] Ad CD, corr. D 2. 10.
/u d
M] mut.in # p D 2. TraZtv dt, Inei] -naliv ABC, Tra^w; d'
tni D, TraAtv ^' inet D 2;conf. p. 312, 4. 11. A4M] r&v AA
xalJM D. KM~\ xf\sKM TSTgdycovov D. 14. f|?jxovra] deleo.
^'xoiTa 15./y^J mg. D 2
;in textu TWV avr&v ioriv |f, quae
del. D 2. 16. ,72] -^ in ras. C, y- e corr. D. Deinde add. rov
Lt^~
v D. M] mut. infi [i
D 2. t^] t? D. 17. ccito] anb
D. TgTpccycoycovov A, sed corr. M] mut. in ft fiD 2
.
^^] corr. ex J&S D 2.
Ptolemaeus, ed. Heiberg. 21
322 KAATAIOT nTOAEMAIOT
xal [iijxfi, aga street, rj4K x rov Xvroov ov6a rov
roiovrav %7t& rj, O'LCOV 6rlv ^ KM ex rov XEVTQOV
ov6a rov Znixvxkov Qtjxovra. &6re xat, olcov etiriv
5 r\ [israt.v r&v xevrg&v rov re dia p&ov r&v ^cpdC&v
xal rov srtixvxAov e^xovra, roiovrcw sGrcci, xccli\
sx
rov xevrgov rov STUxvxAov id. xaC fanv 6 ccvrbg
Adyog r& dia r&v TtaAaioreocov sxfafyecov
10fjjtd'G) dq Ttukiv 7il rrjg ccvrijs xarccygccipiig KTCQ
rov K xsvrgov xd&erog enl rty AEA v\ KNE, xal
7t%SV%d'K) $1AK. 7tl OVV, OLG)V
rj4K
i?, roiovrcov i\v xal ^ ^V ^E sv&tfa
d NE ruiiGeiK ovaa rijs AE [Encl. HI, 3] r&v av-
15 r&v (Snv pd xrj,
caGrs xal o/b?i> rr\v 4EN rcbv av-
r&v %it^ ~v$ ft^ xal of
i(ov 6rlv aga y 4K vitorsi-
vovGa ^jc, roiovrcov xalfj4N <5rai, QI& ^ AST, f}
de Tt avrijs 3toi,q)Qi,a roiovrov Qoy i lyyitita,
oinv 6rlv 6 xsgl rb AKN OQ&oy&viov xvxhos r%'
20 &6r xal17
vitb 4KN ycwia, olcw pw ti<5iv ai dvo
OQ&al r%, roLOvrov 6rlv ooy tg, oi&v $ ai
T|, roiovrcov 6rlv jrg A^ /.'. xalfj ^sv ME&
rov STCixvxkov tti(Qt,a loi&v <5ri,v :rg A A
2. tptgovTog] corr. ex nsQLyeQovros D 2. 4. OVGCC] om. D.
5. xs] om. D. 7. s] e corr. D. 8. TW] TW g* D. 10.
ccno] ini D. 11. 4EA~\ AE D, J add. D 2. 12. ini-
&v%fra> B. 15. t<>riv\ comp. B, om. D. x ^] xrj BCD,corr. D 2
. uvrcbv] avr&v yiveG&ca D. 16. iTg] -g e corr. D 2.
K] -K e corr. D 2. 17. rj (pr.)] ^ fisv D. 4 N] -N e
corr. D 2. 18. df] S' D. In] corr. ex bn D 2
. 20. >E] in ras. D 2.
w<7T 21. T^] om. C. 21. iariv] comp. B, fGTca D. 22. ievfv']
om. D. f] ^g BC, corr. B. 23.1] A, /.' BCD.
MA0HMATIKHS STNTAEE&2 A'. 323
AA& r&v hoiit&v is rb YiyunvKfaov 97 xa A. rav d
avtojv idnv fj A$ 7iQLfp0ta Y}{ii6ia ov6a rijs AE[Eucl. Ill, 30] [loiQcdv ft A^ A
fyyiGra' xal Aotjri) aoa ^ -AA7tQl,(pQia [IOIQG)V ititlV \IB fty.
vitmsiro d xalj]AB
avr&v QI> na' xal
AB 7COi(pOLa^ r^v
GfArivr] rov aitoyeiordrov
rOV XKt[lVOV
rav
OCQCC %
xccrcc
10
yiv VTtO
y&vfa fatedEt%fhi TOLOVT&V TCS Ay
,oiwv at d OQ&al T|, fj
15
[Eucl. I, 32] el ^n
Ufa V1tXirO d KOIfj
A4B 0^77 T&V avrcbv % ^t/3,xccl koutii aga fj
vitb A4Bijtig V7torivi, xv\v acpat,Qov[ivr)v xi\g ^0rj xara 20
TtaQodov rov dia pfaov r&v <pdfav xvxAov
7tQi(pQi,av x Ttjg itctQa xj\v AB yi,voiivrj$ rov iiti-
&vm(utJifa$y poiowv fatal d K. Kal Kara pijxos
aoa fieti&s iti%v % ffe^wj xara rov pfaov %o6vov
1. i] A, /_' BCD. 8] S' D. 3. i] A, L' BCD. 5.
comp. B, -v del. D 2. jte] -8 in ras. D 2
. 7. xcu]*a D. ago] om. D. 8. AB] corr. ex AB D 2
. 13.
corr. ex Int D 2. _ r\\
ins. D 2. 14. i8s%r\ D. 17. stg]
corr. ex ^g A. 18. y] in ras. D. vnonsiro C. xat] seq.ras. 1 litt. D. 19. ^4z/] -z/E in ras. D 2
. olrj] seq. ras.
1 2 litt. D. 22. AB] corr. ex 4B D. roi)
D.
21
324 KAATAIOT UTOAEMAIOT
tils dvtoccs sx&efys&s tov Koiov ILOLQKQ x& A,
dtfxeQ axQip&s zitetyev poious xe t, otfag xal 6 ijhog
tcbv Xyhcov.
,'. Ilol tijs dioQfr&Geas t&v5 tils 6A>ijvvjS [iijxovs rs xal avopcchtag.
'Eitel rotvvv Iv p^v rri devrsga r&v Ttakai&v sx-
attdsfi-ccusv r^v tieAtjvrjv xara rbv [is<5ov
7te%ov6av 6^A? Kara pijxos [isv IlaQ&evovid ftd, Kv&paMas de ano rov aitoyetov rov
10 STtMvxAov poiQag t/3 xd, iv ds rfj dsvtsga r&v xa&
tQi&v sxhefysiDv d^ioicag it%ov6a ftfVog CCTCS-
Kara pijxos i&v rov KQLOV poisons x& A,
$ dttb tov ajtoystov ^lOi
on, xccl iv tip [ista^v %o6vG) TK>V XQOXsipsvcov
15 tyG)v STteAccfls [ifaas v\ GsArjvr] ftcO1'
o'Aov?
[iijxovs [isv /itot^ag 6xd pg^ avcs^ia^iag ds [loioas vfi
id. AA' 6 iiTa%v %oovos TOV rs devrsoov srovg Mao-~
I'YI lg rrjv i&' rtab /_' ual y' a
tov {i6ovvxTiov xal tov i&' tovs'
20 vov Xo'Cax ft' fig t^v y' nob fi
tOV [IBGOVVKtlOV 3tQiB%l, j4fyv7ttlCCXK trj &vd Xttl
O/ KKl COQCCS i^^fQLVag CCJtA&
xal jtobg ta o^icda
2. sitei%e D. 4.']om. AD. diogftwcicog] om. D.
ivriGt&v D. 5. rfjs <TfArjv7j?] diOQft&Gfcog D. 6. na-Tta^iai&v TQI&V D. 8. nata] seq. ras. 2 litt. D. 11.
C. 13. lr[\ corr. ex As D. 14. xca'] supra scr. D 8.
15. BTtslKfisv D, corr. D 2. 16. JUTJXOVS] supra p ras. A.
17. 6] seq. ras. 3 litt. D. 18. a &QUS] rjpsQccs D, del. D 2,
mg. ro^aj D, piae wyccs D 2. 20. Xvdv. D, corr. D 2
. y'jC. 21. Irtt C. 22. ndUv] om B.
MA0HMATIKH2 STNTAEE&S A'. 325
/la
y'9 rtddag 6% f)[iQag M xal ptyyty xal agag
vag xy y', aig VQfaxo[iv BTtifiakhovdag [16&
xvxhovg 7tov6i'ag x rcov 7tQOxr&t,[iva)xara rag Ttgb rijg dioQ&mGf&g V7to&6i,g
jioiQccg 6xdjiTcr, av&iLaAiag d [loigccg vfi 5
Aa, ag r^v plv rov [iijxovg itov6iav
fog (paiiv, fvgriG&cci, TTJ dice r&v XXL^IV(DV
i)<p ruicbv Gwajfoefari, tyr ds rr^g avcDpccMag
&iv QqxoGtoZg 1%. o&v itgb ryg r&v xavovt&v K-
&<5G)g vXv Tijg T&v ri^f^^iov^dQo^cov diog&aGfcog 10
ra L^ %r]xo6T(x 7ti,[iQi0ccvtg fig rb TtQoxeiyievov r&v
fiHSQ&v TtA.ijd'og ra xd&rr] f}H>Q(x iti(idMovra o o o o
lajiZ?
A-91
acpA.6vrg rov xgb rr^g dioQ&coGf&g xari-
[p. 2787 16] VQO(iv [p. 279, 14] rb di&Q&coiiwov poi- 15
pwv Ty y vy 1^ tj w 1/-91
, alg axoAovfrcag xal rag
r&v xavovicw
r&v b^ia^&v rijg
xivirj<3G)v [itjxovg r xal av&paAiag.f
'Ivu $ xal rag 7to%ag avr&v 6v6rrj6(D[id'a fig rb 20
avrb TtQ&rov rog Na(lova66d()ov xary
(daft u rijg [i6r][i(l()iag) Ad(lo[iv rov ivrsv&ev
vov p>%Qi> rov ii6ov rijg dfvrfyag SxAefapecos r&v
Ha1. M] (ivQiddccs ha D. 3. TJ/^rjfftW] j]plv rj^eQrt 6i(ov C.
4. rag itQO T^J] rijs ifQatris B. 8. Ttteovdfeiv] -dfew e
corr. D 2seq. ras. 5 litt. 10. ^ftf^rjatcotj 17- ins. D 2
. Sg
dLOQ&motas] mg. D 2,in textu fa&saemg D, del. D 2
. 11.
KQGTO.S D, corr. D a. 13. dto^cofffcug] seq. ras. 2 3 litt. I).
14. rf]s ccv&iJicdiKg] supra scr. D 2. 18.
rj'~\om. D. 21.
D. 23. T%] seq. in ras. 4 litt. B.
326 KAATAIOT IITOAEMAIOT
xal eyyvrdg&v rgi&v, r\n^ cos <paiiv, ysyove
^7tddov xar' Alyvnriov &&>& itf
/.' xal yr
a cngag farjpSQwIjs rov pe-
(SovvxrCov Gvvdysrcci ds ovros zrtibv Alyvitnax&v x
5 KOL f}[ieQG)V l^ XKi G3QG3V CCTth&S T XCCi C
Ice 5', xal ttccQccxsivtcci, T& roGovra) XQOVG)
eitovtitas [iijxovs [isv [lotQcci, guy x/S, d
ds ILQLQKL ^7 A' as &v a(pe&G)[iev r&v sv
10 ay' sxccrfyas oixsi&s, %o[iv ig to TtQcatov stos
xar Alyvxriovs cod' a trjs pe'dcos ity 6&rivriv xara plv pijxos Tavgov
Ta Xj8 5 dvaiittMccs $ dftb fov dnoyfiov rov
7ti,xvxA.ov ponces 6^1 f*^5 djto%fjs $ drj^ov6n
15 o AJ, litfidr^TtsQ xal 6 rjAtog t$ tbv avrbv
r&v '!&va)v itG)v loias o i.
diOQ&G)6G)S t&v xard
jtaQodcov rijs Gskiqvris xal r&v 7to%wvavrcbv.
20 Tds plv ovv rov [irfxovg xal r^g dvco[iaMas
MQiodixas xwtf(3is xai n rds iito%a$ avrcbv did r&v
roiovrov <p6da)v GvvfGrrjtidnf&a, Irii ds rcbv xard
xal avrol
1. syyvTEQco D. TJVIS] ^trt C, faHefysmv ijtis D. cpupsv D.
yeyovev B. 3. y' a] ya C. 4. ovroos C. Mg. (H D. 6.
g'l t? B. ncnQKyiKitKi D. 7. snovafa D. 10. NU^OVVK-GCCQOV D. 12. ju,7]xovg C. 13. d] supra scr. D 2
. 16. &TIO-
8sl%frri C. ane%cov D. 17.-8-']
om. D. 18. ce^rjvrjs]
comp. AC. rcbv BTCO^&V] rfjs sno^fig D. 21. 810. rmv~\ -cc r-
renouat. D 2. 23. diri^ugra.vo^v'] SL- in ras. 3 litt. D 2 et
supra scr. D a. 0vy^9a>ftfi/ot] -vy- et -co- e corr. D 2
.
MA0HMATIKHS STNTASE&S A'. 327
%gd)[ivoi, Kara rbv "IititaQftov rtf rr^v 6A.ijvr)v %axo-
6idxig fiei> xal rtfvrrjxovrdxig fyyitira xara[irolv rbv
ffiiov xvxhov, dig de xal f}[ii,6dxi,g rbv rfjg 6xiag xara-
HTQiv xard rb ev ralg Gvtvyiaig p&tov ditoGrrjiia'
rovr&v ydo vitox^^dvov xal rijg Jtrjfaxorrjros rrjg sy- 5
rov Ao|oi) xvxhov rtfe Gshijvrjg oi r&v Kara
avriig sxtefyscov OQOI didovrai. 2.cc^iftccvovrg
ovv dia,6tK6i$ xtei,7tri,xag xal dnb rov ^y^d-ovg r&v
xccra rovg ps'tiovg %Qovovg 7ti,6xorr)(3G)v r&g dxQifotg
xara nhdrog itl rov Ao|oi) xvxAov naoodovg d(p dno- 10
roov rcov 0vvd0^G)v fm^oyi^^voi did rs rijg aito-
xara rr\v dv&iiccMccv dictcpooag dytb r&v
rag 7toi,odt,xag diaxoivovrg ovr&g
rdg r xarti rovg [i6ovg %g6vovg rcbv xfofyG)v tito-
%ag rov TtEoiodixov nhdrovg voi^xo^v xal rqv v 15
(p ftf^' oAovg xvxhovg ixwtifav. vvv
%aQie6rQai$ ecpodoig xal iiydwbg r&v
&i,nVK)v 7tido^8VKLg Ttobg rqv rcbv
xccrd^^iv rtjv r $t' XiVK>v STtiksko-
rov nhdrovg itdgodov VQO^,V di^v6^ivr^v 20
xul dnb rtfg vvv x&olg XIVCDV xarihr]ii[ivr)g xal rdg
V7tod'6ig avrdg rdg 7tol rd [if'y&r] xal rd
fiara pr} ovr&g %ov6ag ^ f>y^avrg di>G)Q&c
rb $ opoiov rt7toirixa[iv iiti r r&v rov KQOVOV xal
D. g|axo(TtaHts] m\it. in |axo<7ioireoug C 2,
e corr. D. 3. TT;S] tf) D. 7. xlel0a>i> (-vcorr. ex g D 2
) avr^g D. SiSovui D, corr. D 2. 8. rcov] corr.
ex rovs D 2. 14. re] supra scr. D 2
. 17. %ttQiGTiQOis C.
18. vTtoTi&stitvcov D. 19. inikl.Q'yiG\\Ltvifiv A, f7rt^Zoyt|(7ju,-
vi\v A 1. 21. natiJir}[L[isvr]s~\ pr. -rj- corr. ex 1 in scrib. C.
22. v.a.1 rd] Kurd C. 23. diOQd-caGdfis&a CD, corr. D 2. 24.
8s] d' D. in] xal ini D. r&v] rov C. xat] xai r&v D.
328 KAATAIOT UTOAEMAIOT
TOV(
EQ[IOV VJtO&GG)V XWtJGaVT^S TlVtt TG)V JtOOTOG)V
ov itccvv axaificbs efari[i[ivcov di& TO v6TQOV ddi-
6TttXTOTQCCl,S TrjatJGfGl, 3tQLTTV%r}X8VCCl,.
rotg t<p OVTL <pi,A,cchvjd'G)s xccl fyryrix
5 ftfooQia 7too<5Q%oiivoi,s pi} nabs [tovqv rv\v T&v ita-
r&v litl rb adi6TaxT6tQOv VQ1,6x0[isvcav
xal yfobs TT)V rcbv idicav^ av ovr&s h'%G)<5i,
10 7tcc'yyMaSi xav vn* aM&v xalfti) [i6vov T&g?' av
TilS && VO <XXQI,(l<3TQOV TV%G)6l dlOQ&TLVK [lV OVV TQOTtOV SKK6TO, TOVT&V K
V Tots (p%ijs trf's 6VVTK&&S xar& TOVS
T6rtOVS <X7todd)60llV. TQ^6^ld~CC $ V TG)
15 KKOkoV&iCtg VSKGV 7tl T^V T^S XaTK TthttTOS
CpodoV TOLCCVTrjV.
TtQKtTOV [lV OVV 1$ ify ttVTi]S T^S [l6V]S
TG)V
20 JtfaiGTOv %aovov, xa&' as TCC T ^iyd"rj T&V 7ti6xo-
Tt]6ov faa ydyov xal 7tQi TOV avTov Vvvdetfpov, xal
d[i(poTaas iJTOi, an aaxTcovtjdnb ^i6rj^i^QLag^ xal STL
(ol TO l'6ov] iiv dnoGTriua. TOVTCOV dw ov-
1. vno&EGtav} mg. B. TCQOTSQOV D. 2.
corr. ex adicczcrxTorsQccis D; deinde del. KCLTO, D 2. 7. r&v~] corr.
ex TOV C 2. to] supra scr. D 2
. ccdiacTayiTOTsgov D, corr. D 2.
8. ovrcos] supra scr. D 2. ftrjd' D. 12. TQOITOV] corr. ex
D 2. 14. ds~\ d' D. 16. St-l&iv A. f] ^ D, T D 2
.
20. TO] corr. ex Y.KTO. D 2. ^fyf-9-ft D, corr. D 2
. 21. L'GK]
in ras. D 2, mg. t'. ysyovtv BD, corr. D 2
. 23. TO] TOV C.
f}v~\ seq. ras. 1 litt. A. ajrdffrjjfia] &.- in ras. A 1. drj]
yd$ D, non male; corr. D 2.
MA0HMATIKHS 2TNTAEE&2 A'. 329
rcog %6vT(av ccvdywr] TO KBvrQOv r^
rcbv sxhsfyscov iitl ra avra
rov ccvrov Gwdfapov xccl dtd rovro rr\v axQiflij
ccvrrls oAovg xccra nAdros xvxAovs sv trca
jtQt,%ei,v. 5
plv eKteityiv rrjv enl dageiovrov jtQ&Tov rerrjQrjiis'vriv lv BccpvA&vi r& jtg&TG) xal
G) ccvrov erst, xccr' AlyvitrCovg Tvftl y' fig
COQCCS %' |it<?^g, xcc&' TJV diaGcccpstrcci,) on J
|-
fj 6&v\VY\ KTtb vorov daxrvhovs /3.10
sQccv ds rv\v rsrrjQrjUEvrjv iv 'AK&>av8Kia, r&
b'rsu 'Adgiavov XUT' Afyvitriovs IIa%G3V i% stg rr\v
yiQO rpi&v aQ&v faYjpSQivcov xal rgi&v
&Qccg rov peGovvKrfov, na& r^v oftotojg
rj 6e^vri rb sxtov [legos ffjs SiayihQov aito n<5- 15
]v ds xal fj [iv Kara jt^drog TCcc^odog rye;
TCSQl rov xccra{}i,(ldovTcc 6vvd<5[iov iv xarQa r&v
rb yKQ rOLOVrOV Xttl IK rCOV dA.06%Q6TQCOVV7to&6G)v Kur&.'kapft&vsrvii. rb d aTto^rr^icc fyyiGrcc 20
i6ov Keel utxQco rov p6ov itfQiyfiorfQOV xal rovro
TG)V 7tQOCC7toddl,'y[lVC()V 7tQl Trj
1. avdywr)] -y- corr. ex i in scrib. C. 3. TOV avrov] corr.
ex TOV D 2. 5. %qov(p"\ corr. ex XQOVCQV D. 6. Mg. a D.
fyla/3oft D, JAa^oft D 3. drj] corr. ex ovv D 2
. itQorrjv C.
fiev"] ins. D 2. 8. trsi ccvro^ B. Atyvmiovg'] -ovg in
ras. D 2. Tv/3t] T- e corr. D 2
. 9. s'] om. D, wrr)s D 2.
dtjaffaqpffrca A, dia\aacpiTai A 1. ^|e7ft7Tv] supra -8i-
scr. i D 2. 11. Mg. {3
D. trca]corr. ex T&V D. 13. rgi&v
7li\LTlX(QV\ TQLTOV V.O.I TCSflTtTOV D. 14. ^^L7t8V D. 17. jWfV]ins. D 2
. 20. ds~] 8' D. 21. nsQiytiottQOv] -to'- in ras. 4litt. ]3
2.
330 KAATAIOT IITOAEMAIOT
yivtrui dr\kov. Emid^ ovv, OTCCV ditb VOTOV
V\ 6h?jvr]) floQl,6TQ6v B6TIV TO XEVTQOV CCVTriS TOV
, (pctvQ6v, on xal xafi'' EXCCTEOKV T&V x-
i'Gq) TtoorjyEtTO TOV xaraf$i{ldovros 6vv-
5 ds6[iov TO XVTQOV Trig Gehrjvrjg. dhhd xciTa yiev rr\v
aitsfyev fy 0e^rjvrj TOV anoysiov TOV
xal %r]xo6Ta i-9" 6 ycco 4u(?og
sv BaftvAcbvi,i
y8iyovv nob riyu&Qiov TOV ILB&O-
vvxTiov, v 'Ake^avdQEiK d ttob [lias TQLTOV (boas
10 i6rniEQivYis, ual 6 ccTtb Tijs tito^s Trjg 7tl NafiovccG-
6&QOV XQOVOS 6VVKy8i TVl 0VZ XCil f)[lQCC
thcbs per I rS, nobs ds TK
i d', xccl dia TOVTO EAccTT&v rjv r\
S TtSQLOdlXrjS 71BVT8 [lOLQCCtS. KCCTCC $ Tr\V
15 dsvTBQKv Exteifyiv ani%ev j] Gfhtjvrj TOV aitoysiov TOV
7tixvxA,ov lotott 6vcc w' xal v&dd ao 6
Trj C3occ Kul fjpsoas 6v<5 xal wooes t6r][iQi,vas
[iv rj xal dvo jr^jrra, dxQifi&s $ n xa
20 did TOVTO $ xal ^ dxQififjs rtdoodos TtfaCwv i]v Tr^g
%OOVG) TG)V
i XCCi
2X mg. D. 6Tw] comp. B, ICTL in extr. lin. D. 3.
[isocav] (IG<QV T&V fadtoov D, corr. D 2. %at] corr. ex Y.&V D 2
.
6.rj] ins. D 2
. 7. ^] seq. ras. 1 litt. D. g^xocrra] om. D,
^|a BD 2
. 8. iv\ fv pv D. ysyovs D. 9. ^Zflavd^fat A,
'Ateccv6
D. 10. NapovvctGciQOv D. 12. r*] ^ BD, / AC,
dt' supra scr. D 2. 13. TOVTO] corr. ex TO C 2
. skaTtco C,corr. C 2
. T\V ri\ corr. ex fl'r] D 2. 15. ctntiitv] untile fisv I),
ptv del. D 2. 17. rjjg] rfjG\6 D. 19.
rj (alt.)] corr. ex o in
scrib. C. xca (alt.)] comp. supra scr. D 2. 21. ~S vy] post
ras. 1 litt. D, 8vy AC. 22. nEQitxovTi\ -i in ras. 2 lilt. D 2.
MAOHMATIKHS 2TNTAHE3S A'. 331
xal cogag farjiiSQiv&s KM [_' y' rj (lev CC
xata TtAdtog rtdgodog tf}g 6^vrig okovg 7tSQie%i,
, 17$ ItEQloSiXri VAt,7tV s$ ohovg XVX?iOVg
taig fj an,<potQ&v t&v avco[icdiG)v Gwayoiiwaig poi-
gcug # vy. eAfofasL de ex r&v itQOSXTS&eiiievcov xaxa 5
rag tovc
lTtita^%ov V7to&6i,g [ifa&v Ttagod&v sv rc3
G) ?g ohag attoxaTcc6ra6t,g iioiQccg i xal
a fyyitfra /3* jrAftov agcc yiyovsv TIKQCC rag
rj iL6rj xccta Jt/Unrog rtdgodog QqxoGroig &.
ovv 7UiiQfaavrg fig to nkri&og r&v x rov 10
y.fi
7tQOXl,[lVOV %Q6VOV (JVVayO^VOV f]{lQG3V M %& fy-
ytfra xal ra x rijg 7taQa($ohrjg ysysvruiEva o o o o77
AO- Irj 7tQo6d'vtg TG3 xat' Ixuvccg tag V7to&6i,g ngo-
ajcoddi,'y^VG) fjHQr]GiG) p^GG) xivrman [p. 279, 4]
VQO[iv [p. 279; 16] to dicoQ&KHLBvov poiQCbv !/y ~iy ~\Tz
15
AO" ^ ~v% AJ, alg TCukiv axo&ovd'&g xal tag
t&v KKvovCwv litiGvv&BGEig 7tQai
yiiatv6d[id'a.
d$i,'y[iivrig d ccTtafc, tov tgditov tovtov ti\g
dixfjg xata rthdtog xwYjtif&g ,fjg xal ig tqv t&v
avtrjg <5v6tct6iv ^rjtt]&a^v nafav dt,d<5ta<5iv 20
1. rjfiSQUL D. mQca l6r]peQivul D. xa C. y'] seq.ras. 3 litt. D. Supra ajt^tfSrjg KKTK ras. D. 2.
iD, post -do- ras. 1 litt. nsQisfytv D, -v del. D 2
.
3. svehnsv D. 4. poigaig GWKyo[ivcit$ D. 5. vy] v y A.
ds ex] corr. ex 5J
Ix D. 6. rov] supra scr. D . sv\
ins. D 2. 8. |3] dvo corr. ex 8va D. y^yovs D. 10. ovv]
per ovv D, corr.D 2. 11. M] ADB 3
, ^ BC, *J3 D 2.
^-9- CD, corr. D 2. 12. TO: ex] corr. ex raaex D 9
.
D. o (quart.)] ins. D 2. 13. rm\ ins. D 2
.
corr. ex tnovaff C 2. 14. ^fpijcioo] -co corr. ex -oav in scrib. A,
^- corr. ex v D 9. 15. SioQ&cofisvov CD, corr. D 2
. 17. em-ult. corr. ex t in scrib. A. 19. xca] comp. A.
8- postea ins. A.
332 KAATAIOT nTOAEMAIOT
txksfys&v dvo, xcc&' as rcc psv
rolg TCQOTSQOV Gwdfiawsv, TOVTS'GTLV TK TS aito-
rife GsAtjvys syyiGTa faa syivsro xccl aC siu-
facu, rs xal JJTOI TfQOs CCQXTOVS 1} Jtgb
a^(p6rEQa,i^ 6 $ tivvdeGpos ovxsrt, 6
6 svccvrtos.
xal rovrwv d% rcbv txfafys&v itQ&rrj
'K xal 7CQO$ r^v tfjs avco^ct^ccg
ds rc3 /?' srsi MagdoxsiiTtddov xar
10 TLOvg cod' itf slg tnv l& & ^ v BafivAcbvi, rov
de 'Aks^avdQeia ago L' y' pi>&1
'
r^v diaGccyeZrai, Extehoiitvicc fj
ccjtb v6rov daurvAovs y.
devT8Qcc de, ri Keelr
'l7t7tccQ%os 6vve%Qri
15 Tc5 K' erst, dagsCov rov pera Ka[i{lv6r]v xccr' Atyvit-
sis rfv nft' rijg VVXTOS TtQOsh&ovGrjs
y', KK& tjv Oftotog s$sA.st,3tsv fj
aitb VOTOV TO rzrccQTOv ti]g dia^BrQov^ xal i\v
6 [i6os XQOVOS sv iiev Bafivk&vL XQO Svo Tts^inrcov
20 [lias &QKS l6yiiQ(>vfis fov psdovvxriov ,snsl TO ^i-
vvxnov i\v TOTS MQcbv^forjusQivcbv g /_' d' syyitiTcc, sv
'AAs^avdysia ds TCQO cc d' CDQCCS faypSQiviis TOV
VVXTLOV.
D, -cc- eras. 2. GVV$UIVEV\ -v eras. D.
comp. B, -v eras. D. 3. I'GCC ^yytcra D. sys-vovro D, t supra scr. D 2
. 5. ovntri] corr. ex ot>x ?Wt D 2.
6. all? D. 7. TtQwrriv D, corr. D 2. 9. Ss] comp. ins. D 2
.
11. HQO\ -6 ins. D 2. 14. l7tncc()%o$] 6
r
'ImtccQ D. ysvo-
(UfVrj CD. 17. tj y'] % T C. Q&tmiv D. 18.
d' B et seq. ras. 4 litt. D. 19. uip-jitov D. 20.
VVXTIOV D. 21. /'I in ras. A. 22. 'AHE^avSotcci A.
ins. D 2.
MA0HMATIKHS STNTAEE&S A'. 333
TBQK
E dl xal TOVTOV rcbv sxfofyecov EXKTEQK T^g
negl TO frfyttitov ovGqg ajro'tfr^a, aMarj [lev
TOV avccpi,pdovTa GvvdsGiiov, % de dsv-
rbv xccTapifid^ovTcc, csg xccl EVTCCV&CC T& i'6c)
sivcu rov dia [is'dcw sv avralg TO KBVZQOV 5
6x03 dr\ 6 Ao|6g ccvrfjs Kvxko<s b ABP TCEQI did-
TO [lev A Grftistov b
G)v tivvdeGpos ,TO
ds F b xaTccfiipd&v, TO ds 10
B (loQi6TaTov 7tQccg, xal
aTtElAtfcpd-GXyaV fcai, 7tQl(p-
QiKi d(p' XCCTQOV TfOV A, F6vvd6[iG)v as JCQOS TO B /3d-
QIOV 7tQCCg Oil Ad KCcl FE, 15
&6TE KCCTK {LEV TVJV ItQOTSQKV
Kara TO A ivca TO
/3' XCCTK TO E.XBVTQOV
fiv iitl
TK)V 6TIV
KCCTK
Kttl tj Xttl G)Q(bV 20
v catkcbg TE xccl ccxQifi&g la gr
,xccl dia TOVTO
cc7tl%v rj GEhtjvr] onto TOV anoyEiov TOV Eitixvxkov
t/3 xdj jtfaicov TE %\v ^ JtEQisodixrj ttdgodog Tijg
ig v&' b dl litl Tqv SEVTEQCCV E'K-
bpOLcog T&v AlyvTtTiccK&v 6{i xccl YULEQ&V TX^ 25
xccl a)QG)v v catk&g {ilv ~i C d', ds
1. s*lfytcov D. 7. 6 (pr.)] postea ins.D.^
Ho6? D. 11.
E] B TO D. 12. TttQicpsQsiui] cone, ex nsQiysQua. A. 13. A,
T] AT B, A Y.&.1 r D. 17. TO (pr.)] TOV D. 18. TO] TOV D.
&U' D. 20. IOTLV] ins. D 2. 21. Ante 5' eras. F A. 22.
ccTto] om. D. 24. 6*6] 8' D. 26. i'] corr. ex [_ A 1. /.' d']
in ras. 1 litt, D 2. dx(uf3oog Ss T d'] mg. D 2
.
334 KAATAIOT HTOAEMAIOT
Id', xal dt,a rovro aitsfysv fj 6s^vrj cbro rov aito-
ysiov \rov srtixvxAov [IOLQCCS ft ^d, itteicw rs i\v rj
Ttsoiodixri itdoodog rijg dxoiflovs sfyxoGrotg 1/y. xal
6 iiera^v ds r&v rrjotftisav %oovos Ttsoisxcov Alyvit-
5 naxa srrj Wiy xai ^BQKS r& xal &QKS faypSQivac; ny
i$' Gwdyei, Kara ryv aTtodedei'ypsvqv rov
enovtiiav ftot^ag p xal
ovv dia ra exxsipsvcc xcclr\ [is0rj jr
rov xsvrQOv r;jg Gshtjvrjs sjtl [iev rijg Ttgoregccs
10 i[>G)s xarcc rb Z, snl ds rijg devrsgas xara rb H. xal
i\ [isv ZBH itZQifpegsia. [IOLQ&V s6nv Q% xal
, r\ds 4Z sfyxotir&v v^, r\
ds EH s%rj-
Ty, 6vva%%"ri<56rai xal ^ ^E TtSQiyegsia [ioi-
v. xal 6vva[i(p6r()a{, per aga ai Ad, ET15 r&v Aoirt&v slow sis rb r\^ixvxhov ILOLQ&V i& I, sxa-
rsga ds avr&v, sitsl faai sidCv^ r&v avrcbv ^
fj axQiftrjs itdgodos rrls GsAtfvrjs xara psv r^v
sxAsiiluv VTtshsfasro rov avafti,ftd^ovros
xara ds r^v dsvrsoav rov xarapifid&vros
20 xal O^TI ply aoai\A Z rtsoiysasia JIOLQ&V s6nv T Ad,
dsrjHP poiQ&v ft xfi. &0rs xal
fj
rijs 6s^vrjg xara [isv rr^v Jtoorsgav
rov avafiifla&vros 6vvds6pov iioioaig 1 Ad
1. xal i&\ in ras. D. ano] om. D. 2. sniv.vy.\ov] -xvx-in ras. D 2
. Tt^ftcov] -ft- in ras. A 1. TF] 8s D. 4. F'TTJ
Alyvmiana, D. 6. cvvdysi] -a- supra scr. A 1. ajrodf^ftyjjttf-
vr\v corr. in encoded i\ynevr}v A. 7. ^j]v.oGr&v D. 11.
ZBH] ZH D. 12. EH] E- supra scr. D 2. S&KOGT&V]
comp. B. 14. ET] v.al EP D. 16._^] om. D, 8' suprascr. D 2
. stGiv} comp. B, -v del. D 2. #] corr. ex o D 2
seq.
ras. 1 litt. >U] /I- in ras. D 2. 19. itgoriyeito rov nctra-
fit,pdf;ovto$ D. _ 20. poiQ&v] om. D. GTW] comp. B, -v
del. D 2. 23. Id] i j C.
MA0HMATIKHS STNTAgESS A'. 335
xal U7tl%v aitb rov B jSoofiov 7toarog [loiaag tfjr
Ad, xara $ r^v dvroccv Ttaoyytfro rov xarafiipd^ov-
rog yioiQttis & xfi nctl aitetyev rov avrov fioQZiov vtBQa-
rog [loioag it Ay.
rov pfaov ryg 7tQoroccg faAffyfcog 7tov6iav
jtAdrovg ^oigag 6xg ift, ravrccg
Kara ryv iito%r\v ryg
avrccts Zva nvKkov, ^o^v xai els to <*>'
srog NccftovccGGaQOv xar' AlyvxrCovs wO1 a ryg 10
li6ruifiQia.<s r^v rov jtSQLodixov nhdrovs 710%^ aito
rov floostov ttSQcctos {loiaas rvd 7f. xccl ngbs rag
de rCbv Ttsol rag Gvvodovg xai itavGekrivovQ
^qqiocpoQicbV) sitsidrj Kara rag rotccvras
ovdev 7tQo6drjd"r]66[i&ci rijg anodeix&rjGo- 15
devreoag &vtopcdfa$, x&fjtf6n&a r&v xccra pe-
QO$ T[ir][ittta)v xavoviov dia r&v yQapn&v itahv,
xccl 7tl rov ^/U'ov, r^v itQCfyiiccreiccv avr&v
xotl 6wy%Qr}6dnvoi, pv r<p r&v Qtfxovra
xccl d' A(5y, dieAovtes ds catiavrcos ra plv 20
r& ctTtoysicp rrccQrr][i6aia dia ILOIQ&V s1
,ra ds
trc5 itfoiyfiG) dice ^loiQCbv y, cog ndfav rr\v rov
xavoviov diccyaacpriv bpofav yCvstiftat rf} iitl rov rjMov
1. &nefysv] corr. ex &ne%iv D 2. 2. ngoriyti D.' 3.
iBi^s D. 5. Ss~\ 8' D. 6. &d,</i/>eog] rfbv fatefyfaw D.
8. GTC Ad corr. ex Gnk d D. 10. NuowaudOv D. a']
D; similia saepe omisi. 11. 6.7to%riv D. 12. niqaros]corr. ex niqug D 8
. 13. xi] v.al rds I). 15. 7tQOG8ei]6Q-
HS&K D. 16. r&v~\ TO r&v D, supra -d ras. et ante -&-ras. 1 litt. 19. ffwronadfievoi, D. rw] seq. ras. 1 litt. D.
t&ptorca] I D, g D 2. 20. wC] om. D. Adyw] -w e
corr. D 2. SiMovxss BC. Ss] d' D. 23. T#] T'TJS D!
336 KAATAIOT HTOAEMAIOT
V, TGJV
dvo 7tQi%6vrG()v rovg aoi,&iiovs r&v rijg
rov $
5 yi,vo^vrjs Kara r^v tyrppocpOQiav iiti t rov
xal rov Ttkarovs, orav 6 rffc dvG)[iccMag aito rov KTCO-
ysCov rov itMvxhov Gwayd^vog aai&tibs &S ^[loiQ&v ft, ri}$ d 7tQo6&6G)S) orav rag ^
v7tQTtfarr}. nai tGriv rb navoviov roiovro*
1. GEliSicov] -li- supra scr., -8- in ras. A. tQi&v] y B,y D. 4. itQOG&cHpcciQSGSLs] -&- corr. ex o D 2
. 5. yivo-
^f'rTji^D, corr. D 2. 6. 6] 6 ccno D. 7. sag] corr. ex tog D 2
.
8.TI jaot^ag] supra scr. D 2
. 9. v-JtSQitinriri] -y corr. exft D 2
, vntQwninTy B. EGTIV] CD, comp. B, isxi AD 2. toi-
ovtov CD. Deinde add. in imo mg. fol. 93V : inzl^v j\
ro5 a ETSL vafiovvaGaQOv rov daft vsoprjvfa elg TT\V \
\L IK X
&no%f]g |/ ft o A nldrog fiogsi TISQ p TVJ Ts : ?-
|4^
\D.
MA0HMATIKHS STNTAgE&S A'.
Ktt.1
337
Y.OIVOL
(T
itQOG&acpcci-G
v
TtQOG&CtCpUl-
TUT]
Y.& QY. Ice
is
30
I
Is
3
vy (JH-91 Gld
Gun]
GY.S
n
X
6^8
G7C1]
QV
oogGO
gvsQV&
Gift
GLS
GiyGl
y
y
y i
G8GK
is
vy
35
40
ty
c,y
<f
90
GVK]
Gve
vy
45
te
tTJ
1.(,'] B, om. A CD. V.KVOVIOV 2. Gslijvris] om. D. 3.
Offt. f at '1 T\iiQK(pQGi.s D, nQOGvcupKiQ C. 4. cc p y J om. D.
Ha] corr. ex X D. 13. va] corr. ex v D. 31. cl8] Gla D.
35. ffx(5] postea ins. D. Omnia sub uno capite codd.
Ptolemaeus, ed. Heiberg. 22
338 KAATAIOT DTOAEMAIOT
id. "On ov Ttaoa rag diatpogag r&vnaoa rovg EitiAoyiGiiovg 8ir\vyxev xard
rbvf
'Iit7tao%ov r\ ytrjAixorrjg rrjg
5 Tovrcov ovrwg aitodsdsi'ytiEvcov Eixorcog civ rig
sititfitYiGeiS) dice Ttotav alriav EX r&v vnb rov
%ov 3taQKt&ei[iva)v Gshyviaxcbv sxfofyscov xgbg
rrlg roiccvrrjg avG)[iaMag eititiKstyiv ovts 6 avtbg
TCCL hoyog r vg>' f][iG)v KTtodsdsLy^sva) ovrs
10 6 TtQ&tog Keel dia rrjg xcct' HxxsvTQorrjrcc
r& devrsQC) KKI dice rijg xarJ
ertfavxhov vno-
3ti,foA.O'yi,(j[iVG). xata filv yap r^v jtQcotrjv
dwdyei rov hoyov rfjg x rov xwtgov rov EX-
xwrgov agog rv\v pEru^i* rcbv XEVTQCOV avrov rs xal
15 rov dia [lEti&v r&v Z&di'cov xvxhov, ov E%EI ra yQ[id
Jtobg ra rxt, rB syyiGra, cai Adyw 6 ccvrog 6rt,v 6 r&v
| Ttobg ra g Z?, xara ds rrjv dsvrEpav Gwdysi rbv
Aoyov rrjg EX rov xsvroov rov dia [lEGcov rcbv ^radtov
pEftQi' rov XEvrQov rov ErtixvxAov itobg rr\v BX rov
20 xEvroov rov Eitixvxkov, ov E%EI ra yoxfl [_' ftobg
//, G> hoyc) 6 avrog fanv 6 r&v \ nobg ra d
Ttoisl ds rb JtAEiGrov rrjg dvK)[taMag didcpooov 6
rcbv 1 itgbg ra g 8' k6yog poiQcbv ftO1
,6 8s r&v f
B, om. A CD. tag] seq. ras. 1 litt. C. 7. naga-D. 8. loyos yCvEtai D. 11. vrto&sofas] -g in
ras. D 2. 15. /j^ttf] yy- corr. ex FA 1
, r mut. in I) D 2.
16. ^tj] rt D. r*] r ABC, r B D, Si? D 2
. scnv]icriv g' D, corr. D 2
. 18. Adyov] alt. o in ras. 2 litt. A. 20.
^(^(3] jT Q-x.pD.
[^~\in ras. D 2
. ngog] nqbg rd D. ffj^//]e corr. seq. ras. 2 litt. D. 21. scnv] sen xca D, xat del. D 2
.
23. r&v (pr.)J supra scr. D 2.
MA0HMATIKHS 2TNTASE&S A'. 339
ta d~JLS [loiQcbv d Ad, KK& faces rov T&V
ra~
d' koyov poiQcbv syyitircc XOIOVVTOS ttyv wti-
[lV OVV OV TtCCQK rrjV T&V 1)710%'6 G)V
G)S ol'ovrcct tivs, fj TOiavrrj TtaQrjxoA.ov&rjGsv 5
,xal t& Adyw yiiKQ& jrpdfrfrfv tpavegbv fair
yfyovev SH rov x0-' MCCTSQCIV uvr&v ra avra <pcuvo-
psva GvpfiaCveiv ditccQccM.dxrcos, xal dia rfbv aQi&p&v
fo', el ftshriGccinsv TOVS eitiAoyiGiiovs TtoislG&ccii rbv
CCVTOV CCV VQOl[lV yiVQ\lVQV AoyOV f'| tt[KpOTQG)V TG)V 10
)si rots ccvrotg \iivrQi
p exccregas xccl ^dvvccTov y&Q ovrcog k'tircti
TtCCQCl TOVS T&V dlCC6rCC0G)V 3tlAo'yi6[lOVS ify K^KQtLaV 15
Qr^6o^v yovv xal iit Xiv&v r&v
TCCS ^V 6vvyiccs vyi&s TfT^p^jifWg xal
j^vccs rcctg v(p'
xal rijg dvco^id^ov xivvJGfcos V
$ i&v dia6Td(3ov iitiKQyiGpvvs, 81 d)vf} it^i- 20
rov Adyov SeiKwrai) ^ liti^^&s^ &S ^vi pd-
ysyevYiyisvQvs. dfi^opfv ds tovrcov
ditb T&V
1. <?(alt.)] A D. U~\ seq. ras. 3 litt. D. w&s rov t&v] -s
tov T- e corr. D 2. 2. [IOIQCQV] {* D. 10. yivofisvov] om. D.
11. fqp' SKccreQccs axoAov-^Tjaaififv D. 12. diacpogois] dia-
qpo^eog D. 14. v7tOT8&inVG>v D. ccvrds'] -tag add. D 2.
rug T7]-] e corr. D 2seq. ras. 1 litt. 15. ^m^oyiG^ovg A,
sndoyi\6}iovs A 1. 16. evQioo^sv C. 18. -s tats v-] in ras. D,
rat's supra scr. 21. TOV loyov] rovrcov B, rov C. SVL] e
corr. D 2. (idhcrcc] ft- in ras. 2 litt. D 2
. 22. rovrov C.
340 KAATAIOT HTOAEMAIOT
TCCVTCCS [iv di) rag rgsts SfJltty&g
KTtO TG3V X Bafivh&VOS dIKXQyilG&eLGcbV O)g Xi
syovzvcci ds TVJV TtQcorrjv KQ%OVTOS
vv\6i <&avo6TQKTov [irjvbs IIoGsids&vos xal
5 Ttsvat r^v 6^vrjv fiQa%v IIQOS TOV xvxhov
Qivr[$ dvatohijs rijg VVXTOS AOITCOV ovro$
xal hi, <pri<sCv, xA,faov6ccr
dv. yivtiui toivvv
6 %(>6vos Kara, TO T%$' rog aitb NccfiovccdtiaQOV
Atyvjtriovis ^f, cos ccvr6s (priGiv, cod" x<s' slg xi]v v^'
10 \JLSrCLf /.' &QO,g XCUQlKCiS TOV llSGOVVKtlOV , 7tldlJ7t()
i\v ffjs VVKXQS fjiM&Qiov. ahAa rov fjAiov ovrog
tec k'<5%attt TOV TO^OTOV v BafivAcbvi, fj Tils
%QOVG)V <5TiV1/Tj' ^ yp VV%
Kttl dlJO ItfyltTOV' CCi 3tVT ij[ll,6V CCQCC
15 XKigwal tivvdyovGiv iGyufQivas &QKS S KKL TQLK
Jt[MtTCC. $1 KQ'xfl KQK T^S xA,fyG)S yfyoVf (JLTa Irj
l,6 [l
CC L'
20 k'yyiGTK, 6 $ [i6os drjhovoTi, [iT<x tO* y' CQQKS
QIVKQ. v 'j4A,%avdQic{ Ttakw aQa yfyovfv 6
XQOVOS Tils xfafyG>s f*^ t^ /.' COQKS l<5rniQiva$ Tils
iv TV} x$' ftf^i/ft/3()tag. KKL i^tiv 6 anb Tils wtu TO
1. ^TJ] ovv Set D. TtccQutid'fG&ccL D. 3. Trpcbrrjv] a' B.
mg. D. 4. IIoGide&vos D, corr. D 2. 6. XotTtov] -v
corr. ex i C 2. 8. TO] ins. D 2
. NK^OVaGGa.gov] -CCGG- in ras. A,GccQov D. 9. dz] ft-aft v& D, alt. -O1
postea add.
b'] om. D. 12. tfjs] -fj- e corr. A 1. 13. lmtv\
D, comp. B. atgiav ZGTIV iGrnisgiVcav D. 14. nevte
ypusv] ?/.' BD. 15. rgCci] -i- ins. C 2, y corr. ex ty D. 16.
nsfiTtTK] F D, e" D 2. 17. %cct] in ras. 1 litt. D. TQICC
itsfjintcc] y D, y t" D 2. 18.
|u,s'(>og]om. D. 19. eo^a?] comp.
AC. 22.trj] corr. ex 73
D 2.
MA0HMATIKHS STNTA&EgS A'. 341
'
frog Nafiovao'o'dQov eTto^g %Qovog ^#pt fov i)ito-
STtbv Alyvitnax&v r% xal Y^LSQ&V us xal
ftLQiv&v aith&g [iv Trj /.', dxoip&g d Irj
''itobg ov %QOVOV 7tt^oy^6}ivoi xara rag *xxt,[ivag
V V7tO&6ig rOV {llv yklOV VQfaxO{lV aXQlfi&S 5
To^orov [toiQctg xrj Irj, rrjv d
xal xara rrjv av&iiaMav aittysi rov
rov 7tixv%Aov [LOLQas 6x jUy.
JJV %ijs xA,tipiv (prjGiv yyovvai, aQ%ovrog 10
<&avo<jTQaTOv
iv, djtb &8Qivi\g avaro^g rijg jc^corrjg cngag
yCverai drj xal ovrog 6 %Q6vog xara
to T|S' f'zog anb NafSovaGGaQov <&a[tVG)d' xd' ig xrjv 15
xe' Ttgb ? /.' CSQCOV {idAiGTa xaigixcbv TOV [i6ovvxTiov.
aA,A,a tov ^iov ovrog Ttfgl ra 6%ara r&v 4t,dv[jiG)v
y rqg vvxrbg figa iv Bafivtibvi %QOVG)V 6rlv ifi' au
aga /.' xaiQixal agon TtoiovGiv foqptytv&Q d xal dvo
n[iiira. q aQ%r] apa rqg &cteAfrGti ytyovtv pierce f 20
fioag t<5r]iiQt,vag xal rgta ne^nta ryg iv rrj xd'
1. (H mg. D. NCCPOVVCCGKQOV D. TtQOHflllSVOV D. 3.
comp. e corr. A 1
seq. ras. 1 litt., om. BC, del. D 2.
4. itQOs ov} corr. ex nocov D 2. 5. rjp&v] corr. ex vp&v D 2
.
~
TOV D. 8.
corr. ex sl%e D 2. 10. qpijeti/] -v del. D 2
. &Q%OVTS<S D, -s-
del. D 2. 11. 'A&i]vr]6i BD. cyu&QotpoQi&vos D, corr. D 2
.
12. St] supra scr. B. l&Jiiieev D, -v del. D 2. 13.
a B. 15. NK^OVVKCKQOV D. 16. pcikiGta. MQ&V D. [ie-
GOKTLOV C. 18.17] corr. ex i\i A, om. BC. tart D, comp. B.
_ 19. "/_' KQK D. KCCI] -K- in ras. A. dvo nl^inrcc] ft? g' D,
^ F" D 2. 20. yeyove BD. 21. co^a?] 5- in ras. 2 litt. D 2
,
-a- in ras. A. TQICC nf^nTa] y' s" corr. ex y s D. -r^g]
corr. ex rfj D 2.
342 KAATAIOT nTOAEMAIOT
rj[if}()icis- &W fad o n&s %Qovog rijs
tQi&v <xva<yQK<psTcci,, 6 ^<?o dyhovoti ysyovssvvsa xccl dexarov cogas fttyptyttri}?. iv
'
CCQCC oysifoi, yeyovsvcci [ista vjd' syyidrcc Syces
5 Qivag r^g ev rij xdr
iLsGrjuPgias. xai i6n ndfav 6 dnb
TG)V S7CO%G)V %QOVOS TG)V AfyvTttlCCX&V T^S KO,l i\^QG)V
&y xal MQcbv tor}(iQt.v&v uicA&s y&v n ^'> KKQI^&Q ds
5 11 y'm
ftQOS ov %g6vov svyfoxopsv rbv per ijfaov
axQijS&S 7ts%ovta ^didv^cov [IOIQCCS xa jilg, tf}v 8s.
10 6s^v^v [t6(QS [lev To^6rov [tongas H/y ^vr^ axQip&s$ lOiCCS MX L( &C1$1XB XCCTcl x) dvCOCi^iKV CCTt-
rov K7Coyiov rov
(5vvKyrcci ds xal$} $ufartKft$ j]
coco rv[ rtQ&vrjs sx-
fofyG)S fal inv dsVTSQCCV f}[lQG)V Q0% XOi
15 xccl rQi&v TtfyrttGOV i6r][iQi,VG)v, [loiQcbv d, as o
Qoy xrj^ rovr
Irt7tccQ%ov TtoirjGa^vov
cos tfj? dt,K6Td6&s fiiiSQ&v ILSV
far]HQiVG)V 1/y H d\ ^IOLQ&V ds
rb oydoov [ISQOS [lifts [loigas-
20 rfjv $ tQitriv (prjtilv yfyovsvcu CCQ%OVTOS''
Evavdpov [irjvbs IIo6i,dsG)vos tov TtQorsQOv xccrd
2. peGog] post (i- ras. 1 litt. A. 3. EVVSCC] & BD.
tov] FED, i" D 2. IcTiiiSQivfis] ABC, corr. ex IGT]^QIV(X.<S D 2
.
4.rfi ri KCCI D. d'] mut. in 8" D a
. 5. 6] ins. A 1. 7.
cry] in ras. D 2. iGr}[LQiv&v] corr. ex lc TI^ISQIV&V D 2
.J\ ^']
in fine lineae add. D 2,in initio sequentis f) d' del. D 2
. 8. y']in ras. A 1
. ngbs oV] corr. ex noaov D 2. 10. xy] -y in
ras. D 2. 11. &7ti% corr. ex iTttfytv D 2
. 13. ngwrris] a. B.
14. fovTffttv] B B. 90^] (isv QO D. 15. TQI&V nsfjiTttmv]
sy" D, f" TQI&V D 2. 18. famovccav] -G&V in ras. D 2
. 19. rb
oySoov] i] D, j\" D 2, mg. yg. rb oydoov D 2
. jtt^oe] jcW^m, -si
in ras., D. fuag] a B. 20. cprtGi D. ysyovsv D, corr. D 2.
21. rov TtQorsQov (irjvbs TIoGsidscovos D. y.ctra\ ncer' C, Kara, df D.
MAOHMATIKHS STNTABE&S A'. 343
00)0- i$ els fty *'' &teut6V de,
dnb &SQI,V&V avccrohcbv d agcbv. ywTat, d?) xal ovrog 6 %QOVOS Kara TO
r' hog drtb Napovattdgov (bO- i$' ig r^v i itgb
]3 // ftaAttfra COQ&V rov iisGovvxttov. aA.A.a rov fyCov 5
ovrog itSQi ra dvo [isQiq tov TO^OTOV sv BafivAtivi, fj
rilS wxrb$ aya XQOVWV itiilv Irj b'yyiGta,' ai KQCK, @
i' GDQCCI xaLQixal xoiovtiw fayiUQivag &Qas y. >E
rflg sv rfi i$' lUtiypPofae. aM.a sxsidfj 6'A^ s&AsiTtsv, 10
6 ftfv itas XQOVOS syyitita ysyovsv GOQ&V d
yb ds [i6os %QOVOS drjAovori, ^ira la cogag
6
sxrov
rrjg iv rf/ i$ ps&r$k$Qfa$. xa i&nv 6 anb t&v 15
r|g xal
xal &Q&V l<5rnLQW&v aith&s plv Ttakuv I
dl -91
/.' y'm
itgbc; ov XQOVOV t&Qfaxapev xbv fiv ijfaov
To^orov {lotgas tj A, rr}v ds <?aA^'-
[i6G)s pv ^didv^KDv [lOiQag tj ncc, axQip&s ds t 20
^, dia TO xaTa TJJV ava)[iaA.iav UTtiyziv TOV axoyftov
TOV 7CLXvx^ov oia jta i. (3vvdTai $ xal f
1. ts'] corr. ex ty D 2. ii-ttutsv D, -v del. D 2
. 2.
KQ^Kfisvri] om. D. <? cb^cov] corr. ex SOOQCOV D 2. 3. Stf]
$ D. 4. NK$ovvttGa.Qov D. tg'j corr. ex v.' D 2. 6. sv]
ndliv sv D. 7. Ivtt D, comp. B. ^ /_' CCQK D. 9. fV
Mtfjscos A. ytyovs D. ft] corr. ex p D 2. ^ffrjjtisptvag]
om.D._
10. &U.'D._ i^ilinev D. 11^ yc'yove D, corr. D 2
.
14. F snrov (OQUS] t? D, F g" D 2. 17. T?'] corr. ex Ig D 2
.
18. 7tQO$ ov] corr. ex TTOGOV D 2. 19. TO|OTOV ax^i^cog D.
20. xa] -a postea ins. D, supra scr. x. 21. TOV] <Jbr6
TOV D.
344 KAATAIOT HTOAEMAIOT
cbro trig devttQag STtl xv\v tQiryv sxAeityiv did<5ra6ig
V [lV Q0% Xal l0r]^lQiVG)V COQG)V /3, [IOLQ&V $
tovr
Iji7tccQ%ov Ttdkiv v7tod'^Lvov xal rccvrt^v
yilv po xal &Qag a rB
5 ds (>o ^. cpccivsrcci, ovv v rots t&v diaGraGecw iiti-
koyitiiiots dt,si(jvc>[i8vos iitl [isv r&v rjusg&v g' re xal
y' pias G)Qa$ t6vuLQivi\<3 ,itl dl r&v poig&v xgiffl
Tti\LTi'tQi fyyiGra KCL& XCCTQCCV [lifts poiQas, aitQ ov
rrjv rv%ov6av v TTJ jnyAtttdr^Ti rov koyov10 cc7f^ycc6a6d'cct, dvvarcu.
a dfj xccl iiti rag v6tQov
rovrcov d rv\v rtQ&rrjv cprjtilv
rrjs dwrfyas xccta
15 KKT' AlyvTtriov
TtQO
CCQCC
dl G)Q&v KcuQixcbv Tov prfovvxriov, itQQ roGovrcw
20 xal farjiifQivcbV) $Xid4ptQ 6 ijhog itQ\ ra
1. SSVTSQKS] dsvrtQag IxAffywg D. f'jdfityiv] om. D. ^t-
corr. ex dtaffTaffet? D. 2. OJQ&V IGTIUSQIV<QV D. 3.
*Init- e corr. D 2. 4. atQccg] wq&v D. rs
~\ J^ Ar
r BCD, mg. a r" D 2. 5.
73]%at
TJD. 6. du-if>VG\[ievos A,
8itf)v\G[ivo$ A 1. 5'] g wZ D. 7. y'] pwt D; mg. ?HTO>
TS XCU TQltCj) D 2. 8. TTSflTTTOlg] D, f" D 2
. jtUCJs] B.
9. 3rr]/l(.x6T7]trt D. 12. a-urai T^ftg] KVTWV D. (jprjatv] ^? D,/J add. D 2
. 13. TfTTje^ffahu] corr. ex rriQfLG&ca D 2. qprjatv]
comp. D, ex parte renouat. 14. hsi] U,' D, U'st D 8
. Kal-hntnov D. 15. %ar'J xara D. (ASGOQL B. 16. TJJUOOJH'OV] corr.
ex (>ag D 2. %6%ctTov] -c- e corr. D 2
. 17. r^tVTjff] corr.
ex f D 2. 19. TT^O] Tr^dg BC. 20. Tstevrai C.
MA0HMATIKHS A'. 345
cotirs [isra cogag
iv rr] tg' [isGyppQiag iv 'Aks^avdQsCa ydyovw 6
rijg SKAefyecctg. 6n ds 6 KTCO rav xccra TO
frog NaflovccGtidQov STCO^&V %Qovog ir&v Al-
yvmiax&v cpii<5xal r\yiQG)v rJLtf xal MQ&V fariiLSQiv&v 5
ov
rvxg g, t^v d GEJitfv'rjv [ifo&g ^nlv '!%&V(DV ^ot-
Qccg xfi) axQiflcbg ds [IOIQCCS K% ^, dia ro Kara TY\V
avco[iccMccv d7t%iv rov aitoyfiov rov fitixvx&ov {loiQccg 10
t xccl
rijg avrijg
$
Xttl
wary
xcc y
V COQCOV XCCl
CCQCC
Tec xal y' cogag
7tidiJ7tQ itdfav 6
dice TO
6tiv 6 dnb r&v 7to%<av
Jjg X- 15
rijg iv ty
g 7t$l ra
X-
rov- 20
2.TJJ~\ A,
ras.
xy A 4, rrji D. tg'] COIT. ex comp. xat D 2
.
D,"
add. D 2. 3. BGTIV D, -v eras.;
comp. B.tfe']
ds Y.KL D. 4. tTOg] t, D, t-,' D 2. JTWV]
corr. ex TWI/ A 1
, comp. D, 5? D 2. 5. TILS] rpz D, supra ?
atQ&v] corr. ex r}(ieQ&v D. 6. /_'] e corr. D 2. 10.
?] bis D, extr. et initio pag. 11. sr]v.oGTd ] |a
D.
12.qp7]fft] tpj]Giv B; 9 D,
spostea add. ra] rcot corr. ex
rco AD. v7
] e corr. D 2;
v8' Ideler Hist/Unters. iib. d.
astron. Beobacht. d. Alten p. 216 sq., qui deinde p. 346, 13 ccvtti
deleri uult. ?rst] e corr. D 2. 13. MS%LQ B. 14. ngoa-
tk&ovG&v D. TQtTrjpOQLOv] r D, mg. yp. TQixruLOQiov D 2. 16.
IK] renouat. D 2. v.ai\ om. D. 17. Jvcm?] ^ BD. faeiSy D,
corr. D 2. 19. %at] supra scr. D 2
.
346 KAATA10T HTOAEMAIOT
rov %aovos ir&v Afyvrtriax&v <p/i xal
xal d)QG)v ior]iiQi,v6)v djt^&s r xal aKQ
1/y y' nabs ov %QOVOV KHSavrcas BVQI^KO^BV rov [isv
ijhov anal/Seas it%ovra r&v 'I%&vov fiotpco? jc? tj, rr\v
5 ds 6s^vrjv [items [iv Xqh&v poiQav a, axQifi&s dl
v poiQas x? 7?, ^td^jr^) Kara ryv dvo^a-
a7ti%ev rov anoyfiov floras Q& xrj. GwayBraidl xal r] anb ri}$ Ttg&rrjs Mfafyfcos litl rqv $vrQavdideraGis YI^QK)V goy xal MQcbv i6r][iQiVG)V g {_' y',
10 yiOiQ&v df ^ la9
rovf
Ijt7taQ%ov JtOirj(3a^vov rrjv
dl%iv G)g rrls diaGrddf&s ravrrjg r^iBQ^v [ilv
00?} K0
rr\v df roirqv tpytilv MteityLv ytyovivai ro5 avrcp
VB BXBI r^s dvrQas XQi6dov xar Alyvitriovs Me-
15 Goorj B', iJQ^aro d rys vvxrbs TtQOBk&ovticav c)oa)v i
TO Kal ^^l,7CV oA^. Kttl XQV ^LB&OV
%QQVQV cprjol yfyovEvai, TIBQI &oas
roirrjuoaioV) rovrttirw pra /3 rgCrov Soag
rov ii6ovvxrtov. dMa rov fjMov ovrog Jtol rd
20 ri]3 IIciQ&Bvov BV 'AXB^avd^Eia i\ rr}g vvxrbs &oa
v&v BGrlv i,d xal dvo ytBiLitrov ai dvo rofaov aga
G)Qat, xaioixal TtoiovGiv farjii0ivd$ EyyiGrcc dvo r-
raorov. &<jr yfyovw 6
1. rcor] U D, U D 2. 5. fioiQuv] corr. ex [toiQfbv D 2
. 7.
-v'del. D 2. 9. joorj] psv QW\ D. 14. STSL] \& D,
*'add. D 8
. MSGOQI B. 15. itgotldovGj}g co^ag D. 16. r*]
lo ABCD, /> A 1. li^ewev] mut. in i&ucev D 2
. 17.
qpTjtftV B, comp. D. Y.GLI tQirripQQiov] r D, yQ- KKI TQurtfioQiov
mg. D 2. 18. tovTSGtw] comp. BD. TQLTOV] r' B, p D.
21. iariv] comp. BD. dvo n^nrcov'] ftse D, J3
s" f" D 2
.
xqirov ago] yaq D, y' &QK D 2. 22. dvo Tgra^rov] (3
^'" D.
23. ftara] |u, D, ut saepe; fta D 2.
MA0HMATIKHS STNTASE&S A'. 347
oivas rijg v rr\ s' [t0r][t^giag. xai
6 ditb r&v 7to%<DV [t%oi rovrov XQOVOS
Afyvnriaxcbv <pjt xal rj[tQG)v rAd xal MQ&Vv&v artAcbs [tv id d', axQifl&s de 1/y [_' d'' JVQOS ov
%QOVOV VQi6xo[tv rbv psv tfAiov sitfyovra
[taigas Tf t/3, t^v 81 GsAtfvrjv [i
T xd, dxgifl&s $ [IOIQCCS is
xccta xv\v ava)[iaA,iccv KTtetye TOV cutoysiov rov
[IOIQCCS 6ll& &. GWCCySTCCl 6s XCtljj
(XTtO
sfyscog iiti r^v tgirriv diKGrctGis ^f- 10
Z xal dvo 7C^,7Cr(ov {iiag G)Qag
xal Tavrrjv rrjv diaGratiiv fipSQ&v QOS xal ^iiag rgi-
rov Sgag farjufQivrjg, poiQ&v ds (>|^ Ay. xal v&dd
aQa g)aivrai di^VGt^ivog eitl [iv rcbv [IOIQ&V $' xal 15
y' eyyitfra [nag [taigas, iiti $ rcbv fi[tQG)v f)iti6i xal
TQixcp xal dsxdrG) k'yyi&ra ^tiag cogas farj[tQivfiS) a xal
avra dvvarai diatpOQav at>i6A.o'yov Ttfgl rbv ri\g VTCO-
ditQi
yd<}a6d'ai.
1.-rf?] tfj D, tr\i D 2
.
f(Trw;]_comp. B, -v del. D 2. 3.
i&v] corr. ex ctirv D 2
. xW\ -18 e corr. D 2. 5. &n-
s%ovrcc B. 6. Gsl^vriv'] D, ut saepe; ^ D 2. 7. ax^tjSws]
bis D, corr. D 2. 9. fiot^ag] seq. ras. 12 litt. C. 10. Ssv-
tQccs~] H B, p D. TQiXj\v~] y' B, y D. 11. xat] corr. ex
xa D 2. dvo ntpnTfov] ^ s" D, corr. mg. D 2
. 12. vs] supra
scr. A 1;v& A, -& del. na.liv\ TtdUv
r\A. 13. 90?] psv
Q0<5 D. pi&g XQitov copag] ccyoQOJV D, ay" top'D2
. 15.
/u-ot^cov] ^ C, ft C 2. 5'] ABCD, supra scr. u C 2 et sura) D 2
.
16. y'] ADC 2, y' |5 BC, o> supra scr. C 2
, Tattoo supra scr. D 2.
eyyiata fttag] e corr. A 1. rjfifg&v^ ftf^cov C.
Tjju-tityft]xat
D,' D 2
. %t] om^D. 17. T^I'TW] r D. _*l tfexaroi]
post ^f- ras. 2 litt. A, tgw '
D; supra scr. ip A 1 et tj3" C, {_ r" i"
cog 'v riGl ccvtiyQa D 2
. fttag] a supra scr. D, fnas D 2.
348 KAATA. IITOA. MA0HMATIKHZ STNTAEESS A'.
yeyovev ovv fftiiv VTI oipw r6 re rijjs
alnov, ual on &ccQQOvvt$ civ In
snl r&v Gv^vyicbv r^g ffe/tofV^g xal avrcov
5 Tovrcov r&v ijttefymv Gvpcpcbvav iidfaGTcc rats
1. fipfv D. 3. Gvv%Qj]6ctipQ'a. D, corr. D 2. 4.
D, ([ D 2. 6. vTto&tGSGi D, corr. D 2
. In fine: Klavdiov
GVVTK^ECOS 4 AC (KkuSiov C), Kiccv-
diov ntofoficclov ^(x^Tf]^a'tiY,fig Gvvrd^ftos fiifiMov J B, KKccvdiov
D.
'.
Tads sv6riv v ret) e' rcav rov IlToA.[iafov
a'. 7tQi xaraGxsvijs a<7rpoAa/3oi> oyydvov.
rijs itQOs rqv dinfo]v dvco[iaMav rijs
y' . stegl rijs jr^AwcoT^rog rijg Ttccga rov f/Atov dvo-
rov A,6yov ri}$ sxxevrQorrjros rov
xov xvxhov. 10
sf
. itSQi rijg 3tQo6vev68G)$ rov rils GsAtfvys sitixvxkov.
g'. Tt&s dice T&V yQcciin&v ditb r&v itSQiodix&v xi-
vrJ6SG)v fy dxQLJUrjs rils Gshijvrjs ztdoodos kccp-
pdvsrai.
'. TCQayncirsia xavovos rils xa&oAov tffA^wcmjg dvo- 15
?)'. xavoviov rils xcc&oAov Gskyviaxils dvco[iccMas.
'. nsol rils xadohov GsArjviccxils ipqcpotpoQias.
i. on, nydev d&oho'yov ywsrai, didyooov Iv rats
Gv^vyiais Jtaga rov SXXSVTQOV rils GsArfvys 20
xvxAov.
1. E'] om. ABCD. 2. r&v [Lcc&riiiccTiyt&v] rrjg
KfrrjiittTLnfis 6vvrd^(os B, om. D. 4. a'] et numerosceteros om. D. 6. vito&sGEcos] om. D. 9. ivY.EVTQo-ir]TOs D.
11. Supra ae^ijVrjg scr. ([ D. 12. y.iv^Gfcov] sito%&v D.
15. avcoiaMag ccv D. 17. Y.KVOVIOV avcoK^Cccg om. D.
350 KAATAIOT HTOAEMAIOT
ia'. TCSQL rc5v rrjg
i xara6xvijg ogydvov JtagaMaxrixov.r&v rijg GsAijvrjs aTtoGrrjudrcov.
id', 7tgl rijg TPYjAixdrrjTog rojv v ralg 6vvyiaig (pai-
5 vo[iva)v dia{irQG)v j]^iov xal GsA.tjvrjg xccl Gxiccg.
is', itegl rov fjfaccxov drtoGrrjparas xal r&v Gvvano-
dMVV[lVO)V CIVTG).
1$'. Ttegl [isys&cav fjMov xccl 6^vY]g xccl yijs.
it,'. Ttegl T&V xccrcc pSQog 7tccQaMd%SG)v rjh'ov xccl
10
iv . xccvcov
T&V
a'. Ilsgl xccraGxevrjs ccGXQokdpov ogydvov.r
'Evsxvju,v df) r&v agog rbv ijfaov Gv^vyitiv 6vv-
15 odixcsv t xccl ytccv6^rjViaxcov xccl T&V XCCT' ccvrdg
ctefyStQV %CCQXOV6CCV
7tl t^ JtQK>Trj$ XCc
xav ccvrb povov ovrcog f][iiv
itgbg pivTQi rag xard pfyog nl rcbv aMov ngbg rbv
20 tffaov 6%yiiaTi,6[i(X)v itagodovg ovxer' av avrdgxy rig
1. TtBQi 2. Tra^aHaHTtxou] om. D. 5. Siay, D.G- postea ins. A. 7. wurw] avr&v C. 8. icsgt yf}g] om. D.
11. TtKQuMcc'X.TtKos] pr. x coTT. ex 1 D. Post indicem add.
'EfiitedoKifis dm^KGiov aTti^siv ri]v ([ anb rfjs y^S sdoi-ccfev,Ol 8s &7t6 t&V [LK&riUCltl'X.&V &KQlpGTQOV 1tl,pdM,OVT$ (sitl-
v' D) 6Kta>y.aiSWJila.Giov : (: om. CD) 'EQaTOG&gvrjg
a7t%eiv Grccdiav ccnb rrjs yfjs (ivgidScov r ncci omanis>
( : no om. C) xr]v ds Gfl'ijvrjv &7t%iv rfjs y^g (ivgid-8(ov tydopfaovrct oxrcb GrccSioov BCD 2
. 13. a'] om. AD,rag. B. Trf^t] nsQi Tfjs C. Post ogydvov add. s A. 14.
o; mg. D 2. Gv^vyi&v] Tijs cs^vrjs Gvvyi&v D. 18. iaja-
D, corr. D 2. 20. nccgoSov D, corr. D 2
. ovvtri, BC.
MA0HMATIKHS 2TNTAJEJE&S E'. 351
avryv evooi, dia rb xal devreoav^ cos <pcc(iv, xccra-
AapfldveGd'ai, r^g Ge^vr^g dvopaMav naoa rag ngbgrbv iqkiov drtoGrdtieig d7toxa&i<3ra[jivr]v jiv els rfv
uar d^ifporeoag rag Gv^vyiag, pzyiGrrpt de
diKporeoag rag di%or6{iovg. xarr]V%- 5
ds sg rqv roiavryv snitiratiiv rs xal itiGiiv
axo re rdbv vjtb rov 'IititaQiov rerygrjuzvcav xal ava-
6e^tjvrjg nagod&v xal anb rCbv fi[Liv
dia rov ngbg ra roiavrcc J^LIV xa-
ra6xva6&vrog bgydvov, 7tQi%ovro$ de rbv rgonov 10
rovrov.
dvo yaQ xvxAovg Aafiovreg dxQift&g rerogvevfievovg
rergaymvovg ralg jliticpavfiaig xal 6v[i[irQOvg [lev red
7tavra%6&sv de fcovg xal bpoiovg d^t]^otg^
xara did^etQOv itgbg og&ag y&viag &ri 15
r&v avrwv eTtupavfiav ,&6r rbv ^ev eregov avrcbv
voftG&Ki, rbv dia peG&v r&v ^codtcoi/, rbv d' eregov
rbv diet r&v Ttok&v avrov re xal rov i6rm,Qivov yi-
6r][ipQi,v6v' s<p ov A,a($6vrg cforo rijg rov
Ttfavgag ra rovg rov di,a pfacov rCbv ^cpdL&v 20
TtoAovg acpooi&vra 6r]iiia xal epTtoMGavreg a
K xvfavdQioig e%%ov<5iv ngog re rfjv exrbg xal
evrbg eititpdveiav xara [lev r&v exrbg evenoMtiaiiev
2. itgog 5. &ii(poTEQtts] in lac. complurium linn. ins. A 1.
3. ano6td6eLs] ccTto^ccrccGtccGet-s B. ano-Ad&iCrcc^vrjv] -iGrct-
e corr. A 1. 7. r&v] -fa- in ras. A, supra scr. D 2
. vno]om. D. 9. KutacneciGd-evTos D. 12. JLuppdvovTSs C. 13.
eiti(puviai$~] 7tQicpQiaig D. 14. 8' I'GOVS corr. ex dsGovg D 2.
16. rov\ corr. ex to D 2. 18. x6v] r&v B. nokav] -H-
corr. ex 8 A. 20. rd] supra scr. D 2. TOV] supra scr. D 2
.
21. tyitoHfaavTee] -U- in ras. D, 73 supra scr. D 2, Ipxod&ttiTOG
BC, corr. B 2 C 2. 22. Qfyovei D. 23. r&v] rijv D. sv-
] -M- in ras. D 2, rj supra scr. D 2
.
352 KAATAIOT HTOAEMAIOT
xvukov axroiisvov 7tavra%6&v dxQificbs rr\ xottr] avrov
7ti(pavia t% xvprifc rcbv 6vvrjQno6iiVG)v dvo KVK^&V
Kal dvvdpwov TtZQLdy^&ai, Kara ^xog 7tol rovg i-
QrftLBVovs 7t6hov$ rov did p^ov rcbv a>dtW, Kara de
5 t&v svrbg 6^otrag aMov nvxhov SVSTCO^CC^SV aicro-
{isvov psv %KL avrbv 7ta,vxa%6&ev cwQip&s rrj
ccvrov titicpavsLqi rij^ zotA^g r&v dvo xvxh&v.,
y6[ivov de 6/KHwg XCCTCC [irjxos 3tQi TOVS avtovg 116-
Aovg t& e^cdftev. dizkovrzs d rovrov rs rbv
10 xvxhov xccl In IQV avrl rov dice pfacov rcbv
XKi 0<? Vd%ZO tOVTCOV ^Q^ VCpTr]Q[l66a[lV CiXQl-
fajttbv xvxMexov dnag fyovra, xccta dia-
OV(}aS VTtb TOV VTOS t&V dvO MJXk&V)
15 07CC3S dvvrjTcci itccocc(p()<5&cci Kara to avrb XLVG) eni-
TtsdoV &S ItQOg XaTQOV T&V XXL^lVG)V 7t6&G)V VXVrqs Kara Tt^drog ytcc^arr]o^6C3s. rovrov d* ovrws y-vo^,VG)v anoGrriGavrss rtl rov di' d[iq)orOG)V rav
itok&v voovjisvov nvxhov a<p xaroov rcbv rov &-
20 diaxov jroAcov rrjv yLsra^v dfdfi'y^vrjv 3tQicpOiciv
rcbv dvo TtoAcov rov r dt {ifacov r&v tydicov xal
rov I^^OLVOV ra yv6^va 7toara Kara did^rgov
dM,t]A,OLs V7toM6a[iv xal avra nobs rbv
2. GvvriQ(ioa\iisv(ov A, 6vvr]Q^o\G^ev(ov A 1, LQ[ioG{ievmv D,
D 2. 5. r&v] rr\v D. KVKitoMGKiitv] A]B 9 C 2
,
BCD, Ivsno^iJGKfjiev D 2. aTtTopsvov] -(.LSVOV
add. A4. 6. (isv v.al ai)xov\ om. A. jtccvrcc%6Q'tv\ nav-
add. mg. A 4. HV^T?) corr. in xv^nyi A. 9. TW] corr. ex
T&V C 2. 10. TOV] x&v C. 11. yLvopevov CD.
'
14. rov]e corr. D 2
,t&v C. 16. cog] corr. ex 6 D. ^yntL^ievcov D.
17. d'] ds D. 23. ivEnoliGctptv] -U- in ras. D 2, -)b]- supra
scr. D 2, ivsnodtGupsv BC.
MAGHMATIKHS STNTAEE&S E'. 353
opoiov [ie6i][ifigLVOV T&V v ao%ri rijg GvvTd&cog VTCO-
itgbg Tag Tijg ^sra^v T&V TQOXLX&V TOV
7tQicpQtag Tr}QtJ6ig, &6ts TOVTOV Kara
&<5i,v XiVG) xaraGra&svtos ,TOVT&TIV
oo&ov re TtQog TO TOV ooi&vTog zitfasdov xal xara TO 5
oixsiov aia rov 7t6Aov rijs vrtoxi[ivr]g oiKij^fcsg nctl
5 TOV <pv6si [i0r]iLf$Qi,vov 7tiitdG),
Qia,'yG}f
yriv a7COTA.Z6&ai, 7tol
TOV iGriyiBQivov Ttohovs a7t avaToh&v 7tl dv6[ias
TG)V oAcov TtQKtTr] tpooa. 10
TOVTOV dij TOV TQOXOV KK&L<5TaVT TO OQ^aVOV,
<paiv6&ai, qdvvavTO o T
xal fj 6&rivY]) TOV [iv ^cod'fv T&V a^TQO^d^covrtl tr\v KO.T Xivrjv TJJV cooav
TOV ^Atov iLQiQuv xal 3tQi,ij'yoiiv 15
TOV di,a T&v jtohcQv xvxAov, OTtcog Tfjs xaTa T^V yfoaxjjv
lioioav T&V xvxkov TO^S agog TOV rjfaov
TQ7to{ivr]g Gmd^GHSiv avTOvg apa 01 KVKk
o T dia [ifocov T&V tydicov xal 6 dia T&V itol&v av-
TOV) ty CCV7tQ CC(3trjQ i] 6 dl>07tTVO^lVOg? OTtCOg TOV 20
vbg T&V ocp&cc^&v naQaT&VTog Tfj TQa T&V ntev-
Q&V TOV Xad'6Td^lVOV ^G)^V XVXhoV VTtO TJJV VTtO-
xt,[ivr]v avTOv xaTa TOV dia pscicov T&V t,a)diG)v KV-
xAov potQav xal dia, T^g aitwavTiov xal ytaoaMtfkovTOV xvxhov ttfavag &6ii XxoMrivo a(oTat, 25
1. t&v] TCOL D. GVVCC&OOS D, corr. D 2. anodsdEiy^i-
. D 2.vcoi D. 5. xat] supra scr. D 2
. 7. naQKUtjlovs D, corr.
9. avcnro^oov] -act- e corr. C. 16. Kvyikov] corr. ex uviiJicav C.
Trig] corr. ex TS D 2. 18. GKidgovaiv C. uvrovg] A, avrovg
BCD. 20. i) idvnsQ] tav SI- 6 D, 6 del. D 2, T) iavnsg CCCTTIQ
rj mg. D 2. 22. -AU^IGTK^SVOV B. vno] ini D. 23. TOV}BDA 4
, roTA, T&V C. 24. ccnsvavrtov] -vav- ins. A 1. 25. tov
xvttAot;] om. D, rw supra scr. D 9. xfttoHT^vatg D, sed corr.
Ptolemaeus, ed. Heiberg. 23
354 KAATAIOT HTOAEMAIOT
avr&v ralg iti<paviaig 6 a6rr\Q iv r& di avr&v s
oj dioitrvrirai. rbv $ sregov Kal vrbg rcov CCGTQO-
KVK&OV 7taQ(pQOn,v itobg ri\v GeAtfvriv T)Kal
n r&v fyrovfisvov, ojreog apa TTJ rov r\kiov
5 rjxal aMov rov vjtoxs^vov diOTtTSvtisi, xccl
r\
rjKal aMo n r&v fyroviisvcov dia rcbv Kara, rbv v
ovrco$ ya$, XOLOV r Kara ft^^og Ttd%i rov dia
rcov tydi&v r^^a^ tTtiyiyvcaGKOpsv x rr\ Kara
10 rriv rov faodvvaiiovvros avrd KVK&OV diaiyztiiv yi-
rov vrbg KVK&OV ropi]g, Kal notiag avrov
y&rriKSv r^roL XQOS aoxrovs ^ ngbg ii6rftL-
figiav G)g 7il rov dia rCbv it6kcov avrov KVKkov, did
rs rils avrov rov vrbg adrgokdpov dt,ai,Q6G)g Kal
15 ri\g VQt0KO^vrjg diadrdtifcos dnb [i0r]g rrjg vjtQ yi\v
OJtf}s rov vn avrov TtaQayoyitvov KVKkCtiKov iiti rr}v
v rov dia ^i6G)v r&v %G)diG)v XVK^OV.
bs rrjv
20 ^Jth&g ftev ovv yivoyievrig ri\g roiavryg
ai ri\g Gfhrjvrjg Jtgbg rbv ijfoov dt,a6rd0i,g, K re
2. Sionrsvrirca] -o- e corr. A 4. de] d' D. 3. TICCQCC-
v BD. 4. roiv r]Tov[isv(Qv] corr. ex to r)rov[ievov D 2.
6. rc3v fcqtgvp&Gv] corr. ex to ^tov^evov D 2. x&v (alt.)]
-&v e corr. D. nuta tov] supra scr. D 2. 7. KWX.UGKOV] -li-
e corr. D 2. vnontevritca B. 9. ^jriytyvebcitoftfv] A, iiti-
yivwGKoiiEv BC, 7tyivmGKO[jiv D. 10. Icodwapovvros] anteS ras. 1 litt. D. ccvto C. SIKIQSGIV} KKta. rj]v diuiQSGw D.
14. &Grgold$ov] actQoldpov KVY.IOV D. 18.f3'] rag. ABC T
om. D. TIBQL 19. vTto&sGfag] hie om. D, qui x-yx^o-u lin. 17
et cc7tla$ lin. 20 coniungit (x-u|xAov a), diremit D 2(xvxiov | a);
TtfgC vno&86co$ mg. superiore D 2 et addito ^ $ mg. ex-
teriore D 3. 20. Tf)g] supra scr. D 2
.
MA0HMATIKHS 2TNTASE&2 E'. 355
6r
'Iit7taQ%og avccyeyQccfpsv ,xal s$ av fipetg irv\-
TCOTE [ISV (J^tt^POVOt XaT&a[l(ldvOVTO TOig XKTK
xal didcpoQoi, 7COT8 [ilv bUym, nors
$' r\lllV Kttl 7tQl,Q'yOTQa$ Ttjg 7H,6TCC6G)S 5
cc TO <5vv%s yivouwys 7i$l rrjv TCC^LV r^g rot-
iiakiag xccr^anftccv6^i^cc^ on 7tQi pv rag
6vvodovg aiel xal rag Jtav6^tjvovg
dia[iaQrccvrai, 1} jS^a^v, xal o6ov av ai
ryg 6^v^g dvvawro itoitv didcpOQOV, itQi ds rag 10
rdvrai, r^g 6eh$vijg xara TO anoyfiov T)
TOV BitixvxkQv Tvy%avov6r]g ,TtfoitfTov d', orav
Tovg ii6ovg dgopovg OV&K nfaiGTOv xal TO Ttaga TYJV
XQCQTrjv av&paMav didyogov 7101%, xal OTL uyciiQe- 15
Tiling pv ovGyg T^g JtQ&rrjg dv&iiaMag iv 6itoTQaT&V dlOrO^OV Tl &d66G)V 6
rijg Ttg&Trjg dcpai,()6G)g
cov d)6avTG)g xal
rfjg itQcbrrjg TtQOG&acpaiQfaf&g, (bg dia TavTqv 20
TYJV rd&v r^dr} GVVOQ&V ^ kag, on, xal rbv
nl MXWTQOV xvxKov q)Q6&ai, v
yivoutvov TtzQi Tag Gvvodovg xal
1. 6] om. C. 2. ftfV] -EV renouat. C. 3. de] corr. exD 2
. 4. Siccfpogoi] Sidcpcovoi D. 6. ytvo/LtfV?]s] om. D. 7.
ucdiug] KVGj{iaM(xs yivo^svj]? D. Hie mg. itsgi p. 354, 18- 19 v7to&6(D<; D (TIQO?] ttg). 9. dia^ccQtdvei D, corr. D 2
.
$QK%V<S BC, corr. C 2. 10. SVVKITO D, corr. D 2
. 12. uno-
ycciov D, corr. D 2. 14. dgopovc; ovGu\ corr. ex dgofiovccc C 2
.
15. noifL CD. 19. nUlov BC, corr. C 2. axyavTcog] -co-
e corr. D. 20. jr^oa^aqpat^^fcog] -at- in ras. D. 22. fVxtVTpov] corr. ex HSVTQOV D. vnoJi^Ttrsov^ post r\
ras. 1
litt. D.
23*
356 KAATAIOT IITOAEMAIOT
rocs 3tav6Atfvovg, itEQiyuorarov de Jtepl d^i(poToag
rag di^oro^ov g. Gvpfiaivoi & av rb roiovrov
v7to&<3G)g roiavryv rwa t^v diooftcs
vosfa&G) yap 6 [jilv 6ii6xvroog r& dia \it6&v r&v
5 (pdiK>v xvxAog v r& Aojep r^g 6%rivrjg ZTti7tB
co6nQ xal vtQorsQov, VKv rov
tovg rov dia {ifacav r&v ^cpdicov tt6A,ovg rodov-
rov, o<?co v3iQ%i, r^g xccra [irjxog mv^saxs % xccra
jtAarog, df 6fajvrj rov Kakovyisvov Infavxhov TIE-
10 QiQ%oiivrj xdfov a)g xar& rqv a^yuov avrov
tpQi,ccv fig ra ytoorjyov^vcc ryv [irccf}cc6iv
axoA.ov&G)g rfj ryg 3tQ(brr]g ccvG)[iccMcc
v drj rovra) r& Ao|w sitiiteda) dvo xwiJGfig svavriag
dMijhcug vjtori&[id'a duahtig xal ftfol rb rov dtcfc
15 p0G)v T&V fydfav Kwrgov diHporfyag, (bv piav \L\V
rfjv 7tQidyov6av rb rov fTttxvxkov %vroov fig ra
rcov ^(pdi&v dxoAov&og rf} xara nAdrog m-
iav d rqv ttaidyovGav rb xsvroov xal rb
rov Iv r<p avra iitntt$& Aa[i(lccvoiivov BK-
20 KBvrgov Kvxkov, tp ov ndvrore rb xwraov 6rcci, rov
7tQi,d'yov6av df fig ra xoorj'yoviiwa r&v
xal rotiovrov, o^c? v7tQ%i rr}g Kara ithdrog
tA,G)d't6a v\ dyto^tj^ rovrstinv ^ vrtQO%rj rqg
xard [irlxog 6&rjviaxrig [i6r]g iuvyJ6cog Jtobg rqv fjhia-
25 MQV. &6r v rri pia ^^Qa hoyov VKev rb [ikv rov
1. T(Xg] Om. D. TtCCVGfkljVOVs] 7tOCV( D.
rov A. 7r(u] Y.CIX' D. 2. cvfifiuwsi D, corr. D 2. TOLOVT.O D,
corr. D 2. 5. ro5] ran corr. ex T& A. Ttyoriyoviisvrjs B. 1.
v] fadicov uvnUov D. 8. OGOV D. rf] i\ B. 10. Kara]ra. C. 15. xsvtQOV a/Ltqpors'-] in ras. D. 16. rov] -v
eras. A. 19. avro5] avrov BC, corr. C 2. la
-ov in ras. D. 23. r) (alt.)] supra scr. D 2. 25.
ras. 23 litt. D 2.
MA0HMATIKHS 2TNTASE&S E'. 357
t7tiXVxA.OV XVrQOV XiVOVflVOV Tag rOV
iy id eyyitira elg rd 7t6[iva r&v ^cpdC&v sill rov dice
li6cov r&v %G)diG)v yaivsG&ai Ttao&dsvxbg rag rov [iij-
xovg poioag Iy Ice did rb okov rov Ao|6v xvxAov avft-
sig td itQO'r}'yov[iva rd rijg vTCs^o^g 5
rgia, rb ds K7t6ysiov rov sxxsvrgov avruts-
i, n&kiv slg ra nQorjyov^sva H.OLQKS la ^V7teQ%ov6i,v aC diitkatiioves rrjs ajto^S polyou
wy rag rov nhdrovg [lotoag iy td. ovr&g yap BK
a[ig)oreQG)v rcbv xwtJGstov avriTtSQwyco'yijg nsgl rb 10
cog scpaiiev, rov dia [istf&v r&v ^cndtcov yi-
rjdia rov xevroov rov minvKkov rijg did rov
xevroov rov sxxevroov JtQo6ajco6rt]6
Htvyvr
x re rcbv Iy td xai r&v la # fioiQ&v
osiav dinMjv yivoptvYiv r&v dnb rijg aito%fi<5 poiQ&v 15
i|3 la {_' syyiGra. xal did rovro dig iv r&u,t<5<p prj-
viaiG) %QOVG) rov Z'xxevroov 6 srtixvxAog TtsoisAevGsrai,
ryg Ttobg rb aitoyeiov rov sxxsvroov voov[ivr]g dnoxa-
ratirddscog ev ratg [ifaog frewooviiwaig 6vv6doig re
xal 7tav6sA.ijvoig vjtori^sfjisvrig aTtorsfoiGd'ai. 20
iva ds jiaMov fftitv vit otyiv ywrjrai rd ryg vito-
oefa&G) it&Kiv 6 v X& Ao|w rijg 6^tjvrjg
d) did ^6ov r&v (pdicov opoxwroog xvxhog
1. rag] post ras. paruam D. 6. S^KOGTO] ^aa
D.
corr. ex TQITU C 2, r B, y' D. 7. ^ot^ag] -ot- e corr. in
scrib. A. 8. dmlaoiovss] -es e corr. D a. &no%fig\ -no- in
ras. A. 9. id] -d e corr. in scrib. D. ovrco D. 12. siti-
yiv*lov 13. HSVTQOV rov'] om. BC. 15. dmJifjv] Si- in
(Hras. D. ano] om. D. 16. /.'] corr. ex t> D 2
. /* mg. A.
17. IxK I>,vadd. D 2
. 22. votiG&aii D.
358 KAATAIOT HTOAEMAIOT
10 TO Z/
K06TO,
6 ABF4 TCBol XBVTQOV TO E XCil dld[lTQOV TYJV AEF,VttOXl6&G) $
a'flO:XUTO, TO A 6r]lLlOV TO T
TOV BXXBVTQOV KOI TO XBVTQOVTOV Bnixvxkov xccl TO j$6Qiov
5 itoag xal rj ao%rj TOV KQLOVxal b [i6og fjAtog. v TOLVVV
TTJ f){iQy6ia naoodc) TO [iv oAov
uvsltiQ'ai i TK
G)S KTtO TOV A 7tl
7tQl TO E %VTQOV %rj-
y eyyiGTct, &6T TO A7tQag yfos6&tu XKTCC Tag
LiOLOCig X& V^+ TG)V
vxb Trig b^iOLag r EA v&icig jfol TO E15 Tt&Kiv TOV dia pfacav TGJV ^cadtcov XBVTQOV
a7tOT^OV^lVK)V 7tl T^g l^Q^GUodov Tqv {iky dice TOV XBVTQOV TOV BXXBVTQOV
Ti] EA 7tQia%&i6KV bpahcog ig TCC Ttoorj'yovpwcc T&V
%G>dlG)V G)g 7tl TYJV E4 TO [lV KTtOySiOV TOV XXV~
20 TQOV (pBQBiV 7tl TO Z/ XCCL yQK(pl,V 7COi TO Z XBVTQOVTOV 4H XXVTOOV, TJjV $ AA 7tQl<pBQiaV TtOLBLV
lioiQGtv ice ^", Tqv ds dia TOV XBVTQOV TOV BTtixvxkov
nBQi TO E itdkiv bfjicch&g TiBQiccffiBiGav ig Ta BTCO^LBVK
TG)V t,(pdi(QV O)g T^JV EB (pBQBiV [lV BTtl TO H TO XBV-
25 TQOV TOV BlllXVXkoV, TT]V ds AB 7tOL(pOidV
TG)V V7tVOCVTtG)V
1. AET] seq. ras. 3 litt. D. 3. SHMVTQOV] fa D, ^K8 D 2.
xtvtQov] om. D, Kov
supra scr. D 2,item lin. 10. 10. |rj-
xoota] g|a D, g ||a D 2. 15. KSVTQOV] tf D,
8add. D 2
. 21.
TOV] AD, TO BC. fxx~D, ?xx01 D 2
. 22. poiQ&v] ^ D, tu D 2
,
et similiter saepe. 24. TttQLcpegeiv D. uivtQov] -VTQOV in
mg. transit A 1
,% D, K
r D 2. 25. TOV] --D in ras. 2 litt. A 1
.
MA0HMATTKHS STNTASESi2 E'. 359
Ty td, &<5ts TO H xevTQOv rov mxvxA.ov aito
(iv rov A POQMOV nsoarog drtfyov (paCvs6&ai rag ly
id pOLaas rov ttldrovg, anb $ rye; aQ%fjg rov KQLOV
rag iy ia [toioag rov [irjxovg dia rb rb A (loofiov ns'oag
iv rotiovrcp ysyQvivai Kara rag r&v 'Iffivcov poioag
x& i>, ajtb $ rov A aitoyeCov rov XXVTQOV rag 6vv-
ayo{ivoig 6weepyorsocw rijg- r AA xal AB 3tQi(p-
wy noiotts, ai 16'iv dt,7tA.a6iovs r&v
{i6r]g d7to%r}g. ovrcog ovv, itidi
ijT dice rov B xal ^ $!& rov z/ XLvrjGig v 10
rov psGov ^VLaCov %aovov rr\v \iiav aito-
itouovvrai Ttobg akkrika^ dijAov, ort iv rc5'
rov avrov %QOVOV xal h'n iv rw i\\ii6Bi nal re-
rccorc) ndvrog dia^r^^ovGLV aAA^'Aag, rovrtGriv Iv
rcctg ii0G)g fi-f&oovpwaig 8i%or6^oig^ rb $ dia rijg 15
EB KBvrgov rov itixvxA,ov dia^r^^av rb dia r^g
aTtoyfiov rov fxxevroov Kara rb itfoiyfiov avrov
(pavQbv de, on xal rovrov ovrcog fyovrcwv avrov rbv XKvrQov, rovr6n,v r^v avopoior^ra 20
ri}g 4B nQ(,(paiag nobg rr\v 4H, ovdlv 6rai dia-
rig EB
1. id] mg. add. A 1. 4. m] corr. ex id B 3
. iioiQccs]
om. D. TO] om. C. A] corr. ex itQ&tov D. 5. Post
TOOOVTCO del. OVTCOI D. 6. IxxeWpov] f'xK D,aadd. D 2
. 8.
Tof] -v$ r&v e corr. A, dmhaGiov SGTCOV C. 9.
corr. ex ins D 2. 6vva.py6xQcci\ ABD,
CD 2. 13. trt, iv raj rjfiLGfi] corr. ex ?rrj b esc D 2
, supra scr.
cl ^n D 2.u in sv rc5 rjfiiGti %ccl ^n D 2. rara^rfij] ~j' B, ijj D, j" D 2
.
14. TOVTEGTLV] supra scr. D 2,
T D, rovA D 2. 15. de] A,
om. BCD, V.DU 810. rovro supra scr. D 4. 16. xfWpov] corr. ex
KSVTQOV D 4. 17. rov] corr. ex TO D 2
. f%K D,"add. D 2
. 19.
v.al on D. 20. lx|< D,'
add. D 2. rovrtGnv] cornp. B, -v del. D 2
.
360
ov rijv 4H rov
rov did [ltd&v rcbv
rb HTJ 7tol rb ZE TtoitiG&ai rr\v
5 avrbv rbv fitixvxhov
avrbv
KAATAIOT nTOAEMAIOT
7tQitpQiav, dMd rv\v
s 3tQiQ%o[ivr]s diet
rov KXvroov, 7tol $ rb
v, naga ds [iovqv r^v tear
iayogccv BK rov 7t-
av^eiv alsl rb naga rv\v
avo)[iccA,iav didcpooov % l'6ov Kara rs d(pctiQ6iv xal
avrbv TCQog rfj o^iv rats 7toiyiotQais d-faftiiv [iiovog aito-
10
ovdfv {iv ovv 6rai
xadoAov didcpOQov, orav Kara rb A dnoyfiov
KBvrQov rov sitiKvxhov, yivopsvov rov roiovrov
rdg [i6G)s &&Qovii8vas Gvvodovg
15 Kal 3tav6&ijvovs.
av ydo yod^o^v itgl rb Arbv MN BTtiKVKkov, b rijg AErrjv AM Aoyog 6 avrbg yiverat,
did rcbv bctefysmv
20 TO d% TtfatGrov 6rai
orav xard rb H rov
Ttfoiyfiorarov 6yiiiov b
jtoiijrai, rqv TtaQodov, fag b
rb
8. TIQO-
1. o^] D (supra est ras.), ov y&q ABC. ^xHsW^ov] COIT.
ex ex D 2. 2. TteQisQxopevTis] -s del. C 2
. 3. IxK D,vadd. D 2
.
5. rov] supra scr. D 2. ytvojii^rjv] corr. ex ]P mg. D 2 et
supra scr. D 3. 6. ywoiiEvov] corr. ex fi
N D 2 et D 3
&6iv A. 9. nsQiysIOTBQCCIS] post alt. 9 ras. 1 litt. A.(/
11. Iffrca] corr. ex sanv D 2. naga] nsgi D 2
. 12. ^] seq.ras. 1 litt. D. 15. itav([ D,
"' add. D 2. 16. A] corr. ex
TT^wrovD. 17. TOV] corr. exro C 2. AE~\ EAD. 18. yivtTKi]
tG-tui D, mg. yg. ytVfTatD2
. 20. ffroj B. 23. 7ro^rt] DA 4,
TtOLflTCCl ABC.
MA0HMATIKH2 ZTNTASE&S E'. 361
tp6[ivos did r&v 8) O 6r][iiG)v. OTCEQ 7tdA.iv
fiaivi Kara rag fiftfog ^scoQOv^evccs 8i%or6[iovs'
[iicov y&Q 6 rris &H JCQOS rqv HE AOJ>O yfyvercci,
Ttdvr&v r&v Kara rag ccMag
7tidr^7CQ l'6rj$ del xal rrt
rov KSVXQOV rov 7tiKvxA,ovfjEH x rov XSVTQOV
TtaGcbv rS)v akkczv &tl rov BXXSVTQOV
y'. Il()l rijs TtrjAixotrjTOS Tr} TtctQa rov ijhiov
dva)[iaA.iccs rijg 0krjvrjs. 10
r
'Iva df} frwG&iiz&a, TtrjMxov yivzrai ro
TtccQa rqv avwiLCtkiccv diucpogoV) orav Hard rb
yi6rarov rov MxwrQOv (pegopevog 6 faiMVittog rvy-
}, 7tccQrrj^t]6cc^v rag roiavras r&v agog rov ijfaov
v cci 01 rs 15
ror
yiv&iui rfjs dv&iiaMag' xccl
rov r\kiQv ccvrrls dno%r] titG&g ^.a^avo^vor xal 6 3tixvxAo$ 7tQi rb
eyCvero rov fxxwrQov, xal en iv eels 20
rovrcov v7tccQ%6vrG)v ovds 7taQtj^2.cc00v xi xccrd ^xogrovrcov yag 6v[i(lcci,v6vrG)v xal rr^g cpaivo-
vrift
diQTtrsvGEi, xard ftijxog dito6rd6a)$ rijs
rf] dxQifal ha[ifidvoiro av dtfcpaAcbg xal
3. HE] corr. ex NE B 2 C 2. ytVsrat D. 4.
mg. D 2. 5. cctsi D. 8. eldrrcov D. 9. y'] mg. ABCD.
7tQi 10. fffArjVTjg] mg. inf. D. 10. avcojua^tag] (3" ccvco-
ILcdt'ccs D. 11. drj] corr. ex de D 2. 12. Post to del. ntgi
TO D 2. 13. fxxfW^O'u] corr. ex x D 2
. 16. xvy%uvov] corr.
ex Tvy%avov A 1. 19. ^yicxa. D. 20. syevero D. ex^" B,
fv add. D 2. 21. nctQijlttCfv D, -v del. D 2
. 24.
-VOL- e corr. D 2(i in ras. 5 litt.).
362 . KAATAIOT IITOAEMAIOT
diucpOQcc Tijg dsvre^as dvco^a^iag. x
TOLOVTCOV TOLVVV rrjgiJGs&v noiovpevoi, T^V infaugfyw v-
OTKV Kara TO TtfoiyfioTaTov ?}6 e
diacpooccv rijg av&iictMag ytvopevijv
5 per rfv [ifayv Ttctgodov {loiocbv ual r yyJr,ds rr\v TtQcoryv dv&iiaMctv poiQ&v ft xal r%.
vnodefypottos ?&$ evsxsv, ivct Inl yu&$ r)dvo rrj-
VTC otyiv f][ilv fj TOLKvrrj diccKQiGLg yfV^rat,
tov T ijfaov xal Trjv 6A,rjvr)v tK> ft'
10 ti 'Avr&vivov uccr' Atyujtriovg <&cc[ivcod' xf' [ita
[iv TTJV avaroMjv rrjv TOV fiUov, ngb itVT $ xal d'
G)OG)v ItiriiLBQiv&v Tr\ pfGrjiiftQias. TOV
di07iTvo^ivov %aT<x 'Tdgoftoov (.loiQccg vij L'
ovoccvovGrjs TO^OTOV poiQas d'r\ 6A.t]vr] stpcci
15 7t%OV6a 21xOQ7tlOV pOLQCiQ ft F, tCCil CiKOift&S $ T06-
CCVTCCS 7tl%V, ttldrj 7CBQI TCC TtQ&TO, {lQrj TOV
'Ate^avdofia a /_' COQCCV k'yyiGrct ait%ov6TOV ii6rj[iftQt,vov xctTa [ifjxos ov&v a
Kdi i(5nv 6 ano r&v 7to%G)v T&V
20 TO a' TOS Nccftova66KQOv [i%oi Tfjs Tr]QiJ6G)s %oovogTG)V AlyVTCTtCM&V G)7t Xttl fftlfQCdV Ity XKl G)QG)V 1(5^-
2. Supra TrjQiJGemv add. ir6 D 2. 3.
77 ] r\v ABCD, -v
eras. D. 4. yivofuvrjv] -v e corr. D. 5. [IOIQ&V f xal r*]
ft J lo in ras. maiore D. j-*] A 1
,Jo ABC. 6. TCQOOTTIV] ngoi-
renouat. D 2, supra scr. a D 4
. z^~\ rQ BC et in ras. D, tf?A.
8. 1^] supra scr. D 4. 9. TW
j3' Iret] BCD 2,
rco i sret. A,root (seq. ras. 1 litt.) si? D. 11. TINTS'] 8 BD. 12. yap]fort. 8j. 13. /.'] corr. ex V D 2
. 15. i*] FB A 1
,in ras. D 2
,
o ABC, dip mo- -D2
- roaavTK B. 16. pegr] TOV] -i\ r- in
ras. 3 litt. D. 17. a] ? C. /_'] corr. ex b' D 2,ut saepius.
18. iiGT]v$Qivov D. [if]Kos] corr. ex (JUJKOVS C 2. 19. TIKQ-
i^la.G6ti D. 20. tog] corr. ex b' D 4. NK^OVKGO.QOV D,
v supra add. D 2.
MA0HMATIKHS STNTASE&Z! E'. 363
v djthcbg is xccl dxQijS&g Irj /_' d'" ngbg bv %QO-
VOV rbv rifaoV EVQiGXOpBV ^<?<3 {LEV 7t8%OVTCC 'TdpO-
%6ov H,OIQK<$ tg K, dxQip&g de [loioccg Irj v, xcc&ag
xccl v r& atfrpoAa/to diG)7trVEro. xal fj 6^t]vrj ds
v- 5
xvy%vivv rov yMov, dvo^a^LCCQ d' ditb rov ccito-
ysiov rov faixvxAov poiQtts jrg tO1
, TCQL as itdkiv TO
TtfaiGTOV yivfTcci didyoQOV Tr}$ av&naMag. shaGG&v 10
CCQCC fj xpt/3ijg Ttdgodog iytv&tQ tv\
t> r dvrl f T&V Kara i$\v jtQcbrrj
itdkw, iva xal ex rcbv vitb rov(
Iit3tdo%ov
[ivcov roiovr&v naQodcw g)avQOv ^Iv rb 7tl r&v
didyooov yevyrcu, TtccQa^rj^o^^a KKL rovrcov 15
cprjtii, rrv]Qr)Xvai rc5 v' rL ri\ rgirris xccrd
Kdfaitnov 7tQi6dov xar' Aiyv7i,rCov$ 'Em,<pl ig' rov
diuoioov rris XQ&rrjs cngag 7taoA.r]hvd'6ros. d()6[io$
[ilv ovv, (prjdiV) r\v GILO,', rov df r\kiov diOTtrfvo^ievov
xard Aeovrog {IOIQCCS rj /_' t/3' ^ ^^nvn <pawto it- 20
%ov<5a TO.VQOV poiQccs t/3 7', xccl dxgifl&g ds itEt%ev
fyyiGra rag avrdg. yivsrui aocci] ^.fra^v rov r\kiov xccl
rr}g 6^vrjQ dxQificbs &G)QOV[ievr) did6rcc6is {IOLQ&V 3t$ IE.
uKKu rov r\Mov ovrog itQl ra Tto&ra {ispy rov Adov-
rog vf
Pddco, onov ^ rrfgyGig f'^Wro, ?5T^S rftiEQag 25
3. tg HOIQ<XS\ ins. loco 1 litt. D 2. 7. obs] tuffTe C. 8.
8'] ds D. 12. r(f] i;> ABC, FB renouat. D 2. 13. xov] f A,
om. D, ? supra scr. D 2. 16. v'] v ABCD 2
,v' D, va' Ideler
Hist. Unters. p. 217, "of Halma. 17. KdUinnov D. 'Enitf D,corr. D 2
. 19. G^ICC'} mwc ABCD. 20. r\ /_'] 7/5 D. i$'\
i(3' AC, tJ5' B, ip D. 23. TT)S] r- in ras. D 4
.
364 KAATAIOT HTOAEMAIOT
<5rlv it, y''
cci ago rr\g ^6rj^^oiccg aocc
y' G)QO,i xaioixal itoiovtiiv i6r]^ioivds g g'*
yovwai xr\v riJQrjGiv nob g g' cbp&v farjpSQlv&v rifc
fV rf/ tg' p6r]iipoias [isGovQavovGrjg Tavoov ^oioag #'.
5 cvvdysrcci roivvv xal svrav&a 6 anb r&v S7to%6)v eitl
rrjv riJQrjGiv %QOVOS sr&v AiyvjirivM&v %i,& XKL
rid xal G)Q&V i6r][iQivG)v drth&s psv i^lly',
ds ifci^d'' JtQOg ov %Q6vov VQi6xo[iv rbv ijAiov xcttci
ras fjustSQccs vnofteGEiQ, STtsidiJTteQ 6 ccvrog 6tiv [i<5-
10 yfipQivos dia(
P6dov xal 'Atefauvtiqstos,
7t%ovra Atovros {IOIQCCS I x, axQifi&s $
xal T$IV 6kr)vrjv d {ifCi&s xctra itrjxog V&
Tavgov polices d x, cbg lyybs flvai xukiv iv\v
&7to%r}v TEtaQiriiLOQiov, avG)[iKA,ia$ d' ajtb rov a
15 rov 7tixvxA,ov {IOIQCCQ <?v ^^, itgbg ccl$
yivBtai rb nkEitirov dicctpogov trijg nciQo, rbv Inixvxkov
av(Q[iaA,ia$. Gwdyfrcci CCQCC fj dicc6ra6i$ y djcb rfjs
u,6qg 6A.ijvr]s litl rbv ctxQifti] r\kiQv ILOIQ&V 97 v.
rriJQr)ro dfy
ocTtb rfjs dxQiftovg eitl rbv
20 ^g Ts' Ttfaiovccg CCQCC iitslyzv r\ GfAijvr]
yovftdvy rfis 6ftaAiJ? ytagodov poiyac; ndhw g ri dvrl
rcov xard r^v 7tQ(brr]v V7tod'6iv. (pavfpbv df yi-
on xccl r&v dvo rovr&v rrjofafcov 7tal rag
1. zgovtov] %- in ras. A. !<mV] -v del. D 2, comp. B. 5.
TOLVVV~] ovv D. Post v.uf del. o C 2. 9. SGTIV\ comp. B, -v
del. D 2,
ietiv 6 A. 14. rfra^TTjjLio^tov] ante alt. Q ras. 1
litt. D. <T] Ss BD. 15.SyyuK*f*** D, sed corr. 19.
anQifiovg] ccKQipovs celirjvris B; ^ add. mg. A 1
, supra scr. C.
Inl TOV &yiQipfj[] om. D, ([ snlrbv cty.gi$fi $ mg. D 2. &v,Qi,$f)\
av.Qi$fi fyiov B, d supra scr. A X C. 21. ra ] lo ABCD 2,
rj D. 22. F] bis C, sed corr.
MA0HMATIKHS 2TNTASE&S E'. 365
cc VQfi"Y] T^S xciTK rr\v Tto&Trjv a
diaxQi6G)s dv0l [loioccis xccl di(ioiQG)) fjds XCCTK TOV
'f
ImtttQ%ov V7tQ(ldMov6cc ratg oLvtai^ liteidfi xal olov
TO itaQtt TJJV avapaMav KK& ^as pv acpccigfTixov
hvy%av, Kara ds tbv "InitaQ^ov TtQOG&STixov. xal 5
f| AAeov df xtei6vcav TOIOVTCOV
QCOV xal r syyitfra VQi6xo[iev TO
^orccv 6 7tiKvxA.os XKTK TO
TOV
'. UfQl TOV h6yOV TilS XXVTQOTrjTOS VOV 10
V xvxkov.
TOVTOV OVV OVTCOS %OVTOS 6TO) 6 XKVTQO$ T^S
xvxAog o ABP itQi XEVTOOV TO z/ xcd dicc-
JJV A4T, ftp* rjs vitoxC<5&& TO XWTQOV TOV
T&V %G)dtG)V TO E, G)6T TO fiV A yivSti&Kl 15
to catoysioTaTOv TOV ZXXWTQOV GyiifZov, TO $ F TO
. XVT$G) de T& F y^Qatpd-G) 6 frtixvxAos
6 ZJf, XCCi ^-^(D (pCC7tTOllVr] KVTOV q
xal 7t&v%&K) fjr@.
BJtsl TOWVV XCCTK TY)V Cptt7tTO[lV'Y}V TOV fJtlXVXkoV 20
Tils 6A>tfvys ywopdvqs TO
1. svtefaovaa D, corr. D 2. TIVQ^TJ D. 2.
i^ D, TBD 2. 4. ct(pKigTj]Y.6v A. 5. rdv] om. D.
6. knra. poiQ&v] f/ B, [IOIQ&V D. 1. r*] PB D et corr.
ex r-> A, r EC. 9. ^] ^ A, fy D. 10. ^'] mg. ABC,om. D, d KQ mg. D 2
. ntQi 11. xvTdov] hoc loco mg. D 2
et mg. superiore D. 13. KSVTQOV] K' C. 15. cjtfiW
y.vHZov D. ytVfff'9'at] vnoxeiG&cci D. 16. aTroyftorarov] a-in ras. A. r] in ras. D. 17. 6 8-1 in ras. A. 18. Z# ]
Z@ D. 19. E@B] E D.
366 KAATAIOT HTOAEMAIOT
diK<pooov GwiGTccTcti) TOVTO
liOiQ&v g ri, sirj KV xccl17
vitb FE yavicc nobs r
XSVTQO) OVtiCC TOV
TG)V ,OiOJV
5 plV i6iV Oil d OQ&CCi TJj,
g ft, otov d' at"
|, roiovrcov IK.
xalr\ {lev CCQCC sal r^
F rtSQicpSQSia roiovr&v
10 iGtlv IS JC, OtCOV 6 7T()fc
TO JTJ@ 6^'9-o^coi/toi' xv-
^Ao? T|, 17d' vn avryv
sv&sta F roiovrcov tg
15 V3tOTiVOV6CC OX. Cd6T XCU,
OiG)Vfj [JiV F X TOV
XSVTQOV TOV 7tiXVxA.OV di%&r] T,
TOV XSVTQOV TOV ditt ftfO'COl/T&V %G)diG)V Jtl TO
yLOV TOV XXVTOOV |, TOiOVT&V k'tiTKl XCCijj EF fj
20 anb TOV CCVTOV XSVTQOV lid TO rtfofysiov TOV sxxsv-
XCCi 8A^ {lV CCQCC fjAF diOC[lTQOg TG)V CCVTG)V
3, fj$ dA X TOV XSVTQOV TOV SXXEVTOOV
\,TK%V T&V XVTQG)V TOV T fiiCC {l-
XCCi TOV XXVTOOV I tO1
. XCCi
TOOV
6TCCl
6(QV TG)V
25 rjfitv xccl 6 vrtb Tf]g xxVTQOTr]TO<3
1. $'] 8s D. &vvay6(MVOv] -ov (o) corr. ex r in scrib. A,-tvov supra scr. D 2
. 2. i^] lo ABCD. yeoWa] T&V D.
3. X^VT^OJ] comp. seq. ras. D,w
add. D 2. 4. Post <<5iW
add. Y.M.VY.IOV D, v- del. D 2. 7.
{3] dvo C. 8. ?j]in ras. A.
10. fWv] comp. B, -v del. D 2. 17. E^] ? D. 7) (alt.)]
ins. D 2. 22. Q#] Q_ e corr. D 4
. 24. F t^] corr. ex ^ A 1
,
~i inter duaa ras. D.
MA0HMATIKHS ZTNTABE&2 E'. 367
rrjg 3tQ06vv6&g tov r^g
"EvXv [lev ovv rcbv TCSQL rs rag 6vvyiag xal hi
Ttfol rovg dij^oro^iovg rijg GsAtjvrjs 6%r)[iari,6[iovg cpai-
vo[iVG)v HXQ 1' voGovr&v ccv Ttg zttifidkoi rcclg rtibv 5
vr^g xvxhaov V7to&6s6iv, x ds
7tQi rag inqvoidelg xal cc^KpixvQTOvg a
6ig &COQOV[IV(QV TtttQodcov^ naff ag ii
yivstui rov t aitoyfiov xal tov TtsgiyMov rov x-
XVTQOV 6 7tlXVXhog, IdiOV XL TCEQl T^V TOV 7tl,XVxA.OV 10
7tl tijg GfAtjvrjg VQfaxo[i
yap v n xal rb avrb xa&ohov r&v
V7toxl6&ai, dfi 6r]iitov, ngbg 6 ndvrors rag T&V v
avrolg xivovyidvGdv a7toxaTa6td6ig dvayxatov tGxiv
ccTtoTffaiGd'ai,) rovro ds xa^ov^ifv dnoyfiov 6ftAdv, 15
a<p ov xal rag aQ%ag r&v rijg xara rbv
xiv?j<3G)g aQi&yiCbv vcpi6rd[i&a, <bg itl rrjg
vrjg xaraygacpijg rb Z, xal dyoQL&rai, rb roiovro
[itov xara ri\v 7tl r&v aitoysiov xal r&v
rCbv XxevrQG)v rov eTtixvxAov &6iv vnb ri]<s dia ndv- 20
rov rcbv xsvrg&v x/5aAhoiivr]g ev&ffag^ cog rijg
7tl ILSV r&v dhh&v v7to&6G)v TCccG&v ccTtAcbg
1. s'] mg. D 2. 7tQovvGco$ D. 3. re] om. D. 4. 6f-
post -s- ras. 2 litt. A. 5. Post ^S^QI del. r&v D 2.
7rt(JaHotBCD, corr. D 2. 6. syufiiiEvcov D, corr. D 2
. ctvtfjs]
a- et -T- in ras. D 2, supra scr. avrrjs D 4
. KVY.IOV C. vno-
ftiosGi, -i in ras. 2 litt., D 2. 7. [ir]voiSf)s C. 9. yivtrcci]
corr. ex TSLVSTCU D 2. MY.EvtQOv\ -g- supra scr. D 2
. 10. n\corr. ex yu$ D 2
. 12. TI\ corr. ex TO D. iTrixvx^oav] corr.
ex vnoKvuloov C 2. 13. fot] corr. ex Seta D 2
. 15. Supra6[icd6v add. ^allov D 4
. 17. ccQi&fi&v] corr. ex KQI&^OV D 2.
v<pi6Ta.iL&ct] mut. in vtficrm^Q'a, D 2. 21. //Er1
] supra //
add. a D, del. D 2.
368 .KAATAIOT UTOAEMAIOT
% TG)V Cpai,VO[lVC3V dvTLJllrtTOV TOO KKl KCHTCC. Tag
rcov 7tiKvxkG)v itaoodovg rrjv dia TOV 7tooxi-
aitoysiov rov 7tixvxA.ov didpfTOOv, TOVTEGTLV rv\v
ZJTH, rr)v avrrjv ftztiiv afel 6vvTr)Otv rr\ TO KSVTQQV
avrov opaAeos TCSQictyovGri fv^fta, cog sv&dds rr^ EF, xal
, OTCSQ av rig xal axohov&ov fiytfticcirO) itdvzote
, zrpog eo nal Iv
iiti d T^S Gshtjvrjs iviGtaxai to. cpctivo-
10 [lVa TG) KCCl V TCilg [IfTCi^V TG)V A KCCl F 7tao6doi$
rov fnixvxAov rr^v ZH dialerQOV ^ Ttgbg TO E Kv-
TQOV rijs TCfQwywyfis VVELV xal rv\v avrv\v rr\ EFftiGiv dia<5d)t
>iv. VQi6xo[iv pao TCQOS fv [iv n xal
TO avrb <5rniiov rcbv itl rijs -dF dia^TQOV rrjv KXi-
15 pivTqv 7to66vv6i,v aid 6vvTrjQov^vrjv^ OVTE pivroi nobs
TO E KSVTQQV TOV diCi [l6K)V TG3V ^G)$L(DV OVT 7CQOS ^6 ^/
rov XXVTQOV) ctkka TCOOS TO ri]v foyv Ty 4E (iTcd~v
rcov xwTotov aite^ov rov E log utgbs TO ttfOiyfiov TOV
MtVTOOV. Xttl On TOV& OVTCOg %t) d&,0[lV Ttd^LV
20 aito Ttteiov&v Tr}ori<j(X)V lK&l[Lvoi dvo Tag pd-
kiGra TO rtQoxi[ivov fpcpavfaai dv^i^a^va^ TOVTBGTLV
na& ag o re &exvx3iog rtol ras [i<5ccs tt7to6rd(5t,g
rjv xali] Gfhrivr] ytsol TO aitoyuov rj
TO Ttsgiytiov TOV
1. xca] in ras. D 2,om. C. 2. Supra Ttagodovs scr. coi> D,
del. D 2. 3. TOVTSOTLV] comp. B, -v del. D 2
. 4. ZFjff] corr.
ex Ztf FH A 1,ZKF
f) B, ZHFrj C, Z7} TIT C 2
,-FJf in
ras. D 2. asi ED. 10. Post TW del. ^ %at ^r\ I)
2. 11.
STCMvnliov] s- ins. A. fwj] fw] D', jlrj' D 2. 14. AF] corr.
ex ABF D 2. 15. aft D. 16. E xsW^o^] corr. ex 8x-
xfVT^ov D 2. 17. z/E] corr. ex z/ E D 2
. 20. M&EIM-VOI]corr. ex K&i[iva)v D 2
. 21. TOVTSGTI B, rovtiGzivnv D, -VTWdel. D 2
. 23. TO (alt.)] om. D.
MA0HMATIKHS STNTAgBSZ E'. 369
)dice to 7tQi rag roiccvrccg itccgodovg rr\v
diCCCpOQCCV ^V^KIVSLV rS)V XXl[lVG)V
VV<3CW.
avccygdcpst, rouvvv 6f
'l7titciQ%og ivf
P6da)
xsvai, dia r&v ogyuvcw rov T ^'/Uov xai rrjv Gshijvrjv 5
r<p 09?' k'rsi anb rijs 'Ate^KvdQov refovTrjg XCCT
ort, rov rjMov di07Ctvo[ivov xara TavQOv [IOIQCCS J
L'd' TO rijs Gshrivris XWTQOV icpaCvBro 7t%ov 'I%d"VK)v
ILOiQCCS KK rB, 1ti%V $ KXQ^&S MC ?''
V\. XCCTK 10
TOV XXl[JiVOV CCQCC %QOVOV &7tl%V fj (XXQl,(}f}
rov KKQiflovs fi^Cov ig ra 7t6[iva {loigccg rt/y
TCBVX
sv rri IK' ftftf??^figices'^CCVTCCL d' Inoiovv iv
f
P6dc3 ror 15
CQQCCS rB fyyidtcc, GwdyErcct, 6 ccitb rrjg
Q6vo$ rcJv Alyvn-XCCi G)QG)V
&v rtdfav1/fj y'9 axQip&g ds
1/ij ftdvcov i$ ov
VQi6xo{iv rov fti> opcchbv jjfaov iitijQvta rov 20
c; [ice, rov d' axQifif} iioiQag t, fZf,
6hrjvr]v xccra ^Kog [iv iitiyjQv^KV
r&v 'I%&vG)v iioiQag xfl ty ? ccv&inaMag d' ditb rov
_ 4. 'Potfw]?
P- e corr. C. 6. 05' hsi\ g^ seq. ras. 1 litt. D,
f f? D 2. 7. $ciQii,ov9l ia'] -I i- corr. ex N A.
{?'] jj D,
add. D 2. 10. r*] corr. ex r A, To BC, PB D, uT D 2
.
inefytv] -v del. D 2. 13. dsw^e]^ B. 14. nsvrs] FED.
15. rff] corr. ex rfj A 4. d'] Ss D. inofovv] int-i ovv C.
16. r*] corr. ex r A, 75 BC, FB corr. ex tp D2
. 18. ~<n&]
in ras. D 2. Post MQ&V ras. 1 litt. C. 19. ^j-V] p D,
D 2. y'] supra scr. D 2
. ^ovcov] mut. in fiovov D 2.
Ptolemaeus, ed. Heiberg. 24
370 KAATAIOT nTOAEMAIOT
{i6ov anoyeiov TOV litixvxkov iioioag oit A, &6T
xal Tr)v Trjg 6[iaA.ijg 6^tjvrjg drtb TOV dxatfiovg YI^LOV
TOVTC3V OVV V3tOXl,[lV(QV (5TG) 6 XXVTQOg Trj
5 6A,rjvr]g xvxAog 6 ART itoi XWTQOV TO 4 xal
TQOV rr\v A ^/.T1
,
&y ^fS UtitCO tb XV-
TOOV TOV dia ft-
()G)V TS)V ,G)$LG)V
10 xvxhov TO E) xal
XVTQG) T(p B y-'
6 ini-
15
anb TOV B 7tl TO A, YJ$ ti^rjvrj r^v KO.TK TOV ini-
20 xvxkov d)g onto TOV Z iitl TO H xal TO,xai its-
rjT JB xal % E&BZ.
i TOiVVV V TG) [l6O) [irjVLCu'o) %QOVK) dvO 7fQC-
a7toxccTa6Tcc6'ig TOV 7UxvxA,ov xobg TOV xxv-
aTCC d Tr\V XXi^LVrjV &6lV <X7ll%V
25 6hijvri TOV pfaov r\Mov {lOioag rtf A/3, lav
GiaGccvTfg TavTag dq)^co^v xvxAov, '$o[iv Tr\v anb
TOV dnoyuov TOV XXVTQOV ysysvrunEvriv ano%riv TOT
6 ZH, 7tQi-
d' 6 {lev
TTjV ?g
TG)V
a)g
1. ftfdov] corr. ex [itcovs D 2. ^Ttiyiv^ov] Ini- e corr. D 2
.
I] in ras. D. 21. vialrj] BD, Y.CCL AC. 22. iirjviccta) -LK-
corr. ex H in scr. A. 24. iv,v,8iiivr\v^ s- e corr. D.D.
MA0HMATIKH2 STNTASESS E'. 371
rov frtixvxAov stg to. ino^va [loio&v 6oa d' metre
xalj] vjtb AEB yovfa r&v koin&v sis tag 8 OQ&as
farcci HOIQ&V TCTJ vs. $%&& dfj xd&frog <x7tb rov z/
7tl rfa EBii4K. 7td ovv
fj vTtb 4EB ycovici)
oicov [iv i6iv CCL d OQ&al r%) roiovr&v farlvjtrj vg, 5
OL&V d* aC dvo OQ&al T|, toiovr&v QO vfi, sty av
KCilrj llV 7tl TyS /IK 7tQl(pQl,K TOlOVtCOV QO V$,
OLOV stirlv 6 TCSQ! TO 4EK oQ&oycoviov xvxhog rj, ^ d'
sitl rijs EK TCOV AOM&V [Eucl. Ill, 31] etg to $\\LMVK).IQV
ji rj.xccl rcbv vit ccvrag CCQCC ev&eicbv ^ V&v 4K farm 10
roiovrav QI& IA^, di&v farlvfj4E did[iT()o$ QK^
fj$ EK TK)V CCVTG)V ^ id. KCtl Ol&V farlv CCQCC 'Y] [lV
r&v XSVTQ&V 7 t#, ^ ds 4B SK rov
rov McsvrQOv ^0" ^JLCC,roiovrcov xccl
i] [ilv z/Kid1 itakiv fyyicira, rj
$ EK djiofas t/3. 15
xcci fad rb KTCO rijg 4K Aeiy&kv [Eucl. I, 47] vitb
rov attb rrjg z/5 noisl rb aitb rY\$ BK, f1*o[iev xccl
rr\v plv BK rav avr&v ^ Ag, rqv d BE oArjv ^Bitel
r\ plv r^g 64uaAijg ^s^viqg ccTtb rov
1. poiQ&v] D, comp. B, (jiOLQccs AC. <?oa] -o- in ras. 2
litt. A. 3. zf] corr. ex A D 2. 4. EB] EJ A. 5. Icrlv]
comp. B, -v del. D 2. vg~\ corr. ex v nai D 2
. 6. dvo~] fiBD.
toLovTfov 8. r] mg. D. 6.vfi] renouat. D. 8. ofav]
-eov supra scr. D. larfv] om. D. 9. i7juxvx>Uov ] QB D,
o* B D 2. 10. awag] corr. ex avr^g D. 11. z/E] corr. ex
~&s D 2. 12. id] -^ e corr. D 2
. 13. z/E] corr. ex AE D 2.
rt-fr] e corr. D 2. 4B~\ B4 D. 14. HSVTQOV] xfW^ov
ovc?a D. 15. tl^] e corr. D 2. EK] EK ndKiv D. 16.
^TTSI'] corr. ex Tzre^t D 2. dK Aftqo^fV] corr. ex <MlT}yftiv
D 2(-?]- corr. ex SL in scrib.). vwo roi) anb
rfj<s~]vnb rfjg D,
ccnb TOV KTtb tfjs D 2. 17. z/B] B/^ D. Post itoisi del. ro
awo rr^s BJ notst D 2. 18. fAV] om. C. BK] corr. ex
KB D. fo'] bis extr. et init. pag. A. BE] EB D. ^]om. B. 19. fast
?j]corr. ex snl el D 2
.
24*
372 KAATAIOT HTOAEMAIOT
fjMov diKtiratiis IIOIQ&V r\v rid MJ, rjds rijg
r&v x rijg r^^^Ecog IIOIQ&V ny ^Li/3,coGrs
rb TCCCQK rrjv avopccMav avrijs didcpogov
oJLtg, ftscoQBirKi <P % b^icc^ itdgodos rife
till xijs EB EV&EICCS, vjtoxsiGd'G)i\ Gehtjvfy
rtsgl to itBQiytiQv i\v rov SJCLKVK^OV^ Kara rb
H <5rnLloV) xal siti&vx&siG&v T% re EH xai ri\$ BHxd&stos anb rov B iJx&G) enl rr\v EH mfikriftslGuv
fjBA. EJIEL ovv % vjtb BEA y&via rtQi,E%i rb
10 Ttaga r^v av&[iaMav rijs (JfA^V^g didcpogov, fir] civ,
Oiwv \iiv i6iv ccC d og&al r^ 5roiovrov o
jiTg,otcoi>
d' CCL dvo oQ&cil T|, roiovrcov a A/3' &6r xalfj [iV
7tl rye; BA V&EICC$ ytEQHpEQEia roiovr&v EGrlv a A/3,
of
iG)v 6 itZQi rb EBA doftoycoviov xvx&os r%, $ df
15 i)7t avrfjv v&ia<Y\BA roiovr&v a Ag, <HOV 6rlv
j]EB i)7torivov6K (w. &6re KCLL, olcov sGrlv i\ tizv
BE v&la prj Mi % $* BH M rov xwrgov rov iiti-
xvxAov 7f, roLovrcov fGrut, xcclfjBA EV&EICC o A#.
xal or
iov (Srlv CCQK TJBH X rov XEvroov rov iiti-
20 xvxhov ^3c, roiovr&v xaifj ^Iv BA evfrelcx, zGrai, id
vfi, % d' fV avrijs nsQMpzQEiK roiovrav id td,
3. ctvTfjs] corr. ex avr&v D 2. 4. d'] Ss D. 5. lni\
inl -to C, corr. C 2. 6. &m<?Tj] -rj corr. ex i A 1
. TCSQL-
yto C. 7. rrjs rs] corr. ex T&V D 2. EH v.ai TTJS] in ras. 2
litt. D 2. 8. xd&STos anb TOV] in ras. minore D 2
. B] rjTain ras. D 2
. 9. rj (pr.)] ins. C 2. BA] corr. ex BJ D 2
. BEA]corr. ex BE D 4
. ymvia] om. D lac. 3 litt. relicta. 11.
o jig] corr. ex ojt g D 2. 12. dvo] B B. A{3] corr. ex Af5 A,
e corr. D 8. >& 13. BA] in ras. D. 14. E\BA] "TTEA B.
d^oycbvtov] corr. ex OQ&WV D 2. ^] ^' D. 16. EB]
BE D. 17. ds B#] d' D. 18. o ;iFj ol^ C. 19. (
SGTIV B. ^ BJf ^x] renouat. D 2. 20. Supra QX ras. D.
BA] corr. ex BA D.
MA0HMATIKHS 2TNTAEE&S E'. 373
sGrlv 6 7tQl TO EHA OQ&O'y&viov xvxAos rjj. &6TS
xalr\ plv vjcb BHA y&vicc TOLOVTCOV faxlv id id,
otrav falv ecujS oo&cci rf, Aowr?? [Eucl. I, 32] ds
f\
into EBH T&V pav CCVT&V t/3 ^3, ofav d' cci d dgfral
T%, TOiovT&v g we' ro&ovrov CCQCC stirai, [IOIQ&V i]H 5
rov sjtixvxAov TtSQHpEQSicc TJjv KJtb rv\ Gshrjvrig 7tl
to uKQifieg TtSQiyeiov ttQt,s%ov6ct diaGraGiv. AA'
fastd^ rov iL<5ov aitoysiov a.7tsi%v fj ^s^tjvrj xccrti rbv
%QOVOV rrjs Trjotftiscos ^oi^ccg gas A, d^Aov, on, xai TO
TtSQiysiov TO {istfov itgoriysirai tijg ^A^V^g, TOVTSGTIV 10
TOV H GruLSiov. s6TG) drj TO M^ xcci dirii&M fj BMN,xal KTtb TOV E xd&Tos 7t avTriv %%&& r\ E&. iti
TOIVVV17 ILV &H 7tQiCpEQl,a $1%^ pOLQ&V g JC^,
rj$ HM V7tOKLTKL T&V CCTtO TOV 7tQLyLOV ^OiQKtV A,
&6TS ohyv Tr^v &M tfwcfyftf-Om yiOiQ&v ~ia va, ir}av 15
xalf}
V7tb EB& 'ycdviK, oi&v yulv i<5iv ai d ogftccl T|,
TOIOVT&V Tec w, oi&v d' ai dvo ogfral r|, TQIQVT&V
ny fi/3.K)6T xal
rj ^lv iitl T^g E& XQi,q)EOicc TOLOV-
TOV 6Tlv ny ft/3, OIGJV 6 7tQi TO BE& oQ&O'y&viov
xvxhog T|, ccvTrj dsr\ E& v&lcc TOLOVT&V xd AO1
,20
ottov 6TivrjBE v7toTivov6a QX. xal ofay itirlv
BE v&Ela ir TOLOVT&V ^TKL xcclr\ E&
2. ytovia] 1^, D, ut saepius. iS (alt.)] corr. ex iu D 2. 3.
~] dvo BC. 4. d'] mut. in d D 2. 5. s] corr. ex I? D.
17] postea ins. A. 9. TO] corr. ex TOV D. 10. TOVTGTW]comp. B, -v del. D 2
. 11. TO] seq. ras. 1 litt. D. 12. E]supra scr. C 2
. xa-9-fTog] Kd&sTo- in ras. minore D 2. 13.
H] supra scr. D, renouat. D 2. nsQicpsQsia] om. D. 14. i]
corr. ex a D 2. 15. CO^TS] 50Tf %at I). ia] -a in ras. D.
17. 8'] Ss D. at] ins. D 2. Svo] p BD. 18.
tptQSLu] fa D, ^ del. et o renouat. D 2. 22. jZrj] om. B.
corr. ex J| D 2, mg. t| D 2
.
374 KAATAIOT HTOAEMAIOT
I xal %r]xo6TG)v dvo. ita'kiv^ litelv\ plv vnb
AEB ycovtcc roiovtcov f\v po i>/3, oiov cci dvo do&al
r|, f\ds vjtb EBN rcbv ccvr&v wy ft/3, eL'rj
av xai
XoiTtri [Eucl. I, 32] r)VTCO ENB y&vCa rcbv avrobv
5 gvd ~L. &6r xalr\ ILSV enl rijg Eft TteQicpegsicc TOLOV-
rcov i6tlv Qvd 7, o'l&v 6 itspl rb ENE QQ&oy&viov
xvxA.os T|, ccvTrj dsr\ EH sv&sicc roiovrcov QI$ 2/77,
oi&v 6tlv ri EN v7toTtvov6a ^M. xal oi&v 0rlv
CCQK YI [iv EH V&ta 7 xccl Qrjxotircov /8, $ dl
10 iira%v rcov XWTQ&V 7 *#, roiovr&v xalY\EN
TIrj. far^y ago, fyyuSta rfj 4E rrjv EN a
^ dice rov [i6ov 7ieQiyiov rrj$ BM v&tccs Ttl tb N
LVCC xal
15 rOV T XXVTQOV XCtl tOV 7tiXVX&OV TO KVXO
% t&v vnb rovf
V 'Podc) dlO.(Srd6G)V TYJV
xar' Alywitxiovs Uccvvl 1% cngag &' xal
1. f|r]xoffT<5v] || B, | D, || et fl^xoffrcov D 2. dvo] corr.
ex ^ D 2. 2.
v$\ corr. ex MB D 2. Svo] B B. 3. T|] r-
corr. ex c in scrib. A. EBN] -N corr. ex H D 2. 4.
r]]
e corr. D 2. 5.
t~]e corr. D 2
. neQiyeQsia] ^ D,() supra
scr. D 2. 6. QvS] -S corr. ex A D 2
. 7. QIC;] Q- e corr. D 2
9. Eg] corr. ex l| D 2, mg. I| D 2
. s^oor&v] | D, ||/*A /*
BD 2; mg. &UCCYOV OVTCOS f^et is || |3
D 4per r^ hue relatum.
10. |Lifro:|v] ft D, ut saepius; corr. D 2. V.SVTQG)V OVGU D.
F i&] TT- e corr. D. 11. T trj] Tl- e corr. D 2. rr\v\ corr.
. TOV]ex xr\i C 2. 13. 7rpoffvfy0tg] -t- corr. ex o C. 16. TOV] corr.
exroD 2. 17. sv] ins. D 2
. 18. diomtvo^bvriv BD 2,
liivr\v C, 8iomBv[Lvr\v D. 9^^'] -9- corr. ex r1 D (or). ITSt]
corr. ex b D 2. 19. Ilavvt] TIccvvij (-77 e corr. in scrib.) post
lac. 4 litt. D, deinde eras. vvi. t'] *- postea ins. D. agcc D.xai om. D.
MA0HMATIKH2 E'. 375
^ rov fjMov diQitrsvopBvov Kara Kccoxtvov
Ta A.Ei7tov6ccs dExdrcj
3te'%ov6cc rov Asovros x
de xal dxQip&s SXEI%V) eTtsidtJTtSQ EV 'Poda itEgl rd
rsfavrccta rov Aeovtog {istci p,Cciv &QKV eyyitita tov 5
ILSGrnLfiQwov Mara pijxos ovdsv
ditstyev CCQK Kara rov exxsi^isvov %QQVQVrov aKQipovg fjMov [ioiQas sis t& sitopeva
g. AA' end yeyovsv rj riJQrjGis psra y xai y'
xcciQixas rrjs ev rrj 1% rov Uavvl {i6r][ji{i()iasi 10
ccvrcci, d' snoiovv svr
P6da) rore
6 cbro rijs
fl&S d y r* els ov %oovov catiavrcos s&Q rov 15
~Lji, rqv $E o^icc^v GEhijvrjv xccra
v 7t%ov6av Adovrog notices x K, &<5r xcti r
O rov axQi,flov$ fjMov
v ^ /Z, av&[JiaMas d' onto rov petiov 20
dnoysiov rov sjtixvxhov poiyus rky t/3.
rovrcov vjtoxEi^evcov sdro Tta'kiv 6 Exxevroog rrlg
xvxhos 6 ABF Ttsgl XSVTQOV rb /I xccl dtd-
2. D. 4. D. 5.CD.-a supra scr. C 2
. 6. nccQaldcGEi CD. 10.
rfj AC, corr. A 4. rot)] bis A extr. et init. lin. Tlocvvr]
11. d' STIOLOVV] in ras. D 2,deinde del. ovv D 2
. 14. d] corr.
ex I D 4. 15. r*] F ABC, mut. in F8 A, ii D, D 2
, mg.&Uaxov cwQip&g 8s T r D 4
. TOV] corr. ex ro C 2. 20. d']
om. D, 7 supra scr. D 4. 21. tnmuv,l.ov\ Ini- in ras. D.
A, BCD.
376 KAATAIOT HTOAEMAIOT
H,roov rv\v AAT, iy ^g h'tirco rb uwrgov rov di:
{iGa)v t&v ^(pdicov xvxhov rb E, xal /
y'y()d(pd'a) 7tol
rb B <jrj[ilov
6 ZH m-5 XVX&OS T'YJg 0-
T
E0B Z.
10 STtsl TOIVVV
rov f xal
15 7tQl,%
9 A, av
i(5iv al 6
jVTCO AEB ycovCa, O'LGJV
T|, roiovrcov 9 A, oi&v d' ai dvo
TOIOVT&V gnu. av xf$aA.6vts CCQCC rrjv BE20 Ka&rov 7i ccvryv aycopfv aitb rov 4 x
xalf)
vno dEK ycovia rcov koiit&v ig
000" G)<3T Xttifj [lV 7ll r^g /IK 7t
Qicc roiovr&v s<5rlv oo&, oicov 6 7Col rb 4EKycoviov xvxhos T| ; r\
d' iitl r$\ EK rijs
1. rov] corr. ex TO D 2. 7. ij T8 JB y.al T\ E0BZ] at
z/B E BZ D (s& corr. ex t& D 2). 16. 9 I] corr. ex T& D 2
.
17. xa 7tQor&coQ7i(iEVK] mut. in TO TCQort&fcoQriiJisv* D 2. 18.
T] e corr. D. dvo] B B. 19. s^dUovrss D, corr. D 2.
BE] corr. ex B D 2. 20. ayeopfv] ABC, aydyco[iev A 4 C 2
D,
bene, sed cfr. p. 381, 2. z/A] corr. ex AK D 2. 21. zlEK]
A- e corr. in scrib. C. 22. dvo] B B. TTf^iqpgpgta] Q D,
9 in ras. D 2. 23. 6] ras. 1 litt. B. 24.
rj]corr. ex e D 2
.
MA0HMATIKH2 STNTASE&S E'. 377
[Eucl. Ill, 31] sis tb fiiiMvxA.iov iioigag a. xal r&v
vn avrag agcc sv&si&vr\ ^Iv 4K 6rcci, roiovr&v
QI& v&, of
ia)v 6rlv f]4E vitorivov6a. QX, f\
de EKr&v ccvr&v a y. &6r xai, o
r
iov <5rlvr\ psv 4E
liTa,v r&v y.dvrQ&v It-9", f]
ds B4 x rov XEVTQOV 5
rov sxxsvTQov [id /la, notr\ yihv /IK v&ia <5ra,i I tO*
, r\df EK Quotas o f. xcci iitd ro TTO rrjs
L^ccv [Eucl. I, 47] TO Kitb rijs '<4K itoii ro
ccjcb rye; BK, e^opw ncti oAyv [iv trjv BK v&iav
prj As1
, Aotjri)v ds rr^v EB r&v ccvt&v^Trj Aa. Tta'kiv^ 10
I plv rr\<s oficcAijg GfAijvrjs aito rov
diK6Ta6i$ [IOIQ&V rjv jilg jit, fjd rij
TO
ttQL TO O.7t6'yiOV f]V rOV JtlXVX&OV) XKT& TO H 6rj- 15
HftoV) xal tti&vx&fid&v rijg re EH nccl rijg BHxd&Tos cbro rov B ri%&G3 iitl rrjv EH r\ BA.
itd ovv % V7tb BEA y&vicc, ot&v piv eltiiv ai
~d OQ&cci T, roiovr&v ftirlv a xg, otcov d' ai dvo OQ-
&al T|, roiovrovft vfi, fft? civ xccl ^ f^v 7tl r^g BA 20
TCQl(pQl,CC TOLOVTCOV /3 V/5, OtOV <5rlv 6 7tQl TO BEAdf
i\BA v&lcc roiov-
1. 7}piY.v'AUov] Q D. Tc5i>] corr. ex r<5 D 2. 2.
corr. ex uvxfig C 2. 3. v&] in ras. D. z/E] in ras. D. Post
EK del. * D 2. 4. a y] D 2
, Sy ABCD. 5. (isrcc^v] ^ D,corr. mg. D 2
. Ez/] /^E B. 6. rov sMevxQov] corr. ex &i
rov %VTQOV C 2. 7. o] corr. ex & D. 8. Ittyctv] corr. ex
D 2, supra add. TO$. Supra pr. TO add. v D 2
. 12.
-ctaraGis in ras. D. 15. G^^LOV] c D, GTJ D 2.
16. ini&v%&siG&v] -G- postea ins. A. 19. Svo] p BD. 21.
3 D, ut saepe.
378 KAATAIOT HTOAEMAIOT
f$ v-9*, ol&v etfrlvj]EB vrtOTivov6cc px. xccl
famv CXQCC % plv EB v&icc p? Aa, i\da BH
IK TOV XVTQOV TOV 7tixvxA.ov Is, TOLOVT&V stirai
xccl-YIBA sv&sta a
t/3.KKJTS xai, oiav fatly
r\BH
5 v7toTsCvov6a ^jc,roiovrwv uai
v\ [ilv BA eGrat, v^ Ad,
^ d' iit a,vri\g 7tQi<peQEia roiovx&v % A(J7ot&
d itSQl TO BHA OQ&oycbviov xvxhos r%. xccl
vitb BHA aQtt ycoviK roiovr&v stirlv x$ Ad, oicov
stalv at dvo 6pwi_r|, % d' vnb ZBHoty [Eucl. I, 32]
10 t&v [isv avrcbv x& xg, oicav d' aC d 6Q&al T|, -rotov-
id ]vy. toGovTcov aga edrlv poiQCbv fjHZ rov
tV CCTtO TfS (fSJivi 7tl TO
ditel TOV (i&fov cirtoysiov a%Z% XCCTK rbv %QOVOV
15 Tils Tr]QrJ6G)g [lotgccg Thy i/3, lav vjto&G)[id'ci TO ILB&OV
aitti'yzLov KKTa TO M xal fjti&vt.avTfs Tr\v MBN xdd'-
STOV 7t avTfjv d f
yd<
y(o^,v ditb TOV E T^V E&, 6Tat,
17 {llv HZM 8A^ 7tOL(pQiK T&V
XVX&OV [IOIQ&V X$ JU^ ? AotJTl) df ^ ZM20 &6T xal
r\ (iv vnb MB Z y&VLCc, TOVTSGTLV [Eucl. 1, 15]
^ vrtb EB&, OICDV [lev dtiiv at d 600m rj, TOLOVTCOV
i(5r\vifi ,
oicdv d' ecu dvo ooftal r|, TOIOVT&V xd 7,
XCcIf] [lV 7tl Tils E^ 7tQi(pQlCC TOLOVTOV 6TiV X$ 7,
olov o ytol TO BE& ogd'oychviov xvxhos r|, avTrj df
4. a] postea ins. D. 5. &>rca] (>a D. 6. iari D. 7.
-A in ras. D. 8. 1^] -tf_inras. D.
_9. dvo] tJ3D.
ZBH] corr. ex ZB D 2. 10.
<?] A, corr. ex 7<? D, dvo BC.
11. ^y] corr. ex nid D. SGTLV'] comp. B, -v del. D 2. 14.
D, corr. D 2. 18. HZM] H- corr. ex E in scrib. C.
21. EBB] EBZ BC, corr. C 2. 22. icziv] comp. B, -v
del. D 2. r] ins. D 2
. 23. E] E^ c^a D. (>rt D,comp. B.
MA0HMATIKHS STNTAEE&S E'. 379
ES sv&slcc roiovr&v %,oiW stirlv ^ BE vno-
w. xal OL&V 6rlv aaafj plv BE ev&eta
Aa, f]ds /IE fisrcc^v r&v xwroov i iO1
,roiovr&v
VTtb AEB y&vfa vnoxsirai, roiovr&v QICCC,OL&V 5
sitilv KI dvo OQ&al dj, ^ ds vito EBN Idefyftri nd 7,
nccl koi7ti]v [Eucl. I7 32J rr^v VTtb ENB XUTCC^SL-
Tcbv CCVT&V QVZ v, yivsTcct, xccl rj [iEv iitl rfls
7tQi<pSQeia TOLOVT&V QV$ v, oi&v itixiv 6 Ttegl ro
ENS OQ&o'y&viov xvxhos r|, avrfj dsv\ ES toiovrcov 10
Qit, Ay, otcov s6rlv ^ EN vitorsivovGcc ^x. xal o'i&v
i&rlv CCQCC YI plv ES sv&sta I xal stflKoGx&v ^, 17ds
AE [JiSTcd-V TCOV XSVTQCOV i-0",
TOtOVt&V Xttli\EN
~i K. xal sx TOVTCOV aga i'Grjv syyiGra rf/ 4ET&V KBVXQ&V rrjv EN nu.'kiv uTtsttricpsv fj
dice 15
rov M fifWu aitoysfov rijs MB sv&SLas iitl ro N
xccl $ aAAcov ds Ttksiov&v TrjQt]6csv tovg avrovg
va /
yo[ivovs fVQfaxopw , co<s x rov-
rb ns^l r^v VTCQ&SGLV rijg 0^t]v^s 20
XCCTCC r^v rov 7tiKVKkov 3tQo6vv6iv I'diov TTJjg ftfv rov
xsvroov rov iniKv^Qv 7tQiayK>yri$ Ttzol rb E xsvraov
rov dice {isGcov r&v ^codicw aTtorf^ov^isvrjs^ rij$ ds rb
ccvrb noil rb xccra rb [i6ov uTtoyeiov rov 7tixv%A,ov 6rj-
1. ES] in ras. D. 2. 97 [itv] infra add^D. 3. ilF] ~^
e corr. D 2. 4. ES] corr. ex E D. T
?j] i| ?j D, rf^D 2.
6. ^^] S' D. Edei%dr]] -%- corr. ex -A in scrib. C. 8. yi-
vsraL] mg. D 2,P D, F% D 2
. 12. l^xoarcov] comp. BD. ^f]
renouat. D 2. 13. T&V] corr. ex TW A 4
. 14. iar\v\ A 1
, foij|v A.21. TtQOGvsvGLV 22. imY.vv.'kov] bis A, corr. A 1
. 23. (ie-
ccov] -ceo- e corr. D 2. 24. TO (pr.)] om. D; mg. alla^ov ovrco
tr}<S 8s Kara TO (itcov anoyeiov TOV m crrj^. acpogifcova' avra>
<r-o D 2.
380 KAATAIOT nTOAEMAIOT
[istov atpoQi&vGYjs avrov dia^isr^ov {i^xeri, agog to EKBvrQOv ri\g b^ia^g TtEQiaycayrig ri\v itQoGvzvGiv tittey
inl r&v akl&v yiotov^vrjg^ a/Ua Ttdvrors agog rb NKara rr\v faqv id ra stSQa didtiratiiv rye; 4E
5 T&V KVTQG)V
diet t&v yQa^i^i&v CCTCQ r&v
fj KXQiflJis rijs 6A.rjvr]s
Tovrcov ds OVTOS djtodsdsi'y^svcov dxoA.ovd'Ov rs
10 ovrog Gvvdtyat,, ruva av tQ63tov xccl snl x&v narcc
rfjs Gshtfvrjs itagodcov rag T&V peGcov KIV^SOV
ipw dno r rov r^ ccito-
dQi&[iov xal aitb rov Kara rbv iitinvKkov rijs
rrjv ywofidvifv itQfa&stiiv ty dcpai()6iv rrj Kara
15 ftijxo? {i6r] 7Cag6d(p rov TCCCQCC rv\v av&iiakiav diacpoQov^
robv yQamL&v fj roiavrr\ Kara^a^,^dvrai 8id-
aTto rGbv 6ftotc3i/ rols 6tt&i[ivoi ^(DQ^^idrcov.
VXv iiti rijs v6TQas rcov
rdg avrdg v7to&G)[id'a iCOio-
20 dixag xiwJGfic; dito%ijs nal dva)[iaMaS) rovrltirw dito-
v rag IK rov SmkaGiuGpov Gvvyyiisva
A, av&paMag S1
dno rov pfaov uTtoydov rov
1. diaiisxQOv] -STQOV in ras. D. 2. TIQOGVSVGIV] -i- corr.
ex r) A. 4. fisra^v'] corr. ex ft D 2. 6. s'] om. C, mg. D 2
.
jroog 7. JLa^dvsrca] mg. superiore D 2fol. 109V
,eadem mg.
sup. fol. 109r(i] axptfiife] diaKQipsi, TtdgoSoi iK^dvovxai) D,
del. D 2. 9. 8s] Stf U. 10. 6Vro?] e corr. D 2
. 12. WQIGKO-IIEV B. 13. Supra rov add. O.QI&IIOV D 3
. Kara] x- corr.
ex y in scrib. D. TOV~\ corr. ex TO D. 14. yivopivj]v] corr.
ex P D 2. 16. fie'v] del. D 2
. 21. (isv rets s* TOV] in ras.
post ras. 1 litt. D. 22. f] e corr. A 4, mg. 9!' A 4
. d'] 8s D.
MA0HMATIKHS 2TNTASE&S E'. 381
xvxkov
rqv NSr&v avr&v
t/3,xal avrl plv rrjg E& xa&srov
,avrl dl rijs BA rrjv HA, dice per
x rov Mtfaftai rag nobg rep E
xocl rag z/E 5
xal EN VTCO-
r&v 4Kxal NB sv- 10
rov
(Srai t i,
HyyiGra ,oiov
H 6rlv ^ [iv 15
% rov
rov
exxevroov pft fia, ^ df BH BK rov xvroov rov
zitLXvx&ov tf, xaroa d rcov EK xal E& r&v
avrcbv o f, xal dia rovror\ {ilv BK 6'A^ f'tfrtu, 20
xa&a7tQ di,a[iv [i7fQo6d'v ,rcbv avr&v
fi/ij Ag,
i\$ BE bpoi&g pr] Aa, ^ ^ -^S T^V AoiTt&v
JJi/rj w;. GUST' 7ti xal ra anb B& xal &N 6vvr-
itoiEl TO ajtb rqg BN [Eucl. I, 47], xal ravr^v
[iijx[, roiovrov [i& Aa, o'i&v i]v i\ N$ v&ia 25
xal oltov 6rlv aoaj]BN v ijtorivov6a ^x,
2. N&] N- obscurum, vt- supra scr. D. aydyoopsv D. 3.
supra scr. D 4. 8. OVGCCS] faces B. 18. KWTQOV] x-
corr. ex a in scrib. C. 20. o ?] g D. 21. ldsLJ-a(iev~\ posta ras. 1 litt. A. 22. Post ftrj del. xg D. 23. onto] anbr&v D. xat (alt.)] supra scr. D. 25. ofeoi>] orco C. TJV]
supra scr. D 2. 26. T L&] TT- corr. ex JV" D.
382 KAATAIOT UTOAEMAIOT
TOLOVTCOV k'tirai xal % plv N& svfatcc x gyyiGra., 17
6' en avTils 7tQL<pQia TOLOVTC3V xd y, oicov <5rlv
6 7tQi rb BN& tiQ&o'yaviov xvx^og T%. &6rs xal ^VTtb NB& ynvia, TOVT&TLV [Eucl. I, 15] r\
VTCO ZBM,5 O'ICDV \iiv L0iv ai dvo OQ&al T%, roiomcov serai, xd y,
OLCDV d* ccC d oQ&al rj, roiovrov t/3a syyititcc. roGov-
TC3V 0rlv CCQK f]ZM TOV BttlMJKhoV 7CQitpQlK.
7C\ rb H 6rj{itov rr\<s 0^vrjg a7t%t, TOV Manoyfiov tag Aowrag ig rbv sva xvxkov
10 xg jiti/,xal komriv f^o^ifv rrjv HZ 7tQi<pQeiav
td ftg' &6T xalfj VTtb HBZ yovia^ oicov piv eltiiv
ai d ogftccl t$, TOiovr&v 6rlv id fi, otcoi/ d' ai dvo
oo&ai T$) roiovt&v xd1
Ad, xal ^ (dv fal tijs HA TCSQL-
<pQLCC rOlOVTCQV 6xlv X& Ad, OIWV 6 7tQ\ TO HEA15 OQftoy&viov xvx&os T(J, ^ d' &tl Tfjs AB T&V koin&v
[Eucl. III7 31] etg TO fmixvxfaov ~QV xg. xal T&V vit
KVTag aga V&IK>Vr\ ply HA Z<5xai TOIOVT&V A Af,
OLCOV 6rlvf)BH vitOTBivovtia QK, q ds AB T&V avTcav
QL /f. K)6T XKl, OIG3V 6TLVJ] [lV BH X TOV XVTQOV
20 fov *TCixvxA,ov f t, f} df BE di%&r] ^trj Act, TOLOVTCOV
xcclfj [ilv HA 6Tai, cc 3c, 17
df AB oftotog . xal
4. rovxiGTiv] corr. ex T-/. D 2. 5. I'ffrat] SGTIV seq. ras. 1
litt. D. 6. i'yYL6TU D. 7.
17]xal
17D. 8. 67](ji8tov] <?* D,
D 2. aTr^Fi] corr. ex &nsi% D 2
. 11. xai'] bis 'C extr.
et initio pag. HBZ] HZB C, HBZ supra scr. C 2,corr. ex
BZ D 2. 12. rotoimoi; 13. TOLOVTCQV] mg. D 4
. 12. f'crrtV]
comp. BD. d'] de comp. D. 13. T|"] BD, supra add.A 4
,om. AC. TOIOVTCOV] etiam in textu D. HA] HA
&QK D. nfQLcpSQficc TOiOVTcov] mg. A 1. 14. HB A] BH D,
ERA D 2. 15. <T] 8s C. 18. Post BH del. if D 2
. VTTO-
TSivovGa] -v- corr. ex o in scrib. C. 19. Mg. rotovrcov soriv
ice [ig oi'cov ds CCL dvo OQ&al T D. 20. jitr]]corr. ex fTnr D 2
.
21. a x] ax AC, ut saepe. ylB] -E e corr. B 3.
MA0HMATIKHS 2TNTAEE&S E'. 383
KQK rjEBA TOIOVT&V EGTLV vj> A, otcof xal
fj
AH r\v a %. Km, ETCEI Tta.'kiv TK VLTI avrcbv GVVTE&EVTCC
TtoiEi rb CMQ Trig EH TETQccyovov [Eucl. I, 47], E^O^LEV
xccl rr\v EH ^KEL T&V CCVTCOV wy A HyyuFta. &6TE
XCCl) OICOV <3tlvfjEH V710TIVOV6CC ^K, TOlOVr&V XCil
ij [ilv HA 0rcaft v&, r\
d' ETC
roiovr&v ^ v/3, oi&v fatly 6 itEQl rb EHAVLOV xvxhos T$. xal
fj vjtb HEA CCQCC y&vtcc rov
Ttccga ri)v KVcopaMav diccyoQov, olW fidv EI<?LV at dvo
OQ&ccl T%, roLovrov 6rlvft vft, OL&V d' cci d OQ&al T|, 10
TOlOVt&V a 3CS" OTtEQ ItQOEXELXO
Kavovog TCQcc'y^arEia rijs xafrohov
r'Iva ds Tt&Kiv xccl dia rijg xccvovixrig
E% ETOipov didxQiGiv r&v Kara [iQog 15
) TtQOGavsjtArjQ&GaiiEv TO HUTU T^VV V7t6&6lV 7tQOXT&ElllVOV r^LlV XKVOVIOV TOtg
xal Tijv di7tki\v ccv&iiaMav TtQO^ELQ
dvvcc[ivot,g GEfadfoig dice T&V avT&v
%Qr]6d{ivoi, Tcclg Ecpodoig. ^IETK plv y<xQ T<X TCQ&TK 20
dvo 6E&idi,cc TCC 7tQi%ovTcc Tovg
TQLTOV GsMdiov 7tQi%ov Tag
1. EBA] corr. ex EBA D 2. tGiiv\ comp. B, -v del. D 2
.
^,5] corr. ex vg C 2,
corr. ex Js D. 3. EH~\ corr. exEN D. 4. EH] corr. ex EN D. injyiti, fyytcra] in
ras. D. 6. HA] EA B. 9. dvo] B B. 10. r|(pr.)] corr. ex
T in scrib. D. tariv] forat B, om. D, comp. ins. D 2.
j? v]|3jv
D. 12.']
om. A, mg. D. KKVOVOS 13. ccvcoficcli'a?] mg.superiore D. 15. pt&odfvuiifv] -co- corr. ex o in scrib. C.
16. TtQoo&acpcaQfGiwc; D, corr. D 2. 17. TtQOwrs&Eiiitvajv C.
21. Supra rovg add. KOIVOVS D 2. ccQi&\[iovs A, <xQi\ft(iovg A 1
.
384 KAATAIOT IITOAJEMAJOT
rep Trjg *fl>fH&U$ apfifytcS jr^og TO TOV aitb TOV
a7toyiov, rovrfan rov M, GwayopEvov ex T&V
Ttaaod&v iistafpeQSG&ai nobg TO axaif&g K
TOVTStiTlV TO Z. OVTtEQ yttQ TQ07COV ETtl Tijg XXl[JiEVr]g
5 dito%ijg T&V 9 A [loiocbv sds^cc^isv TJJV ZM itSQicpSQeiKV
H,OIQG*V ovGav i$ a, IVa, sxsidrjitSQ TOV M [isGov dno-
ysiov K7tei%sv r) ^e^vri poiyus thy tj3, rv\v axb TOV
Z axaiflovs ajtoyetov dictGtaGiv avTfis SVQCD^LSV 6vva-
yopwriv [loia&v dyhovoTi, r^s Iy, nobs as ^ ^^ rov
10 &tt#wdov rtQoG&cKpaiQStiis T^g xaTa ^xog ufayg KLVT^-
<5EG)g ocpzCksi, AaiLpdvsG&ai, , ovT&g xal iiti T&V
Tag yivo^ievccg
foxoTrjTag dia rCbv KVT&V ^a^dvovTeg^ LVK{if}
15 sxcctiTov iiaxaokoycbijisv, Jtaas&rjxaiizv oixefag
T&V KOid'^&V V T& TQiTG) GshldtG). T&V d'
GEXidlWV TO [IEV T8TCCQTOV 7tQLE$l, TCCg
ETtl TOV a xcivovCov diatpooag Tijg naoa TOV 7tixvxkov
ccva)[iccMccg cog Tijg ^yL6Trjg 7tQo6&a<paiQ6'EG)g ^%^^20 T&V a poiQcdv yyi,6Tcc cp&ccvovtfrjg XKTK TOV Tcbv f
ytobg TCC Te Adyoz/, TO df
Tag v7tQo%ag T&V yivs-
lLvcov diacpooav x Trjg dfVTaag
1. KQiftpiov D, sed corr. 2. TOV] corr. ex TO C 2. avv-
corr. ex Gvvayco(ivcov D. 4. rowceGZi D, comp. B.
6. 9 I] 9a A, cfr. p. 380, 22. 6. [IOLQCCV C.^1. "rly] -y
corr. ex f C. 8. owccyo^vriv} corr. ex ovvccyofisvcnv D 2. 11.
dqpftAet] corr. ex dyetti] D 2. OVTCOS] -TO? supra scr. D 4
.
13. 7iQOK8i[ivr}$] corr. ex ^yKftfievrje D 2. itQOG&ctcpcuQSGsoos]
-&- ins. D 2, -ECOS in ras. D 2
,deinde eras. cog. 14. lapovtss D,
-t- supra ras. D 2. 15. Ixadroj] mut. in fxacrTov D 2
,00 supra
add. D 2. 16. aetfyt<Bi>] Oft D, renouat. D 2
^.T^tTw] f BD.
17. 7r900fy.Tf-9-7jjti.fVag D, sed corr. 20. a] om. D.' jtemf]-m supra scr. D 2
. 22. didyoQOv B.
MA0HMATIKH2 STNTASESE E'. 385
cog xccl svrccv&cc rrjg {leyfarrjg jtao6d'a(pcciQ6a)g
ri xata rov r&v | xobg rarj
,LVCC rb {iv d' GeMdiov
rj trig xara to
rov xxvroov 7tQi rag 6vwytag ytvo^V^rov 7tMvxkov, rb ds e' r&v evvcfyonEvov v7tQO%G>v tx 5
rrjg Kara rb TtsQfyfiov rov sxxevrQov Ttsgl rccg di%o-
t6[iovg denoteA,ov[i8vr}g avo^a^iKg.f'vsxsv d rov xccl xara rag [ira%v rcov dvo rov-
rcov &6O)v TtccQodovg rov fjtixvxkov roc Zitifi&Movrcc
rCbv jtaaaxfiiiw&v vitQO%G)v ava^'ycog Aajipcivf- 10'
<5Mdiov itQid%ov ra QyxoGra,KK6rov rijg a7to%ijg doi&iibv rov TCCCQK-
diacpoaov A,K[i($ccv6[iva 7CQo6ti&6&aL rr\
7tQK>rr]v av&piccMccv KXi^ivr] xccra rb d'
. xccl rccvrcc d fj[iiv 6vvrtaKrai rbv 15
rooitov rovrov.
6rG) yap itdfav 6 XXvtoog ri^g tiMpi^g xvxkog 6
ABT TtQL KBVtQOV tb Z/ XCii did^tQOV X^V A Z/ F,
&P ^ff vrtoxffad'G) rb %vtoov rov dice [ifacov r&v
t,<pdiG)v rb E, xal aito&rjyid'ffayg rrjg AB 7tQHpOiag 20
yocc(pvrog r 7tol rb B rov ZH&K 7Cixvxl
^ EBZ. dd6<5&a)6ccv df Aoyov VXv ditoxijg
|, cj<jr dia ra ccvra rolg itQOttitoddiyn,tvoi$ tlvai
rr]v vnb AEB y&viav rcbv diTtkatiiovczv rrjg
2. p] Io BC et in ras. A, t(3 D, FB D 2.
^
3. csh'diov ]]
corr. ex aeMdtov D 2,-ov in ras. A. 4. yti/ofif'vrjg] -ij- eras. A.
5. e'] nsiinrov B. 8. jjvswx D. xat] om. CD. 10. &VK-
loyov D, v supra scr. D 2. 11. |rjxo(7ra] |" D. 13. Supra
-ueilLsvov add. ^ rat s' cekiSlq) D 2. ^afi^dvofjisv C, corr. C 2
.
14. 7tQmrr]v] om. D. 15. nQOGccyctiQSGsi D, corr. D 2. 20.
7ro/,Tjqp'9'ft<77]g] D, ano\EiyQ'Ei6ir}g ABC. 21. re] supra scr. D.23. TO. amd] corr. ex ravrd D 2
.
Ptolemaeus, ed. Heiberg. 25
386 KAATAIOT HTOAEMAIOT
xal
BE $ TOV 4 A,
OCTtb TOV
5 E XWTQOV 7il rrjv
sv&sicc fp-
^isvrj rov iiti-
)
r
iva TO
10 TtteldTOv didcpo-
QOV
EMN,TS { BM.
15 ensl TOLVVV vivitb AEB ycovCa ,
oi&v \iiv sltiiv
ai d oQ&al T|, TOIOVT&V vnoxsiTai, ^sc, otov ds ai
dvo OQ&al T, TOLOVTCOV ~6JL, i7i av xccl i] vrtb AEAT&V Aoirt&v is T&g dvo oo&ag ^x. KHST xal rj [lev
Bill TfjS dA V&ia$ 7tOL(pQlCt TOIOVTG)V 6TiV ~QK^
20 Oicov 6 7tQl TO 4EA oQ&o'y&viov xvxAos r|, fide
7tl TYl$ EA TG)V koiTt&V [Elicl. I1I? 31] 1$ TO
nkiQV 5- xal T&V V7t CCVTKS aocc sv&zicbv r} {l
TOIOVTCW 6TKl, J, Ol&VJ]/IE V7tOTlVOV6tt ^3C
z/A T&V avT&v ^y v. KKI otcov aoa i6x\v
EA
1. fioLQ&v] D, ft AC, B. 2. irfljiQ-SLOcx. B. 4A] e
corr. D 2,6 AA B. dt^oo ^ xat rj REKA\ om. BC. 3.
ex HEX^ D 2. 4. ?)] om. BC.
T.^v&sfaom. A, -cpccm- in ras. maiore D 2
. 16. df] d5
D.
17. dvo] B B. Ante ~GJL del. r?D 2
. 18. Svo] ~jlBD. 19.
~
corr. ex ^yt D 2. fcrtV] comp. BC. 20. JEA] corr.
ex yfE^ D 2. 7)] corr. ex st D. d^] d
j
D. 23. fWi]fdTtV D. z/E] seq. ras. 1 litt. D. 24. zM] //- corr. exA D a
.
MAGHMATIKHS STNTAgES E'. 387
sv&sta ~i ift, rjds 4B dpot&s lift jZa, TOLOVTOV
6Tai, xcclf} fttv EA sv&sZa I eyyitira, fj
ds dAo^ioicog rj vg. xal fasl TO anb rijg B4 fatyccv TO
CMO TfjS dA TtOiSt TO CC7CO TJJS BA [Eucl. I, 47], ^KSi
aga sGrau xal okri [isv ^ BEA ev&eiayi/rj vy, koiitii 5
8s fjEB TOiOVTOv ^vy jily,
otcov 6rlvfyMB BK TOV
KSVTQOV TOV 7tt,XVxA,OV i. XCcl OIG)V CCQK Itftlvi\
EB vTtoTetvovGK ^3c, Toiovf&v sGTcci, xccl % {ilv BMid x, f)
d' m KVT^Q TCSQL^SQSLCC TOIOVT&V 1/y
otcov stiTlv 6 TtBQi TO BEM OQ&oytiviov Kvuhog 10
xalr\
vnb BEM agcc ^covta^ r^xig itSQifysi, xv\v
diacpoQccv T^g fawafuxfoisct, of
icov piv sfaiv ecu
T|, TQIOVT&V BGTlv 1/y fl^, OIG)V 6' Cti d OQ&alTOIOVT&V g v8. diijvs'yxEv agcc KKTK TCCVT^V T^V
aito%ils ait60Ta6i,v TO ytccoa tv\v av&paUav did- 15
Tcbv XCCTK TO cutoysiov yivonsv&v HOLQ&V a
oiQa noil ^rjxotiToig vy. <5Tiv $ TO okov TO
TOV TCSQiySlOV dlCC<pOQOV yLQlQ&V ftAt)" KCil O
f
iG)V
CCQCC 6TLV TO [ifylGTOV dlCCtyOQOV |, TOlOVTCdV <5TCCl, TO
Tys pices ILOIQKS xccl T&V vy QrjxoGTcbv ft/3 A^ ?a xal 20
1. z/E] corr. ex AE D 2,AE A. T i&] T T- corr. ex H A,
e corr. D. 4B] corr. ex AE D 2. 2. %ca] v.- in rae. A.
F] seq. ras. 1 litt. D, Is C. 3. jBz/] corr._exBA C 2
. teZil)Kv~]
"k- in ras. 2 litt. D 2, supra -ft- ras. 6. ]Ty (alt.)] infra add. Dr
supra scr. D 2. MB] "BM' B. 9. <T] ds D. V] corr.
ex tin' D 2. ccvtrj?] corr. ex avr^v D 2
. 11. ^'rigj corr. ex
f ris D 2. 13. f] dvo C. IGXIV\ comp. B, -v del. D 2
. d]14. SirivGyv.$vo C. 14. SirivGyv.tv] mut. in dnjvtyxs 8' D 2
. %ara] corr.
ex KUT' D 2. TTJV] supra scr. D 2
. 15. &no%fig] a- et -TJS e
corr. D. &#OfUfi&t* A. 17. pi&i (lOiQca ABD, jtttat ^oiga C._ d _
i-r]H06toi$ ry] -TJ- e corr. in scrib. C, vy D, vy. B,comp. B, -v eras. D. TO (pr.)] om. D. TO (alt.)]
corr. ex TW D 2. 19. SGTIV] comp. B, -v del. D 2
. roiovrcav]corr. ex TOLOVTOV C 2
. 20. f^xocrcov] comp. D, ut saepe.
25*
388 KAATAIOT nXOAEMAIOT
OO TG)V
ooGavrcog df xal 7tl roov koijtcbv r^irj^idroov
itdhv dice roov avroov ra ovroog ha[ifiav6-5 [iva [iQr] trig roov dvo dvoo^ia^ioov vitoo%fig TiaQe&rj-
rotg oixuoig doi&noig ra sxiflciMovTcc exccGTG)
x^S QrjxoGra r&v oh&v \ dr\-
Kt diTtkccGiovi r&v
w, os 6nv Kara rag QX rov
10 ysiov rov exxsvrQOv.xccl
'
ds 7CQO<3&tfxa[iv GfMdiov TIBQIB^OV rag%ara ttkdrog yivo^vccg TtaQodovg rr\g Gfhtjvrjg iyKccrQcc ra pfyrj rov dt,a [ifacov r&v tydiwr cog iitl
rov dia rcbv Ttoh&v avrov xvxhov, rovr6nv rag ayto-
15 A,a{i{lavon,vag rovrov rov xvxhov noi,(pQiag iira,vrov re dia u,6G)v r&v ^oodi&v xal rov 7tol rb avrb
%vroov Ao|oi) r^g 6htfvr]g xvxhov xa&' xd6rqv roov
xara [iQog 7tl rov Aojov jtaoodcov. %%otfn&a d
xal Ttabg rovro di'%i, rr\ avrrj, di rjg xal rag [ira%v20 rov r i6rj[iQivov xal rov dia [i6'G)v r&v
7tQi<pQLag rov dia r&v itoAeov rov farjiifoivov
yiGapzfta, Ivftade ^advroL cog ri\g {ira%v rov dia
roov %G)diG)v xal rov POQLOV t)voriov 7toarog rov
Ao|oi) xvxhov 7tQicpQiag rov di a[i(porQcov roov
25 jtohoov avroov yQacpo^vov {nsyiGrov MJK^OV 7tvr ftot-
QOOV vitaQXOvGrjg, 7tidijitQ xal r^iiVc, xa&dtto xal roo
'IitTtdoxq)., dia roov 7tol rag /3oQiordrag xal voncordrag
itaoodovg cpaivo{ivoov
1. TW (pr.)] corr. ex TO C 2. aQi&po)] corr. ex CCQL&P&V D.
5. ccvopaHiaiV C. 6. fxaffrcu] -w e corr. D. 8. Q] ins. D 2.
9. api^ju-w] corr. ex KQL&^I&V D. og] corr. ex o D 2. ZGTIV]
comp. B, -v eras. D. 11. '] sfidopov B. 12. ywoutvas] corr.
ex yivoptvovg D. 13. TO] om. D. 14. MKlov] om. C. TOVT-
iati'v] comp. B, -v eras. D. 16. nsgl TO] TCSQL post ras. 2 3
litt. C. 18. ;ioio] lo^ov KVK).OV D. ds] om. B. 23.?)|
VOTIOV A 4, 5) v\oviov A. 24. Ao^ov] inc. fol. 106r B. 25. no-
Acov] corr. ex Ttollcov D. 27. (Sopftorarag] -a.- in ras. D.
VOTIOTKTKS C.
MA0HMATIKHS STNTAEE&2 E'. 389
TOV c)dia%ovr\ ttfafarri ndgodog
xaTaAa[ifldvTai,, xai ndvrcc 6%sdbv ra
rag tygijtieig avrrjg Tag rs JtQog Tovg a6TQagTag did Tcbv ogydvov dscaQovpevag
Talg TrjAtxavTaig xaTa
fag xal dia T&V (pe%ijg
Tai. KCLI iGriv TO Ti^g xa&oAovxavoviov TOLOVTOV
1. fqp'] i] sop' D. 17] om. D. TtctQodos] corr. ex TVKQ-080) D 2
. 2. KccTahccfificivETai] mut. in xatfAajLt^avfTO D2
. 7.
taxi D, comp. B. TO] in ras. D. 8. roiovrov] des. fol. 136rA,
fol. 136 V uacat. Post VOLOVTOV add. fol. 106r B:TO rfjs v-aftfaov G&Jiviwfis tivapcdias V.O.VQVIQV n^d^i Iv
\L\V TOtff 71QWTOIS $VO GSildlOlS tOVg KOLVOVS KQL&^IOVS T?Jg Tf TOV
anb TOV ccTtoyslov TOV y.y,vrqov V.LV^G(OS KKI KVTTJS
Gf^vrjs &rtb TOV axptjSovg dtnoytiov TOV nmvy.l,ov nol txi
sni TOV Ko^ov uvxris ngbg xbv 810, (IGCQV xa>v ^codiatv :r^>
V 8 TO) y GSfodlCp XK<S 8lCCGpOQCtg XOV [18GOV KTCOySLOV XOV
TtQog xb axQtfisg anoysiov : Iv 8s xoj 8 xag SiacpoQag
xfjg nciQa xbv 7tinwx.lov avooiiaMag xov 7tiKVKl.ov nuxct xb ano-
ysioxctxov xov iv,y.vxQQv xvy%dvovxog, xijg 8s G^VT]g inl xov
slg xa. nQoriyov^svci (pfQO^vrig :
iv 8s xoi f" vnsQOiag (comp.) x&v yivofitvav avw^aZiagiv. xfjg V.UXCL xb itSQiyEiov xov SKKSVXQOV fttGscog ngbg
xbv KCLXO, xb anoytiov ctvxov &SGLV xov snwuv.l.ov xfjg Gehrjvrig
xag Kvxug sv SY.CCXSQK &Gi anb xov KKQifiovg anoysiov ini-
Y.V-A^OV ft ccfpiGxap* : iv 8s TW s xag v7tQO%ag x&v naxa xag
[Ltxu^v xov anoysLOv %ai nsQiyefov xov SKKS'VXQOV nagoSovg xovimy.vY.lov yivo[ivcov {isyiGxav nccga XTJV inl xov iniv.vY.^ov
luscrjv xrjg Gs^vrig ft^Giv SiacpOQav nQog xr\v inl xov anoytlovxov SKKSVXQOV &ZGLV xov iniY.vY.lov yivo^svr\v (iyiGxrtv avco^a-
Mav <ng tf]g iiyLGxrt g vnEQO%i]g xrjg nctga. xi]v B avco^a2.iav nQogxr
tv a ijxoi xi]g naqa xr\v inl xov negiysiov xov iv,Y,vxQOv ftscecog
xov inwvy.'kov vnSQO xfjg yivo^vr]s ^yiGxr\g av(0[iahLag ngbg xr\v
inl xov anoysiov xov SKKSVTQOV &GIV xov iniY,vy,1ov
avcoiLaMav x&v B A<9 ft (isxa^cp&tiGi^g ttg s^r^ooxd.
iv 8s xoj xag anola^i^avo^svag negicpSQslag Itp'
xov <xt8iaY,ov (jisxa^v xov 8ia ^GOJV x&v aj8i(ov Y.VY.IOV v,al xov
ko^ov xfjg 6lr\vr]g Y,vv,lov xa-91'
Y.a6xr]v x&v Y.axa ^Qog inl xov
l.o,ov Y.VY.IOV xfjg GBlrjvr^g nagodaiv xov SLU x&v nohcov xov 8ia
piGiov x&v o3Sicov Y.VY.IOV :
390 KAATAIOT HTOAEMAIOT
'Y]'.Kccvoviov rfjg xad'ohov
'
IT
MA0HMATIKHS STNTASE&S E'. 391
QY.&
<wgle
QP*
QV&
Q&P
QOK
ffxrj
GV.B
6*$Gift
tfiy
Gi
G8
GCt
Q7t
IK
ICC
v8
o
rf
LCC
io
xy
XT]
ty
X
&V?
He
IT]
LCC
P
~v'p
(17}
V
vcc
^Lv8
v8
vs
vr\
vy
ir\
[IS
v&
Ifis
vs
IE
8
xg
35
vy
y 40
IK
X
18
V
v8
V?
45
vrj 50
O votiov
1.7]'] mg. B, om. ACD.
fol. 113 VD, totam tabulam fol. 106V B, coll. d om. C.
coll. cc 8 fol. 113r, reliquas
4.
t; corr. ex aTroyft'ov D 2. nlccTovs ncci (i^ovs] corr. ex
v D 2. 5. itQOG&acpKiQEGELS (pr.)] TtQOG&aycuQilGsojg B C,
D, -^aqp- in ras.; TtQOG&ctcpcciQeG^? D 2.
(alt.)] TT^o^'d'aqDa^sfffcos B, 7tQOG&cc<paLQGg D. 6.
add. D 2. dbroyft'ov] om. D. fjnxvjt^ot;] om. D. 8. (36-
A, om. BCD. 9. i>#] vrj B. 10.ITJ] trjt D. x]
11. v?] v D. 12. %<?] xa D. 13. a] corr. ex J int^, A.scrib. D. y] et reliqua pars columnae ad lin. 43 in ras. D.
rfiS D, et similiter deinceps in hac co*l. (w=
c). 20.
18.
31. ^f] ^D. 32.
^xs] ?tg D. 35. pxtf] ^t-9- D.
43. Zij] corr. ex te in scrib. C.
45. vg] corr. ex (^g in scrib. C.
50. l\l seq. ras. 1 litt. D. 51.
in ras. D. voxiov TIEQCCS] A,TO.
la. D. 33. xe] v.8 D. 34.
tf ] y D. 36. t? (pr.)] g D.
^; (alt.)] t D. 44. ttf] tf B.
tg D. 48. 8 (sec.)] t<? D.52. o (sept.)]
Infra add. A:
slclv ovta)$
]
pfr\ in ras. Dom. BCD
tf.
Gvvta&i8V TW F
A /I /I Xl
J Z i;
392 KAATAIOT IITOAEMAIOT
f
O6axis ovv eav jtQOcuQcbiis&K T^V did
TOV xavoviov iprjcpoyoQiav Trig G
7tonq6a6&ai , ka(l6vTs ra XKTK TOV vnoxijLvov v
5 'Aks^avSQsCa IQQVOV [isGcc M,vij[iccTa xi\<s
xovs rs xal aito%fis xal avo^icc^ias xccl
xbv vitodedsiynevov rgonov rbv 6vva%ftvra
xilS dito%iis aQi&iibv SntKuGiaGuwtts itdvxoTS xccl dcps-
k6vT, lav %K>yiV, KVKkoV ffawsyXOVTSS T tg TO T^g
10 civcopaMccs XKVOVLOV Tag yfaQccKi^ivas CCVTG) [loiQccg V
X& y' 6kldiG) TOV {liV CCQi&lLOV TOV
COg ^t ILOLQ&V OVTOg
an avT&v, nal TOV yv6^vov15 aQi&yibv i00L6o^iv lg TO ai)TO xccvoviov xal xr\v
vr]v CCVTG) 3iQo6&acpcciQ6iv v
Xttl Ti TO 7taQaKlllVOV V TG) 7t{JL7CTG)
o^^cc %&$. [iTK df TCCVTCC xccl
TOV ddi3tha6i,a6tivov T^S u>
20 Vyx6vT$ ig TO, avTa ^fAtdt9
otia av
Ct VT(JJ
XTG) ^fAtdtOJ, TO, TOGKVTCC
ov
1. -91
'
i/>rjqpog?o()tae] om. D. 2. ECCV] s- in ras. D 2.
om. C. 3. ffffojvtajtTfc] -t- in ras. 2 litt. D. 4. TO] om. D.
8. Supra aq>l.6vTt$ add. avf^o^t D 2. 9. xvxAov iccv f'^co-
ptv D. Tf] supra scr. D 2. 10. {LOLQCCS iv] corr. ex ph D 2
.
11. ajH-ttyiotJ] -<&- in ras. D 2. 14. ywoptvov D. 16. rs-
taQTO)] 4 BC. 17. jrf'fiTTTw] f^BCD. 18. ctTtoyQaitxaufd'a D,sed corr. 20. a.v\ tdv D. na^d-Ativxcn D. 21. 'HTCO] zBD. TO] corr. ex TO C 2
,om. D. 22. anfyQai^d^.ed'd] a-
niut. in I- B 8. 7tQoc&rjCo^tv\ A 4
, Tt^oc^r'jOo^lv A.
MA0HMATIKH2 2TNTASE&S E'. 393
Gopsv ccisl ry xr$&6ipfrfl rov d' Gskidiov JtQ00&a(p-
aiQG(, xai rag 6vva%&i0Kg ^LOLQCCQ^ lav [iV 6 rfjg
dnb rObv rov ntfxovg xal r&v rov
OIQ&V, sav d5
VJISQ rag oft, 7too6d'^&o^,V ccv- 5
rats. x<*l rGbv ysvo^ievcov CCOI&[IGJV rov jilv rov [itj-
xovs Ixfiahovrss ano rijg xara rr\v jto%rjv
oitov av Karakrferi, Xt rqv 6Atjvr]
s, rov $ rov ithdrovs rov Kitb rov fiogziov
L6oi60[iv LQ rb avrb xavoviov, xai, otiai 10
av <b6iv a 7iaoaxi[jivai avrco iiotoai, v rd5' 6-
Atdto) rov jthdrovs-) rodavrag ay^su rov did ii6ovr&v ^(pdi&v rb Kevrgov ri\g 6eA.ijvr]$ 7tl rov did r&v
xoAcov avrov yoacpo^vov iisyitirov Kvxkov^ xal fdv
[ilv 6 d6tvrp>y\LivQ dQt,&[ibg v rolg ng&roLs f T 15
(m'%ot, &g nobs rag aoxrovg, av d' v rotg V7t
avrovg, cog Jtobg ^o'rj^oiav^ rov plv itgarov r&v
idiov 7iQi%ovrog rr\v dit aoxr&v 7tgbg
iav avrijg itdoodov, rov dl dvroov rr\v ccnb
iag Ttobg rag ccoxrovg. 20
1. &tt D. d'] TtraQTov C. 2. 6] r\v 6 D. 3. [ioi-
(corr. ex 9v D 2) D.
rf\om. D. 5. Q7t\ -n e corr. D 2
.
r. D 2.BC. 7. ly.dM.ovT$ D, corr. D 2. Post
del. TO D 2. 11. ^'] corr. ex D 2
. 14. %ca] comp. ins. D 2.
15. ^] j] AC, om. B. Is] in ras. D. 16. Post Gfi%oigadd. OTL pr]dv a^iokoyov if
1
Iv xcci$ Gvvyiaig tbv tv.%- xf]g 6t-
l-r}vr\s v.vD, del. D 2
. 17. KVTOVS] corr. ex aviots D 2. 19.
tr\v] om. D.
394 KAATAIOT IJTOAEMAIOT
i. "On, ntjdlv d^iohoyov yivsrui diayogov sv
ralg 6vwyiai,g itaga rov exxevrgov rijg
xvxkov.
dxoA.ovd'ov i6uv ditiTaGai Tivdg,
5 xal Ttsgl rag Gvvodovg xal rag jtavGehrjvovg xal Tag
v ravraig fafotyetg a%Moy6$ XL$ diayoQK TtccQaxo-
xal dia rbv SKXSVTQOV rijs GsAtjvrjs nvxkov
TtavTore xal xdvros &v avratg lit avrov rov
TO xwrgov rov STtMvxAov rvy%aviv,10 AAa xal acpsGxavai, avrov 7teQi<pBQeiav Cxavrjv dvva-
tiftai dice rb rag [isv xar' avrb rb dndysiov &6is sv
rats [i6G)$ &a)QOviLvais 6vvytai,s aitorzhBiG&ai, tag
<f axQifais Gvvodovg xal 7tav6htfvov$ psta rijs xar-
QOV rcbv qxhtcw dv&iiaMas ^a^dv^^ai15 7taga6Tij6at, rr^v roiavrriv diacpogav [ir]d[iiav
auaQtiav itZQl ra yaivopEva xara rag 6vvyiag dvva-
\nivr\v a7tQ'yd6a6d'ai, xav py 6vv7ti2.o'y%r]Tai, rb Ttaga
rr\v xxvrQorrira rov xvxhov diacpoQOv.
6rc3 yap 6 XXVTQog T^g 6&nvn$ xvxhog b ABT20 7CQl X8VTQOV TO Z/ Xal did^lTQOV TJJV A AT, (p ^g
i
C3 TO {lev rov dia indtiwv r&v tydicov XSVTQOV
1. t'] BC, mg. A 4, rj mg. D. on 3. XVK^OV] mg.
superiore et mg. exteriore D 2. 4. 7m'] corr. ex inl C 2
.
SGTIV~] comp. B, -v del. D 2. 5. tag (sec.)] om. CD. nav-
nccv(['
D, ut saepius. 6. cc^Loloyos] corr. ex &io-C 2
. nccQd'nolovd'iJGei C. 7. Supra did scr. TT" D 2.
8. sv\ A 1
, f|v A. 9. ccTcoysiovraTov D, sed corr. 10.
8i8oG&ai C,radd. D 2 et mg.
v^'dod^at. 16. v-
s
D. 20. y.tvrQoiv D, corr. D 2. dtafUT^ov] dta D, *Q
add. D 2. Jz/FJ mut. in AEP D 2
. 21. stlriiiy&co D,corr. D 2
.
MA0HMATIKHS STNTASESiH E'. 395
TO E 0r)lltOV, TO <f (XVTlXl'lLVOV T& Z/ Tijg
xoo<5vv0G)g 6r]ptov xaTa TO Z, xal en
^ CCTtO TOV A K1tOyLOV
AB 1tQKpQLCt
[iw 7tgl TO B o H0KA 5
ds ^ T B4 xul1}HBKE
Kdl tinrjBAZ.
itd rouvvv Kara dvo
rQOTtovg dvvarcct, diacpQi,v 10
TO TtCCQK TfjV KVG)ILCtMaV
KKTCC TO ATOV 1tlXVXOV i T TO
CCVTOV yivopsvov ps^ova. Ttgbg rc5 E ywvCav a
ncci dia TO tv\v itQ6<5vv<5i,v Tijg XCCTK TO {i6ov 15
Kttl TtBQiyeiOV dlCC[lTQO
XSVTQOV, odha Ttgbg TO Z 6rj[itov yi
$ 6VVl6TaTCU TO [lV TtCCQCi TYJV 7CQG)Tr]V CCiTLKV SlK-
,OTCCV Kcd TO TtccQcc T^V civo^a^Cav T^g 6Avjvr}g
TO d XCCTa Ti]V dVTQKV) OTCCV 7tQl TO 20
aitoyuov i) TO TtegCyMOv rj ffs^vrj $ TOV STtMvxkov,
drjAov, OTL, OTav plv TO naga xty it^x^v afaiav did-
(pogov nfalGTOv GvyLfiaivri, TOTS TO ply nccQa TYJV
dVTQccv avfitaiG&rjTov b'GTai itavTfh&g dice TO Tyv61tl T&V (CCltTOlVG)V Vd"L(X)V OVGCtV TOV 25
1. atyittfav] c D, ut saepius. rc5 //] root Cj D. 2. ccno-
,-tC- e corr., D; ft del. D 2
. 3. A] supra scr. D 2.
5. H&KA} H&KA D, ut uidetur. 6. la&tncW] om. C.
8. ^rt] -i postea ins. A, corr. ex ianv D. 14. TW] TO D.
16. itQCysiov\ -v e corr. D. E] corr. ex IH D. 20. 77]
corr. ex r\v D 2. 21. TO] om. D. rj] T\V TJ D, j TJ
D 2.
om. D. 22. Supra alriccv add. ccvcapKMccv D 2. 23.
D, corr. D 2. 25. OVGCCV] corr. ex OVGK C a
.
396 KAATAIOT I1TOAEMAIOT
ddidtpooov
dvvarbv d'
isvsyxetv 6vvcc[iq)OTQoi,s rots ftccoa rr\v uvw-
dicccpooois excctsQov r&v tpcorov rov (ikv nark
5 TCQOti&SGLV OVTQg) TOV df KO.X CCCpKiQEGlV, OTKV ds rb
xccza rr\v dsvTQccv rb
TtteiGTov (Sv^aivri^ tore TO plv naga xi]v
ndhiv dveTtafad'rjTOv ittiv dia rb xal o'Aov rb
rr\v dvo^ah'ccv ^ ^dfv 7} ^K%V TtavrdxaGt,
10 rr\g 6ehtjvr]$ Ttegi rb anoyeiov T)rb Ttsyfysiov rov
xvxhov rvy%avov6r] ,diofasi d'
r\
rfjs [isG&s &G)aov[ivr]g {IOVGJ TK> itaoa rqv
drj 6 yikv ijAiog TTJV
15 7tot,oviivos T&V ^ wy yioiQ&v, f)ds 0^tjvrj na&rov
xal avrri rrjv ntefarrjv dcpaiQtfw itoiov[ivr] r&v cc
v, Iva xalYJvnb AEB y&vi'a rag 6vva[i(porQK>v
d IIOLQ&V dinka.6iova$ itai%r] idjiZ??,
xccl u.%-
ditb rov E g)K7Cro^vrjs rov rtixvxkov rijg
20 E 7t&v%&G) riB0 xdfaros [Eucl. III
7 18], xal hi
dxb rov d 7il rr^v BE xd&rog %%&(*) v\4M.
iti ovv r\VTtb AEB ycovi'cc, OLWV psv zltiiv ai
d oa&al r^ rowvr&v 6rlv id ft^, otcov $' ai /3
roiovr&v x-91 Ag civ xal i
1. adidcpoQov] supra scr. D, corr. ex SidrpoQov C 2. 5. XT']
mut. in y.ctxa D 2. 6. TO] om. D. 7. av/ji^ccLVfL D, corr. D 2
.
TO] supra scr. D 2. 8. Ttdliv] -iv in ras. D. IGXIV\ comp. B,
i'cTKi D, ~ supra scr. D 2. 9. nuvrdnaaiv BC. 10. ccnoytwv] -e-
e corr. in scrib. A. nsQiysiov] -I- postea ins. A. 11. d']ds D. 12. T&5] TO C. 18. TtfQi^i C. 21. JM] post ^ras1 l litt. D. 23. amV] comp. B, -v del. D 2
._ttd] D 2
,
T| 8 D. d'] tf D, ^g D 2. p] 8vo C, corr. ex Zp' D. 24.
itrj p. 397, 1. icxiv] supra scr. D 2. 24. i/Jg]
?supra scr. D.
MA0HMATIKH2 STNTASE&S E'. 397
AM itSQiysQSLK roiovr&v x& Ag, o"ic3v stirlv 6
rb A'EM oQ&oy&viov xvxhog r, 17d* art r?\
TWV Aowr&v [Eucl. Ill, 31] sis rb f)(it>xvxfaov ~QV nd'
xal rbv vx avrag agcc sv&ei&vi\ psv AM roiovrwv
ftircti A Ad, oicov ztirlvfj4E vttorstvovGa ^%, ^ ds 5
EM robv avrobv (>tg a. w^rf xat, ot'ov l<5rlvi\ per 4E
pera^v tcbv XSVVQ&V I 1%-, i\ds B/l sx rov xevrgov
rov sxxevrQov fid1
jiia,roiovrcov xal
17 pav AM Utitai
ft A??, r\ds EM &(iota)g & v&. xal iicel rb aitb rijg
jBz/ ksfyccv rb cbro rijs AM jtoiei rb aitb rrjs BM 10
[Eucl. 1,47], yivsrai, xalr\ plv EM sv&sicc p& A?, fj
3s BME oA^ roiovrcov v& Ag, oi&v 0rlv xal y B@IK rov xs'vrQov rov STtixvxkov i Te. nol OICQV stirlv
CCQK ^ EB VTtoretvovGtt QX, roiovrcov xcclrj psv B@
sGrcci I A(J, 17d' at' avrij? XSQUpfysut roiov- 15
xt |^XO<?TWV g, otcov ^tfrlv 6 jrfpl rb BExvxhog r%. xal
f]vnb BE CCOK ycovia
rov ttfaitirov diatpogov rrjs avcoiiaMas, oiov [LBV sltiiv
CCL drfo oQ&al r, roiovrczv 6rai I xcd sfyxoGrcov g,
OLCQV (f ai d OQ&ccl r|, rowvrcw f y avrl f a rcbv 20
1. 6 2. T] supra scr. in ras. D 2. 2. z^EM] ^M D.
ot'oov fffrlv KQK onfQ (coir, in 6 nsQL D 2) TO z/EM dpO'o-
ycovtov xvxZog T| TOIOVTCOV Grlv rj snl tfjs dM v.& kz r] D.3. koinwv] civraiv B. ^fUKViAtov] r\- corr. ex JV in scrib. A.
QV V. 5. I] e corr. D 2. 6. EM] ME B. 7.
i|
A 1, > A. 8. W>r0ov] - in ras. 2
litt.^D. z/M] e
corr. D 2. 9. inti to] supra scr. D 2
. 11. per BM EV&SIO]in ras. D. 12. BME] -M- corr. ex E in scrib. D. <mV]comp. B. V.KL] om. D. 14. B0] corr. ex X@ A 4
. 16.
neu] comp. supra scr. in ras. D 2. s^v.oGrmv'] comp. e corr. D.
?] corr. ex xat D 2. 19. dvo] BD. T] 5e>ta corr. ex
%at D 2,T supra scr. ncti s^-noar&v] e corr. D 2
. 5] corr.
ex y.cti D 2.
398 KAATAIOT HTOAEMAIOT
Kara rb A aitoysiov fivrog rov
dir)V'yKv aoa naoa ravryv rv\v alriav rb icaoa rfjv
didcpogov %r]Ko6rots dvtilv
$ dvvarai [nag cooa
5 Ttdfav vTtoxefa&G) xara rb A psdov 7tQi /
yt,ovf
iva drikovon ^ vno AEB yovia rag
d w,10 Kal fai&vx&eforjs nl
rfjs biotas Karayga-
(pi]<S rfjs EA v&iasKd&roi, rjx&coGav ITCI
rrjv BE ano [iv rov A15 ^ AN, aifb d% rov z/
^ z/M, JTO $ rov Z7il rqv BE K^^d-l-
<5av f)Z &. Kara ravra
dJJ rOLS H>7tQ06&V , 7tldlJ7tQ fj 7COOS t& E20 oiav [iv ffaiv ai d oo&al T|, roiovr&v 6rlv d jig,
oiwv d' at dvo uQ&al r$, roiovrcov & A/3, iv av
Kal ai [iv (p' xaroas [Eucl. I, 15] rcbv 4M Kal
Z& 7tQi,(pQi,ai, roiovr&v -O1
A/3, OLOJV sfalv OL 7tol
ra E4M KOI EZS oa&ovavLa KVK^OL r- ai d' la?
1. A] supra scr. D 2. 3.. Svci B, (3
D. 4. tg'] TABC. 5. A\ supra scr. D 2
. 7. nsQis^si D. 11.
seq. ras. C, -x- corr. ex i D 2. 13. Inl rijv BE
D. 14. BE] B BC, corr. C 2. 15. anb ds rov 4
z/M] A, om. BCD. 17. sni rrtv BE] A, om. BCD. Ix-
ri&ttou. B. 18. ra CCVTK D. 20. iorlv\ comp. B, om. D.22. MCCTCCTSQUS C. xt (alt.)] om. D. 24_>tat
/
]om. D.
xvxioi] *v D. ^|] ^" AIA TO ICHN 6INAI THN A TH Z D,corr. D 2
.
MA0HMATIKHS ZTNTASE&S E'. 399
xarQccg r&v EM xal E& r&v hoLit&v [Eucl. Ill, 31]
SIS ttt yilMVXA.LCC O MJ. XCCL T&V V7t aVTCCQ CCOCC
v&i,G)V xaroa [iv r&v AM. xal Z& roiovrcov
& vrj, oi&v 0rlv xarQcc r&v AE xal EZvovti&v QX, xccrQa de r&v ME xal EH v&i&v r&v 5
avt&v QI& Af tiers xai, oi&v <5rlv XCCTQCC [ilv
xal EZ v&iG)v I i&, 17db dR x rov
JLt^, 0TCCL Xttl XarQtt [lV TG)V
O va, XKTQCC ^ TGJV ME XCil
T&V avrcbv I t. xal 7td rb aito rifc BJ tetyav rb 10
onto rijs AM 7toil rb dnb rij? BM [Eucl. I, 47], 0rca
xcclrjBM ^YIKBL rcbv ccvr&v fyyiGtcc ft-9
1
f
xalfj iilv BE V&IK forai v& vrj, r\ de B&
roiovrov o tf, otov ncclrj Z3 f)v o we. dt,a ta avrcc
$ xcclfjBZ v7tOTivov6cc t&v facw fyyitircc ztirai, o 15
l. XCCi 6tl,V, fog fjBZ 7CQOS XCtTQKV tG)V Z& Xttl
jB^, ovt&s f)BA agog xccrQccv rcov AN xal BN
[Eucl. VI, 4]* &Gre xcci, OL&V 6rlv r\ (ilv BA X rov
XWTQOV rov 7tixvxA,ov ^ If, fjd% BE Idffy&vj v& vri,
roiovrov xccl ^ [isv AN h'Grai o d, ^ d BN r&v 20
syyutira tf, Aot^T) dfjNE roiovrcov vd jZj>?
1. >tat] om. D. 3. %ai Z&~] coir, ex xca S'Z C, corr.
ex Z D 2. 4. z/E xat'] Ez/ D. 5. ^] seq. ras. 1 litt. D.
ME %ai\ EM D. E#] -S e corr. A. vv&si&v 7. ev-
&EiG)v] mg. D 2,
in textu TOLOVTCOV QL& P. v,ai ol'cov KQCC SGTLV
SKKTSQCC r&v 4E, EZ sv&sicav D. 7. T t-91
]in ras. D, i i& C.
~
corr. ex JA D. 8. I'ffrai] seq. ras. 1 litt. D. 9. xat (pr.)]
comp. supra scr. D 2. o] o D, o D 2
. 13. tv&sictG C, corr. C 2.
14. o] o AC. Z3] SZ D, 3- renouat. D 2. j\v\ corr.
ex T\D. 15. o] o A, 6 C. 16. rcbv 17. BN] mg. D 2
,
in textu r&v AM, END. 17. ?] -S in ras. A 1. ovrat
CD. AN] post ras. 2 litt. D. 18. BA] corr. ex BJ D\20. r] (alt.)] in ras. D. Hyyicra r&v avr&v D. 21. NE]EN B.
400 KAATAIOT nTOAEMAIOT
olcw y AN i]v o d. eitsl df dice ra TCQOXSL^SVK xccl
y] EA VTtOTivov6a ccdicccpogsl T&V KVTOJV vd\t,y,
<5vvKyTa.i, on xa^ oi&v sGrlvf\EA vTtorsi'vovGK QX,
TOIOVTOV xali] [lev AN ev&etct <STCU o
77 lyyiGru, i\
5 ^' iit avrijg 2teQiq)Qia TOIOVT&V oTJ TCCC^LV^ di&v
6rlv 6 Jtspl TO EAN oo&o'ycbviov XVK^OS r%. xali\
vitb BEA &QK y&vici, ^v dnqvyKv ^ Gs^vri naga
rrjv 7il ro Z TtQo6vv<5iv, o'icnv [iv zlo'iv ai dvo
ooftal r|, roiovrcov o ^, ol&v d' ai d oofral r|, TOIOV-
10 TCDV o d. S)0r xal v&dd TO TCCCQK rrjv avcoiiaMav
trig 6&rivr]s ditjvf'yxw %r]xo6tois d, artQ ovd' avra
7tOl,L TIVK CC^iO^OyOV K^KQTiCCV 7lQl TO, KKTK Tag 0V-
vyias (pcuvopfva [iqd' oydoov fyyitira dvvct[iV(x, i
COQKS, o6ov xal 7tK() ccvtas rag rrjQr}(3is ov
15 6ta,i, itfaovccxis dia7t<5iv.
TCCVTCC [IWTOi 7CKQ^^^CC OV% G)$ [IT} OVTOg
rov xal xgbg rag r&v Gv^wyi&v m6xilji,
xal ctvTas ravras rag dicccpOQas, xav
20 dirjiiagrrjiiwov xara rag dice r&v &utG&Si\rfvayv
VLKX&V X&fy(DV aTtodfi&ig TtttQa TO p
Tri SIK rijg xxVTQ6rr]Tog avanii^riQG)^vri dice T&V
1. AN~\ corr. ex AN D 2. xat] comp. supra scr. D 2
. 2.
tLvovGcc] -a supra scr. D 2. adicccp^QSi D, corr. D 2
. 3. 9%4. lyytara] mg. D 2
,in textu diccysQfi r&v avrwv seq. spatio
14 litt. (del. D 2) et deinde ei>9sfa %6rcci o
T\ fyyutra D. 5.
TttQupsQfia] comp. ins. D 2. n&kiv] om. D. 9. o] icrlv o D.
d'~\ Ss D. J] dvo C. TOLOVTCOV] -v ins. D 2. 10. ^]
oj A; o d D, ut saepe. 11. d] corr. ex A D 2. 14. OGOV]
D, OGOV mg. D 2. 22. avaTtsn^Qcofisv^g D, corr. D 2
.
MA0HMATIKH2 STNTAEE&S E'. 401
IK'. IIsQl r&v rr\g Gshrfvyg jt
Ta plv ovv agog rag xarahtjfaig r&v axQifl&v rrjg
tfelyvris nagodcov 7taQaha[i(lav6iiva 6%sdov ravra av
l'rj. Gvpfiaivovrog d' rti r^g Gshrfvyg xal rov ^defa&rjGiv rr\v avrr^v yivsGftui r^v (pcuvoiievyv 5
TtccQodov rr} KXQL^SL dua TO ^ 6r)[iiov Adyov
G)g (pa(isv, trpj yrp> JtQog rb KJto6rrj^iK xr\g
avrqg uvayKctiov av sty xccl axohovdov rcbv
rS aM.G)V (pKLVOHSVCOV SVSXSV KCCl llttfaGTtt t&V TtSQi
rag rov r\Mov txtefyfig ftscogoviisvcov rbv jtsgl rcbv 10
av avrilg 7toit]6a6^ac hoyov, f| cov dvvarbv
dice t&v agog rb XBVTQOV ri]g yv\ nai rov dia
r&V ^G)dlG)V KVX&OV VOOV[lVG)V CMQlfi&V TCaQO-
dov ncd rag aitb rr^g ofa&g r&v 6^oavrcov 9rovrstinv
an6 rivog smyavsiag ri\g y^g, &G)QOV[ivag diaxgivfiv 15
xal itakiv rb wavriov ajtb r&v cpaivo[iva)v rag axgi,-
felg, TtaQaxokovftovvrog d rft rouavrri 7tt,0x^i rov
Wrs rag xara ftf^og 7tr}fax6rr]Tag r&v TtaQaMd&ovavv rov do^vai rbv rov aito^rrnnarog koyov dvva-
6&ai iiQtt'yiiarsv&rivtti, ^r avrbv rbv rov aytoGrrj- 20
parog koyov avv rov So&i]vai nva
LIV r&v
1. m'] C, oi B, om. AD, # mg. D 2. TISQL
Ifojv] mg. superiors D 2,in textu
(j) OCQ supra scr. D 2. 4.
gt'rj]
supra scr. D 2. sTtt-Gv^uivovrog D. 6. T^] corr. ex xv\v D.
Aoyoi/] I- corr. ex z/ A. 10. TOV] corr. ex t&v D 2. 16.
ax(H|3erg] KKQifisig rtKQo8ov$ D. 18. Tra^aHaleoc^] -a|f- in
ras. C. 20. Ante prize add. rets t&v TtctQcdld&GJv StdoG&cuKVSV TOV &fivai rbv rov ccnoGrrJiiccros Myov D, del. D 2
. ccvrov]
supra scr. D 2. 21. rivet] rrfv D. 22. nccQcdacGovrcov C.
rovricriv} comp. B, -v del. D 2.
Ptolemaeus, ed. Heiberg. 26
402 KAATAIOT IITOAEMAIOT
afj yfj 6yiLiov Aoyov %i) ovds TOV TOV
koyov drjkovori, dvvaTOv av ydvoiTO
T&V 7ictQcckktt6<56vT(av , CQGXEQ
av [lov&g TO did TWOS
BGyg TOV rov ajto6Trj[iaTog Aoyov SVQELV dia
TO TOiavTrjv \LV TLVK TtaoaMaxTMrjv fYigrfiiv xal xatf
dvvaGdau ^atal^^vai^ Tqv ds TOV
TtrikiKorrita iiydapcbs. 6 [isv
CCTtO TOV fjkiOV lldkilSTCC TTJV TOICCVTYJV S^TttGlV
10 rpai' itidri yap 0,716 TIVCOV akk&v 7tgl TOV ijhiov
v[i{3Epr]x6Ta)V) VJIEQ (bv v Toig %ijs
TOV Adyoi/, aKokov&si TO TOV KKTO, TO
ZTEQOV T&V (p&T&v K7to6T^a.TO<s SO&EVTOS Ktti TO xctTa
TO ETEQOV dtdotf'lhu, TteiQaTCU TO TOV Y}MOV XClTCl6TO%a-
15 6[lVOS OVTC3 XCCl TO Tijg 0^tjVl^S CCTtodEMVVElV TO [lev
ttQ&TOV VJtOTl&EHSVOS TOV ijklOV TO EA(JC%l,6TOV Ccl<5d"1]TQV
liovov itctQttkkaGGEiv, Iva xal TO ajt6c>Tr][ia avTOv
[lTtt d TCCVTCC Xttl filtt T^g VlC* OVTOV
fjfattXilS K^L1^C3g^ TtOTS [lV G)S [lYjdfV ai6&r)TOV, 7tOT
20 ds xul &g ixuvbv TOV r\kiov 7taQcchkcc66ovTOs ,E'V&EV
&VTG) XKI OL koyoi TOV Tr\g 6^vrjg ccrtoGTruiaTog did-
(fOQOl, XK&' Xtt6Tr)V T&V XT^L^VCOV VnO&6K)V XCCTE-
fpCHLVOVTO di^TCC^O^VOV ItCCVTCCItClGlV TOV XCCTCC TOV ijhlOV
ov povov v TW TtoGov, aM.cc Hal si oAeog Ti
1. a] av C, S av C 2. 2. Post ttyov del. a D 2
. 8f]lov-
OTL] -j]- e corr. D. 3. TtKQakccGcovrcov A et -QK- supra scr. D.7. ncctcdriiicpd'iivai D, corr. D 2
. 10. nvcav] -i- corr. ex ft D 2.
rbv ijkiov] xr\v aelipnp D. 11. ri]v Gel.ijvr]v] xbv ijhov D.15. OVTO> D. 16. TO] supra scr. C. 17. na^ccl \
GSLV A,a.66tw D. ccvrov~\ corr. ex uvrri D. 18. itccQated'si-
D. 20. ttca] om. D. naQccid66ovTO$ D. 22. MCC-
C. 23. itu.vta.itciGiv\ -v del. D 2, comp. B. 24. 6'Acog]
ins. in lac. 3 litt. D 2. ri\ supra scr. D. TtaQcciccGGai D.
MA0HMATIKH2 STNTAEE&S E'. 403
f',ivcc [irjdsv T&V ddrjAwv slg TYJV
i ov dvvrj&ir]Hv av <bs svi [idfoGra dxoL^&g Trjorr
ai, itoGov xal KTCO 7Cr}Mxv]s rov Kara xoQvyfjv &TIO- 5
7tl Tov dia rCbv
TOV oQi&vTog xccl wvx^ *yQcc(po[ivov usyfarov
xvxkov.
7fOi^cc^v yaQ xavovag dvo TfrQccTttevgovs TO plyovx J.dG6ovas T66aQG)v 7tt]X G}V XQ<>S ^6 TKS 10
xv\v de
dia TO
K7COTTd(yd'cci Gcpodaa dxQifi&s xccl lit
xd0Tr]V T&V JCAfV()WV, JtlTa TCCCQd'yod-
zv&siug yQamias ftp' BXCCTBQOV xccTa ^0r^g Tys 15
TG) TQC3 TKtV XCC-
VOVCOV 7tl TG)V CCXQCOV d[KpOTQG)V OO&
TTQdya)vtt. 7Col [i6r]v xv\v yQK^riv i'6a T xal
kriktt OTtYjV %OV XaTQOV XttTtt TO [1<30V YIXQl,($(D[lV'Y]V
TO [lV TfQOg TTl OfySl 60[lVOV ^7CTtjVyTO $ JtQOS Tfj 20
6^VT] ll%OVCC, OVT&S &6T "JtKQKTL^S^BVOV TOV
TG)V OCpd'CC^flCOV T& TrjV ttaTTOVCC OTtfjV %O
TLG) did TYjS TOV T$OV XCil Sit* V&iaS Oltfjs Tr\V 6-
1. t/S'] mg. AC, Bt B, om. D, i ing. D 2. 7iuQal.ciy.riY.ov D.
4. ax^tpcog] -co? euan. C. 5. trotf] corr. ex Tjjg D 2. 6.
6t D. 7. TroAcov] corr. ex noMcov D, "wdicov C.
10. nri%(Qv D. 11. ftg] ins. D 2. ylvscftui D, corr. D 2
.
13. aW D. ccKQifi&s] supra scr. D 2. sit' v&si<xs~\ sv
sv&sla D, mg. xal 7t' EV&SICCS D 2. 14. ZTCEIXU] -8- corr. ex i
in scrib. A. 15. isGs corr. ex iscov D 2. 17. x&v
corr. ex TO UKQOV C. 18. nuQccllri^u} supra scr. D 2. 19.
v D, corr. D 2. 22. sldcaovu D.
26*
404 KAATAIOT I1TOAEMAIOT
OVV f| L'6OV ExdTQOV TG)V XKVOVGJV XCCTCC
rov ETEQOV r&v itEgdrov itgbg T& rv\v
e%ovn JtQt,6[iaTiG) xal VCCQ^io6Kvrg dt'
5 [i(poTEQa)v aoviov, &6r 6vvdE&i]Vtti n\v vrt' avrov
rciQ KQOS tats 'yQa^alg rcov xavov&v
VTtb xVTQOv, itSQKx.yzG&aL de dvvaG&ai, TOV ra
fyovta, 7tccvtcc%fi noil ddiaGTQoy&g, di,cc6g)rjVG)(3KVts rs
^K0i rOV TQOV TG)V XCCVOVCQV tQV[IT] %OVTCC TK
10 TtQl^lldtLK &dpo[lV 7tl Trjg XdT()OV {ifarjS y^^^S<5rj[iid nva agog rotg yfaQcc ty fiaGEi itfyaeiv TO faov
xcd on 7tA,L6rov aito rov xara rb cfeoviov
K<pe6rrix6ra xal ditto[iv rrjv acp&Q
rov rriv (Id6iv fyovrog xavovog ig [ifyrj \ xccl rovr&v
15 n fuaGroV) stg o6cc fdvvd^d'cc r^^irov avrov xavovog TCQOQ rolg
rag inl rd avra [lEgy xtevodg itgog rf]
^ 7t v&iag dMtjhaig fyovra xccl rb faov
7tttvra%6&Ev rijg avriig xal pforj
20 itgbg rb di avr&v xa&sriov XQi,iivci[ivov
rov XKVOVCC dg&bv xal drtciofyxki-Tov nobg rb rov bgi-
v
2. sxat^cov D, corr. D 2. 3. STQOV C. 4. omjv] corr.
ex olnriv A 4. $t'] ins. D 2
. 5. dftqporf'^cov] -fi- in ras. D.
6. tag] rd B. rate?] corr. ex rdg D 2. KUVOVIGW D. coffTrsp]
corr. ex eb? D 2. 7. M] om. C. 9. rd] om. D. 10.
itf,\
corr. ex TI(SQL) D 2. 11. niqccsiv] -v del. D 2
. 12. xara] xa D.
13. diskopev\ -I- in ras. D 2. dqpo^to/Lt^rjv C. 14. ft^rj]
ftf- in ras. A. 15. oca idvvd^8&a] -a s- e corr. D. 17.
TtQiGfiKTiu] ante -a ras. D. 18. TO] rov C. 19. navra^oO'sv]corr. ex navra^ors D 2
. 23. TtQo8iK^lj]^vr\v C. 710:9-*
in ras. D, ^ D 2,corr. mg. D a
.
MA0HMATIKH2 STNTABESS E'. 405
rco rov OQi^ovrog iiti nvog avfrtiGxoTrJTOv %COQIOV
LGTapfv TO ooyavov OQ&OV, &6T rag ntevQag rcbv
xavov&v, xa& ag yvcovrai, aMrjhoig vitb rov aJoWbu,
TtQog [LftirjiipQfav TSTQatp&ai xaaaMtfAovg yivo[ivag
rf] 7taaaxi[ivr] nsGrjppawfi yQa^firj xal rov psv tv\v 5
ficcGiv %ovra xavova OQ&OV axAiv&s
k'n T adyaA&g 6rdvat,, rov d
i TO a%6viov v T& rov
"IJKa[lV $ Xai TQOVVd"V 7tQ00rj0^06^VOV ^,V VXV 10
rov xal avTo X&QMyetfd'at nQOVicp figu%Z xara rov
rfi (Id6i nfyaTog T^g di^rj^v^g y^a^^ijg,
Ti}g 7tA.i6Tr)g TtagacpOQag rov rb
i'Gov atp0TG)Tog 7toaTog r^g rov TQOV xavovog
^&6T dvvaGd-ai 6viiitQia'y6[ivov avrm TO 15
v TCOV dvo MQCCTCOV yivQptvQv 7t
3toiov[i&a dq TOVTOV rov Tg6itov Tag rijg
Tr]Qjj<)i,g Kara rag in avTov rov ^rj^oivov xal
7tol ra TQOXixa Gy^ta rov Sia [isGcov r&v fydi&v 20
xvxhov ywoiiwag ytaoodovg^ itidr] xara rag roiavrag
6%6ig oi T dia T&V jrdAov rov bgi^ovrog xal rov
xVToov rr\g 6hijvr]g ygafpo^voi yLzyiGroi xvxhoi oi
avrol fyyiGra yivovrai rolg dia r&v itd&cov rov dia
1. TW] in ras. D 2. 3. CC^OVLOV] pr. o corr. ex i in scrib. C.
4. tTQd<pQ-<xL] corr. ex tfzdx&cci D 2. 5. iieGrmpQivy] -vy e
corr. D. 6. &v.ki,v&s] corr. ex aKQifi&s D a. 7. ST<] mut. in
iitt D 2,tni C. ri\ mut. in TO D 2
. 8. Gv^irgmg T^] -? t-
e corr. D 2. 13. itfoiGTrig] corr. ex nfavgas t^s D. rov TO
LGOV] corr. ex TOVTOIS/OV D^. 15. avvjieQiuyo^vov AC. 18.
dry] de D. 20. peGov D. gtodiov D, sed corr. 22. rooi>]
corr. ex TOV D. 24. yivovTuC] corr. ex 1^ D 2.
406 KAATAIOT IITOAEMAIOT
rcbv ^codC&v ypaqpo^aVotg, nobg ovg ai Kara
TtccQodot, r^g ^^tjvrjg ftsoaQOVvrai, KOIi\
axoi-
g atto%Yi rov Kara xoovcpfjv Gr^LSiov dia rovrov av-
5 oovTfg ovv rbv TK TtQiGyiKritt fyovru xavova Ttgbg rrjv
KKT avrag rag itl rov ^I^^QLVOV'
aiig)OTQeov rcov bncov Kara TO
rb XBVTQOV avrrlg dtOTCrfv-O'/J, Kal
7tl rov fanrov KavovCov rr\v
10 rcbv aKgcov rcbv v rolg KavoGw v%~icbi
Tfj dir]Qr]HV'fl ig ra | t[iri-
rov OQ&OV xccvovog fvofaxo^v,0rlv r^^jLccrov % -rijg itQOi,Qr][isvris dicc6rcc(5a)S v-
^fta, oi&v 0rlvf)
x rov xvroov rov vitb rijg ttQicc-
15 yoyijg yoa<po[ivov iv TG) rov ^i6ri^Qi,vo
|, KKI Aafiovrfg r^v VTCO rife
vjtorfivopwrjv 7tQi(pQi,av rccvryv
aitl%v r6r rov Kara xoovtprjv (5r^iiov
rb (paiv6[ivov nevrgov r^g G^tjvrjs ^l fov dt,a rcbv
20 sroAcoi/ rov boftovros nai avrov yaatpoiisvov
xvxhov, og 6 avrbg yivro ror xal TK> dia rcbv
rov T l<5riyiQivov xccl rov dice [isticov rcbv ^c
VXV [lV OVV TOV TJjV yiVO^VTJV KaTtt
25 Tttefarrjv TtaQodov Tijg Grjktfvrjg axQiflcog
1. (itocov] seq. ras. C, corr. ex ptaov D 2. yQcc<po[ie\ D,
corr. D 2. 3. tovrov] corr. ex TOVTO D 2
. 6. Ttccgodovc;] e
corr. D. 7. OTC&V] -n- e corr. D 2. 10. r&v (alt.)] -co- corr.
ex 01 in scrib. C. 11. Sieigrwevr) CD, corr. D 2. 13. sori D,
comp. B. 18. ani%v~] -v del. D 2. 21. og] corr. ex cos
C 2D 2. noUcov D, -II- eras., mg. I D a
. 22. re] om. D.
peoov D, corr. D 2. 25. STuyivcaGnsiv D.
MA0HMATIKHS STNTASE&S E'. 407
K T?j dlO7tTV6l, ItSQl T TO &Ql,vbv TQO-
rtixv 6r][iiov
CCVTO TO TOV Ao|ov avTr\$ xvxkov POQSIOTCCTOV
did TS TO 7tQi TCCVTCC TO. 6r][ita <JD'Lxavbv did<5Tr][itt
Tqv avTrjv Ttgbg afadyffiv XKTCC 7t2.dTos Jtdgodov cupOQi- 5
&6&ai, xal dia TO itgbg KVTG) TK> KCCTK xoQvcprjV
TOT Tr\v 0^vrjv ywopwrjv v1'
ov 7toiov[i&cc rag rt^^tfftg, rv\v
xaT2.ct[i(ldvTo df TCEQI Tag TOICCVTCCS TtaQodovg 10
KSl TO XVTQOV T^S <5kv\V1]S TOV XCCTa XOQVyrjV
xal 17' fyyitiTK ^OLQK^ &s xal X T^S TOLDCV-
pOlQ&V K7todlXVV6&at, T^V Jt&l6Tr}V
XCCTK itk&Tog f'g?' xdTQK TOV did [izG&v T&V
Ttdgodov, oGcus 6%dbv vJtQ%ov6(,v ecu ditb TOV 15
XCCTK KOQV(pi]V 6r][llOV 3tl TOV fat)pQLVOV V'
8iyiidvKi potQcct, I vij tefaovdccL TCC
ditoGTdtff&s [lotQas j$xccl rf T&V dab TOV
V Jtl TO &OIVOV TQOVtiKQV 6r][ltOV dfdMy-
3CJ/VCC. 20
VXV d TOV Hal TTJV TtQOg TCC 7tCCQCcA,A.d%l,S 7tL-
7taQTr]QOV[lV Jtd&lV XCCTd TOV CCVTOV
TQOJtOV Ti]V 0^Vr\V 7tQ\ {lV TO ^i^lQivbv TQOTtMOV
2. hi 7CQi~\ -n ittQi in ras. A. 3. ccvTfjs] om. B, suprascr. D 2
. 4. TK] ins. D 2. 6. ro5] rots rm D. 7. tors]
om. D. 10. 'AK-ctlKiLfiuvopE&ci D. 11. atei D. 12. <*rj-
A. v.a.1 (alt.)] comp. mg. D 2. rfjg TOiavrj]?} corr. ex
ocvTfjs avTfjs D. 14. ptcov D, corr. D 2. 15 OGCCL D,
corr. D 2. 17. dEdiypsvai, A, sed corr. 20. (JLOIQ&V] ft seq.
ras. 1 litt. D, ft D 2. 21. rov] supra scr. C 2
. xai xj\v\ suprascr. D 2
,corr. ex v.a.1 rov C.
408 KAATAIOT HTOAEMAIOar
6rj^lov rvy%avov6av did re ra 7tQOiQr][iva xal
rb TtkeiGrov rors avrqv aystircbGav fag litl rijs
Kara rbv {isGrjiiflQivbv Jtaoodov rov Kara K
6rj[iiov KOI rqv rtccQccMci&v [ist^ovcc xccl v6r][iavror-
5 QCCV 1taQ%lV. KTtO TtfolOVCDV dq T&V XCCTK TCCg TOl-
avzccs jtaQodovg rrrjQ^f
vcov v^atv JtaQaMd&cov pCav
TtK^iv %&rj6oiid'a) di ^g rov T TOV
VQOTIOV CC[IK 7taQCC^TtJ60^V KOI t^
.
10 ly '. 'Artodfi^ig r&v rys 6kijvr]s'
Aiyvx-
rov r^Mov xccradvviv
Jtl rov ii6r}iif$Divov yEyfvrjiiwrjv, xal cpciiVro
15 fftilv dux rov ooydvov rb %vroov avrils and%ov rov
Kara xoQvcprjv 6rj[iiov [IOLOCCS v /.' y' ifi'' rj yciQ iiti
rov fanrov xavoviov dicc6rcc6is roiovrcov r^v we /_' ifi ,
slg ola diyorjro ^ x rov xwroov rov rilg TttQiuywyvis
KVKlov 1, YI81 ryhixavrr] v&ia vnorsivzi rtQi,q)Qiav
20 roiovr&v v L' y' tf' ,OLCOV <5rlv 6 xvxhos r%. ccMa 6
dnb r&v v r& a' r
rov Kara r^v xxi,[ivrjv
KOI r^aQC3v o/3 xal coocov
5. Y.axcc.~\ not corr. in Y.CC A. 10. ty'] yt B, om. ACD,mg. A 4
,t mg. D 2
. 11. ydg] 8s B. x'] xl D, -e in ras.;% supra scr. D 2
. IVft] e corr. D 2. 13. n&ovtos C.
14.' Post SKI del. TO D 2. m^svrifuvi^ D. 18. rj] ins. D 2
.
20. TOIOVTCOV] om. D. ccU' D. 6] corr. ex oi D 2. 21.
a'] r& ici A. ?tft] e corr. D 2. NccfiovaOGov C, Nccfio-
D. %QOVO<S\ corr. ex ^90^01 D 2. 22. %*i[ivr)v A.
corr. ex slew mg. D 2.
MA0HMATIKHS STNTA5E&S E'. 409
// y\ axoificbg ds y'' ^g ov
TOV jw-fv VI^LOV svofaxopsv [is6cog fisv its%ovra
r&v Xyhcbv pOLoag A, axo^cbg ds so?, T^V (? 6s-
A.ijvyv ti6G)g 7t%ov6av To%6rov potoag xs ftd, xl
rr\v [iev ccTtoyfiv poiQcbv otj ty, rag d5
ocTtb rov petiov 5
anoyeiov rov JuxvxA.ov [lotQccg 6%p ac, rag d' ccitb rov
POQSIOV TtSQarog rov nhdrovg {loioag rvdjl. itgoGs-
ri&si ds dice ravra, xal rb TCKQCC rqv &vmptt&fav dicc-
yoQOV navraxo&ev BK rov ofastov navovog diaxgiftsv
[loioag g jcg, &g xal r^v axgiflrj rijg dehtfvrjg &S61V 10
KKr sxetvrjv r^v &QKV iiti^iv xarct fisv rb [tijxog
AlyoKSQG) iioiQccg y 7, xccra ds rb nhdrog STtl [isv rov
Ao|oi) xvx^ov ccitb rov fioostov Ttsoarog
ejtl ds rov dia rcbv nohow rov dia [is6cov rcbv
og 6 ccvrbg syyitircc i]v rors r& (L0rjpfiQivfa cforo rov 15
dia iis6G)v r&v fydiov xgbg rag aoxrovg [toiaag d v&.
ds xal KI psv rov ^[fyoxsoco [loloai y I rov
itobg (isff^fipQtav STtl rov avrov
potoag xy p& 96 ds faij(iQtvb$ rov sv
xara xoQvyrjv 6rj[isiov ngbg [isorj^oiav opoiog [loioag 20
A vij' rb aoa xsvrgov rqg 6shr}vyg a7tst%sv
aito rov xara xoov^v tiqjisiov poioag [i& JS
vsro ds attfyov noioag v ve' TtaorfMa^sv aoa % 6s-
1. /.'] corr. ex K D 2,
ut saepe. 3. Xeil&v D. Ice] e
corr. D 2. s"] ft F D, p ? D 8
. 4. Post p&fo>g ins. (iv D 2.
^] renouat. D 2. 5. d'] dt D. 6. rov (pr.)] renouat. C.
STtwvnlov] SKI- e corr. D 2. 7. rvd] -v- e corr. D 2
. 8.
diet ravrcx] mg. D 2. 9. TtKvra%6Q'sv^ supra scr. D 2
, ^_ add. A.
sx] dtoc ravra EH D. 11. ans^siv D. 13. %VHA,OV anb rov]mg. A 1
. 15. 6] om. C. 17. ctn%ov6iv'\ -v del. D 2. 20.
ojiotcog] bis D extr. et init. pag. 21. nevrgov] *.- corr. ex ain scrib. D.
410 KAATAIOT HTOAEMAIOT
rb 7tol xr\v xxst,[ievr)v ndoodov c
potoav a xal $)pto0cd g exl rov di avryg xal r&v
tto&cov rov OQL^ovrog yoag)o^vov {isyititov xvxhov
dit%ov6a dxQifi&g rov Kara Koovcpfjv
rovrov d^AoO'fVro? ysyQacpftcaGav sv T&
rov dia r&v nolcov rov oQ%ovrog xal rijg
[ifyiGroi, xvxhot, itQi
rb avrb xevraov 6
10 plv rijg yijs pfyiGros
6 ^5, 6 ds
ce rov Kara ryv
XEvroov
6 JTz/, Jtabg
15 ov dsr\
xal xsvroov [isv s
xowbv ndvr&v rb K,f ds 8ia r&v xara
20
dsr\
sv&staf} KATE, V
6y[iiov anfyovGa axoip&g rov xara xoovcprjv
rov P rag 7tQoxi[isvag {LOioag [1& /n^, xal
Kara r
1. V.KTO] corr. ex nccQa, D 2. corr. ex %ara D 2
. 2.
a, 3 |g D, || D 2. tov nolov D, corr. D 2
. 6. dr)Hca-
mut. in 8r] do&svzos D 2,sed rursus corr., sacpcd supra
scr. D 2. 7. xca TTJS os^vr]s] supra scr. D 2
. 8. ft^ytcrrot]
yQcerpofjitvov {i&yiGTOv D, sed [isyioTov corr. in [ityiGroi. %vxiot]corr. ex xvxZov D. Deinde rep. CCTC^OVGK lin. 4 Y.VY.IOI D (utin textu, 5 /Zrj eras., 6 TOVTOV, add. D 2
,7 TrdHoov, corr. D 2
).
16. EZH0] -Z- e corr. D. 21. rj (pr.)] corr. ex N in
scrib. A. ds~\ om. C. //] corr. ex A A4.
MA0HMATIKHS ZTNTASE&S E'. 411
tfTS K4H xccl y Ad, xal ti aitb tov A,
o ywstau oi^ig t&v QQ&VXMV, xcc&ftog psv TJX&G) sitl
tyv KB r)A A, TtaQaU^og dl trj KH ij
AZ.on [iv ovv trjv H TtSQicpEQSiav tolg cbro rov A
Vr\ Gshrjvr}, tpavsQOV ci)6t sty av 5
xal e^rjxoGrcbv f rcbv sx rijs rrjQiJGs&s
7ti dl ttdiayOQO) ^i^G)V <3TIV fjZ
itQicpQt,a rrls H dux to rrjv yv\v oAyv Gqufiov Ad-
yov %iv Jtgbs tbv EZH xvxAov, elti av xal ^
ZH@ 7tQl,(pQl,CC TG)V ttVT&V SyyitiTO, K f. CO0TS Xal 10
^ vjcb ZA& y&viK dice TO it&Kiv adicccpoQtv to Atov xwtQov XQOS tbv Z@ xvxkov, oi&v pw
cci d oQ&ccl r|, toiovt&v 6tlv a ^, olov d3
cd
toiovtwv/3 id. tcov d* avt&v 6tiv xccl
rj fay [Eucl. I, 29] avtf] ycovia ^ vnb AdA ftid' xul 15
fj jlV 7tl tils -dd P^ V^ICCS 7COl(pOlCC XOlOVtOV
6tlV ^ td, OLCW 3lQl tb A /IA OQ&O'ycbviOV XVX&OS
TJj, KVtrj drj AA V&ICC tOlOVtOV ft HOC, OIG)V <3tlv
$1Azl vitotivov6a [Eucl. III
? 31] ^K. tcivtr^g d ddicc-
<pOQG) Ad660)V 6tlVfjAd" KCU, OIG3V &QO, SGtlv
f} 20
AA v&ta sea toiovtcov 6tlv j Ad v%-i<x, X
3. Tra^aHrj^og] oc D, HOG D 2. 6. [ioiQag] ft supra
scr. D, jJ D 2. efrnoGtav f] |J D, if ^ D 2
. 7. ccduxcpoqa)]
a- e corr. D 2. ^eL^cov] mg. D 2
,M. D. 8. rfjs] corr. ex 1% D 2
.
10. ZH0] Z D. eyyiotu] -a. postea ins. A. a} p a D.11. ZA@] corr. ex AZ D 2
. 12. Z] mut. in ZH D 2.
13. roiovrcov 14. rf] supra scr. D 2. 13. $'] Se D. 14.
(pr.)] dvo C. <T] de D. IGTW] comp^B,^ -v del. D 2.
15. rj (pr.)] ins. C 2. AzJA
~\corr. ex ^ 1$ D 2
. 16.
&QK\ comp. supra scr. D. 17. fartV] comp. B, -v del. D 2.
19. Jz/] corr. ex AA D 2. 20. iorlv ilaGccov D, deinde
supra add. 7? D 2. ylzf] AA D. xat 21. ^1^] supra scr. D 2
.
21. ^ ^yl D. AJ AA D.
412 KAATAIOT HTOAEMAIOT
lift jit??, el'rjav not
rjvnb TKA y&via agog TG> XWTQGJ
ovtia TOV xvxhov, otW pv efaiv ai d oa&al T|, roiov-
TCW ftO1
/Lt??,oi&v d' CCL dvo ood'al T|, TOLOVT&V 9^ Ag
5 &6te xcclfj [isv ETtl rils AA sv&stag jtsgicpeQeiK roiov-
rcov 0tiv 90- AST, oicov 6 Ttegi rb AAK OQ&o'yKtviov xvx-
Aoff r, % & sal rife AK r&v tout&v [Eucl. Ill, 31] etg
TO YllLMVKklOV ft xd. XCcl TG)V VTtOTSlVOVGcbV CCQCt KVTCCQ
SV&SLtyV fj [lV AA k'tiXtti TOIOVT&V 9 A-91
,OLC3V 0TLV
10fjAK vitorswovda ^x, ^ df AK T&V CCVT&V o x' foGts
XKI, OLOV vos itinv17AK x TOV KWTQOV r^g yi}s, roi-
ovrcov nalv\ [iv AA k'tixai o ^tg, ^ df KA Oftotog o A-9-.
QX' XCCL OLCOV CCQCC <5rlv flAA V&iCC O ^tSj TOIQV-
15 tov 6tca xali]A/I v&la k& g. r&v d' avr&v i\v xal
KA v&ta o A#, fjd KA x TOV XVTOOV
svos' xal OLOV aoa 6tlvf)KA x TOV xw-
TOOV Ti}s yrls fii/dg, TOWVT&V etirai xalfjKAd oAiy,
7tQi%ov<5a df TO xaTa T^V TtforjGiv rijjg 6^vri$ an6-
20 ^T^fta, A-9- p~.
TOVTOV dfdfiyilWOV 6TCO 6 TijS 6&tjVr]S XXVTOOSo ABF itol xdvTQOv TO z/ xal dtdfiToov Tr\v
TO iv TOV dt
4. dvo] JJBD. 6. 6 Tif^t] corr. ex OTT^ D.
AAK D.'
11. ^4X] -K e corr. D. Supra .KSVZQOV add.
o^ffa D 2. 13. 7]v] ins. D 2
. J^i] corr. ex AA D 2. Ante
rj (alt.) del. fa D 2. ^^stxro] add. D 2
. 14. o] o D, o D 2.
16. efoeC D, tt&tl D 2. o] corr. ex o D 2
. KA] -Arenouat. D 2
. 17. xat] corr. ex gat D 2. a^a] comp. reno-
uat. D 2. SGTL'V] & D, i-
D 2, mg. icri D 2
. 18. xat] x? corr.
ex % D 8. 61?]] corr. ex o D 2
. 19. TT)S] T- corr. ex rjin
scrib. C. 21. ta mg. D. eMfvtQos] ZKHSV- in ras. D.
MA0HMATIKHS STNTABESiS E'. 413
xvxkov XWTQOV TO E, TO
tov eitwvxhov Grjiieiov rb Z, xal ygcupevtog
B 6rtov TOV HKA
HB@E xccl xcclj\ BKZ, v
XCCTCC TO AV Oil AE KCll
7ti TYJV BE aito ply TOV
4M, catb dl TOV Z % ZN.7Ci TOiVVV XCCTtt. TOV %QOVOV
- 10
rj [ilv vyfb AEB y&via, of
icov ffalv ai d ogftcci
T%, TOLOVT&V QV$ X$, XCCTQCC [Eucl. I? 15] $ T&V VltO
ZEN KKI AEM T&V nlv kont&v si<s TK$ dvo OQ&ag ny
3. &uxvx;iov] s 'tf D,*
supra add. D 2. 4. EA\ JB B,
-z/ corr. ex ^f D 2. xca (alt.)] corr. ex v. D 2
. 6. d' ij^co-
GCCV] 8iij%Q'a)6Kv C, corr. ex S' &%&a)6ctv D 2. 7. xM,7j'9'M>av]
corr. ex iv.fiKrift'EiGK C 2, eMp/Lrj^frcra B, ante djrd coll. Halma;
puto delendum esse. 8. ZN] -N e corr. D 2. 10. rd] supra
scr. D 2. 13. dvo] mut. in J A 4
,D.
414 KAATAIOT IITOAEMAIOT
Ad, oi&v d' efalv ai dvo dgftal T, TOIOVT&V
G)6T xalfj {lev (p' xaTQag T&V AM xal ZN
<pQia TOLOVT&V h'tiTai[i 77, oi&v sfalv OL Jtsgl tec
xxiyiva QQ&o'y&via xvxkoi T, dice TO ttivfv slvai TV\V
5 AE TT} EZ, ^ d' scp' exareQccs rcbv EM KOI EN rcbv
avrcbv ghp vfi [Eucl. Ill, 31]. xal r&v viC ccvrccg CCQCC
sv&si&v fxaTSQa plv r&v AM xal ZN toiovx&v 6rlv
[l V-0", ol&V BKttrtQK TK)V AE XCti EZ V7tOTlVOV6&V
QX, xarQa df t&v EM xal EN rwv ocvr&v ^7 o-
10 G)<5t Kcti, oicov iGxiv xarQcc [iv rcjv AExcel EZ fv&fi&v
I #, ^ dl AB x rov xevrgov rov XXVTQOV n& jita,
Toiovr&v xccl exarfyct plv r&v AM xal ZN 6rai dy,
xccrQK df r&v EM xal EN t&v avr&v & x%. xccl
7tl to ccTtb rijg B^J fafyav TO cbro r^g AM 7toii
15 TO artb rijs BM TfTQcc'ycavov [Eucl. I, 47], |o ku.i/ xccl
tr\v pev BM ohrjv ^xi toov avr&v [ifr Aa, rrjv $
BE 0[ioiG)g fi d, Aotjr^v $ rfjv BN roiovrav A A^,
xcclfjZN ^v d
rj.xal itd ra ait avr&v 6vv-
TtOLSi TO (XTtb Ti]S BZ [Eucl. I, 47], %0[1V20 xal Trjv BZ tiitoTfivovtiav ^njxft, T&V avToov A vd~
&6TS xaC, OLCOV tirlvY}BZ vitOTeivovtia QX, TOLOVT&V
xal $ plv ZN k'tiTai 7g ^, YJd' it avrr\<s itQi,(pQi,a
TOLOVTCOV l XCC, OLOV 0rlv 6 7C()l TO BZN OQ&O-
xvxhos T%. xalrj
vitb ZBN aga yMvia^ OLCOV
1. dvo] BE.TJ] ins. D 2
. 3. mu] A D, ^ D 2. 4. T|]
corr. ex rov D 2. 5. tf'] Ss D. 7. eWv] comp. B, -v del. D 2
.
8. z/E] corr. ex AE D 2. 9. o] 6 ABCD 2
,& D, o mg. D 2
.
11. T i&] corr. ex ~H& D 2. 12. piv 13. exar^a] supra
scr. D. 12. ML(alt.)]_ins.
D 2. n;cu] ^_D. 16. ^ let]
in ras. D. 17. ji <?] ^ AD, corr. D 2, ^' A 4
. 18. ZN]NZ D.
22.^1D 2
, |f D. 23. Is] corr. ex ? B 3C 2,
-f ecorr. D 2
. xor] corr. ex v.1 D 2. 24. ZBN] -B- e corr. D.
MA0HMATIKHS STNTASE&S E'. 415
ftfV eltiiv ecu dvo QQ&al rj, roiovr&v ttfrlv i xa, oi&v
d' aC d oo&al T, roLovrcov p, syyttfra. roGovr&v
aocc [loio&v <5nvf)@K rov faixvxAov
jra/Uv, 7tidrj xccra rov %govov r
yzv v\ GeAtjvr] rov {lev [i86ov anoyeiov rov sjuxvxhov 5
[loioccg tf/3 x, rov ds K rov ptGov 7tQiyiov rag
Aoiitas dri^ovori [ira rb fyuarthilUov [loigag 7t{$ x,
6X0.1 Kal % plv KA 7tQl(pQLK [LOlQGbV Ttfi X, V]$
KA o/l^ iioiQ&v 9 o- dofrrj aoa <5rlvi\
vnb @BAyCDVlCC. KH5r fast, OIG)V 0riV
f} plv 4B X rOV XV- 10
roov rov MCvroov n& fta, ^ d BA in rov xvroov
rov 7tMvxA.ov f t, roiovrov xali\EB ddixro ji
xal %r]xo6rG)v d, ra d' ait avrwv Gvvr&zvra 7toit rb
aitQ rr\$ EA rfrodycovov [Eucl. I7 47], s^o^v xal rr\v
EA \IV\KBI r&v avr&v jl M-. rb ccoa xarcc rrp> njorjGiv 15
rijjg 6kijvy$ rouovrov 6rlv ^L x, olcov xal
BA x rov xvr()ov rov faiKVK^ov vitoxeirai
f]df EA
i] ccTtb rov xwroov rijg yv\ iiti rb
rov %%vroov |, r\d EF
i\ccitb rov xvroov
n*< to ^^Cy^ov rov fxxwroov h& xft. tiMa 20
rb xarcc rqv nrJQrjGiv rijg 6&ijvysrovrdtinv r EA v^ta rouovr&v A-9
1
t oiov
1. dvo~] B B. f'orrtV] comp. B, -v del. D 2. 4.
corr. ex fast D 2. 5. Supra unoysiov add. tag loncds D 2
,
sed del. 6. op] corr. ex 5^" D. rov (alt.)] om. D. 8.
IWca] & D, \ D 2,
sarca mg. D 2. 9. &EA] supra scr. C 2
,
AB C. 10. >' D.rj] e corr. post ras. 2
litt^D 2
. 11.
TOV iv.v.ivTQOv\ mg. D 2. 13. ^Tjxotfroov] || BD 2
, |"7D. 16.
iavtv] comp. B, -v del. D 2. 17. rov v.^rpov] mg. D a
. 18. E^4
^] C 2D, fa?] AC, EJ seq. ras. 1 litt. B. 19. fcxeVifOv]
D 2, mg. sxxg'D*. x^ov] D 2
, comp. D. 20.
ax- D, Ix-x- D 2.
416 KAATAIOT HTOAEMAIOT
vbg f)x rov xvroov rf}g y^S' xal dicsv ago. 6rlv
YI [lev EA v&ta rov xard rqv rtjorjaiv ty
a7to6rrj^arog A-91
ji, ^ (f x rov xwraov rfjg
roiovrov h'tirou xal % [isv EA sv&slK rov xara rag
5 GvZwyiccs psGov anoGrrjiiaros vO1
o, ^ df EF rov xara
rag di%or6{iovs [istiov uTtoGriJiiccros Ay fty, ^ ^' tx
rov xsvroov rov 7UxvxAov r&v avr&v i'
d' fip.lv Kara rov sxre&siiis'vov raonov
10 r&v rils GsAijvys ditoGrrjiidr&v axoAov&ov avel'rj
xal
rb rov i\Mov Gvvartodstt.ai, Jtao%iaov xal rov roiov-
rov yivopdvov dia rcbv 'yQa^&v^ i TtaoGdo&ffev rolg
xara rag 6v%wyia rijg GfAtjvrjs d7to6rtj^a6i,v ai
Koryrs r&v v avralg GvviGraiiw&v ytobg rf}
15 y&vicov vito r rcbv dia^ra&v ^Atov xal 6^tjvrjg xal
6xi ag.
id'. Ilfol ryg nyhixoriqrog r&v ev ratg Gv^vytaigxal GsA.vr xal
20 T&v drj Jtobg rrjv roiavrrjv i7ti6Xfyiv Zcpodcov rag
kufv aAAag, o6ai di vdQop,rQiG)v r)
r&v xard rag l<5r\-
u,aivag avarohag %a6vcov doxovGi, rrjv r&v gx&rcov
xarajiErorjO'iV) 7tao^rrj6a^d'a dia rb pr} vying
dia r&v roiovrcov rb itQoxipvov Aapfldvs-
2. Gkri\GeJ(.rjv7]s A. 3. rov xaVr^ov] corr. ex TO * D 2. 4.
Kara] x| C, xa C 2,
V.K D. 5. Gvvgvyiccs D, corr. D 2. i"9-]
corr. ex vo D 2. o] o^ D, supra scr. D 2
. 7. K&VTQOV TOV\om. D. 11. JiUov] fyiov v.uC D, xat del. D 2
. 15. re] om. D.
17. id'] mg. AC, ~jl B, om. D. nsgl 19. ffxiag] mg.superiore D. 21. Supra ?'f
add. xcct? D 2.
MA0HMATIKHS STNTAEE&S E'. 417
, xara6xvd6avrg ds xal avrol rr\v v
vitb rovr
ljt7tdo%ov did rov rroanri%ovg xavovog
roav xal did ravrr^g itoiov[iVOi rag ytaoarrjot]6ig rrjv
plv rov yMov did^iroov VTCO rijg avr^g k'yyiGra yovtag
sx rcav ditoGrrjiidrcav ccvrov
ds rijg Gshrjvrjg rore povov xcd ccvrqv vytb ri\g avrijg
r<n Y\MG) y&viccg 2tSQi,%oiievr]v ,orav v rccig TCKV^E^-
voig rb nfyiGrov Kito^rr^aa rrjg y^g uiifyri xara rb
ov6a rov emxvxkov,xal ov% orav rb 10
dxohovd'cog ratg rcbv itgorsgcov VTto&sGsGw.
itgbg dl rovrois xccl rag y&viag avrdg at>iok6'ycp nvl
shdrrovg xttrKAaiifiavops&cc rcbv xaQadsdopsvcoV) ovxsri,
pivxoi dia rijg iv r& xavovi xara^r^0G)g tTuAo'yt,-
6[ivoi, rb roiovrov, dMa did nvoov Gfkrjviccxcbv %- 15
rb pv yaQ 7tor farjv VTtorWi, y&viccv
r&v diaperQG>V 7tQo%iQov x ryg rov xavovog
ridvvaro yivEGftai did rb iinidspiav znaxo-
7tl rov roiovrov xara^ror]6iv^ rb $ xal
Jtdvv vmlv Karcpaivero diGrd&iiov rqg v 20
ralg Hitifiohaig rov TCi'jtQo6Q"^6avrog nhdrovg 7tl rb
^xog rov xav6vog rb dnb ri\g otyf&g jcl rb TtQiGpa-
nov Ttteforyg ovGqg ytaoa^irori6C3g diaifjv6d"?ivai, rqg
dvva[ivr]g. Inel d' a7ca% i] 6ktjvr] Kara rb
2. Tsrccm]%ovs C, Q supra scr. C 3. 5. Ttavxa.fj\\ -t- corr.
ex n in scrib. C. ^irjds^i&g] corr. ex {.i7]df(iiav C 2. 8. raig\
tots C. TtavoeJirivoLs] -OL- in ras. D. 10. rov] r- corr. ex
S in scrib. C. 11. anolovd-ojg A, corr. A 4. vno&sGSGi. D.
13. tkdfovs D. 14. (LtfVroi] corr. ex [itv n D 2seq. ras. 2
litt. TT?S] corr. ex r? in scrib. D. 15. Post tnUfyeav del.
*a| D. 18. ytVfd^at] corr. ex / D 2. 20. rfjs] corr. ex
rafg D. 22. ft^xog] p- corr. ex x A 4. TO (pr.)] TOV D. 23.
nteiGTccis ofaccLs D, corr. D 2. 24. <f ] 8e D.
Ptolemaeus, ed. Heiberg. 27
418 KAATAIOT HTOAEMAIOT
\kiyi6tQv avri]g aitoGrrjiia xrp i'Gyv rcn v\kito Ttobg rrj
otyei y&viav syaCvsro noiovGa, dia r&v 7tol rovro rb
a7totfrr][icc rrrjQr]^iV(ov <jA.r)viaxa)v sxAsfyecov rr\g vito-
TWO[ivr]g VTC avrijg y&viag rb fis'yf&og iTtikoyiCf>\LVQi
5 xal rqv rov j]Mov GvvaTCodsdsi'yuzvrjv sfyopev avro&sv.
rbv ds rgortov rr^g Toiavrrjs snifiohijc; dia dvo
rcov vitoTerccyiLEVGiv sxfofye&v evxaravoyrovT& yap e' srst NafloitoM.a66K()ov ,
o i<
erog KTCQ NafiovutiGaQOv ,Kar' AiyvTtxiQv 'A&vQ xt,'
10 sis iv\v K'YI coQcig IK A.rjyovGrjg iv Baflvk&vi, ^^|rof] 6^Vrj xA.L3tl,V
,XCCi S^zkeiltSV tO JtA.l6TOV CCJtO
vorov TO $' rrs diKpeTgov. 7td ovv fj yilv <XQ%JI rij?
V [lTa CDQCCg TOV 1100VVXTIOV XCCl-
6 df [i6os %Q6vo H,T<X % fyyiGtcc, aC i]6av iv
15 Bafivkcbvi r6r farmEQival f /.' y' dia rb rbv v\kiQv
ccxQificbg iiti^iv KQLOV poiyus K xal %r]xo6ra y, 8r\kov,
on yiyovtv 6 pfaos %QOVO<S r^g x2.fy(DS<) or rb
Gxiav ^7t7tr(DXL rijg dia^rQov^ v
[ira~
[1 y' (ogccg i<jr][iQivag rov
20 [i6ovvxr{ov, v $ 'Afa^avdofta Tt&'kiv iisra f povccg.
xal GwdyM 6 onto rr}g fcTropJg %oovog rq Aiyvitriaxa,
xal VHLSQKS Tig xal cooag frgjpqpiircfcg aitkag
1. avtfis D. 2. ycovLKV\ corr. ex ycovia A 4, y^ D. TO]
e corr. D 2. 4. uvTfjs] -rf)<s e corr. D 2
. yooWas] y^ D, y D 2.
5. 6vvu7iodiKW[Lvr]v D, Sedeiyfievrjv mg. D 2. sfyofiev] s
supra scr. D 2,
sed del. 7. vxccravor]Tov~] pr. t in ras. A.
8. f'] BD et postea ins. C, is corr. ex xf A. Irft] comp. D,corr. D 2
. Ncc^onccUccaaQOv BC; alt. I add., alt. G del. D 2.
9. s'trog] om. D. Nccovcc6a.QOv D. 'A&VQ\ 'A- ins. D 2. 10.
tfe] corr. ex ss A. rtjv^ supra scr. D 2. Bafivk&vri C.
11. Qitemsv} -v del. D 2. 12. TO] om. A. 13.
-v del. D 2. 16. dx(>t|3c6ff] -Qifi&s in ras. minore A 1
.
B, tf D. 19. [iev] om. D. 22. ws] renouat. D 2.
MA0HMATIKHS STNTABE&S E'. 419
ds rd oftcda vv%ftrm,Qa 7g /_' d'm &6te xal
j) psv iifarj xccra iiyxog itdgodog rr)g 6^v^XyJi&v noioag x A/3, ^ #' axQifirig poiQag xt,
?r6 roi) axoyeiov rov faixvxhov poiQas T\L xccl
f, q d' anb rov (loQeiov rtfyatos sitl rov Aojov xvxhov 5
JTjil.
xal cpavsgov, ort, orav O1 xal y poiQag dtp-
rcbv Gwdstipcov rb xsvrgov rijs G&v\vv\ Jtl
rov Ao|oi) xvxhov nsgl rb pdyitirov ovGrjg
xal % ejtl rov yQa(po^ivov di' ccvrov agog
Ao|c5 iisyfarov xvxhov rb XBVTQOV rf\ Gxias, xa&' TJV 10
at iLs'yitirai yivovrcu, zrtiGxorriGsis, rb reragrov
eig rr^v GXLKV s^ijCLTCrsi, rr}g diaperQOV.
r& % b'rsi Kccpftv^ov^ o i&nv 6xs' erog
xar Alyvnriovs <&cc[iVG)d' i% slg
rqv ir{ XQO piccg &Qag rov peGovvxrCov iv Baflvh&vi 15
QsteiTtsv % 6e^vri ait aoxrcov rb rftiitiv rf\$ diapsrQov.
ysyovsv ago, xal avrTj fy sxfoiijug v 'Ak,avdQia itgb
a i' y ftgag i6ri^QLvi^g fyyitira rov prtovvxriov.
xal Gvvaysi 6 cforo ri}g iiCQyi\g %govog fry Alyvxriaxaxal j}[iQag Q$g xal cbgag farjjifQivag aTth&g [iv 7 20
xal g', axQificdg d O1
/.' y', did rb rbv ijhiov
1. i' 8'] U' 4 D, U" A" D 2. 2. yiura] xeu a D, xaor D 2
.
3. Xr]l&v] corr. ex Xsil&v D 2. 4. ^Trtxvx^oi;] corr. ex ano-
KVK%.OV D 2. fljT^xoffTcT] B, |" D. 6. aqpforrryxst D. 9.
17]
corr. iex r)v seq. ras. D. 81' avrov] mg. D 2,
dia TOV suprascr. D. 11. ywovTKi] corr. ex I'
1 D* XBXUQTOV] ~j' B, <J- D,<? D 2
. 13. TOJ] r<St C, t eras. ^'] corr. ex t' D 2.
^TTFI]
corr. ex h D 2. ^<rrtv] comp. B, -v del. D 2
. 14. Nufiova-
Ga.gov D, .AT del. D 2. Atyvm
l
ov<$ D. 16. |^/lf(,7ri'] -st-
corr. ex i D. %uat>] U* D. 17. SKJ.en})'' D, &tfoti/>? D 2
. 18.
^(TTjju-f^w'^ff] corr. exiGr}{iEQt,v''rjt; D 2
. ^yyiotra] pr. y e corr. A 1.
20. <7x<?] ffx- e corr. D 2.
27*
420 KAATAIOT HTOAEMAIOT
Kaoxwov poiQag ^*j ifi' co6t xalr\ (Ss^vrj Kara
H6G)g \lV 1tl%V Afy6xQG) {LOiQag X X/
1/rjid. aq)i6rrixi $ xal dab [iv rov aitoysiov rov
frtixvxAov iiOLQag xr] ,aitb $ rov ($ooiov 7toarog
5 rov Ao|ov xvxAov VLOIQKS 6%f$ tfl.xal vrv&v aoa
v, on, oravt, notgas Kal 8 nfyrtra rcbv 6vvd-
TtS'm rb xvrgov rr\g GfAijvrjg 7tl rov Ao|oi)
jtol rb avrb [isyio'Tov ovtiyg ccTto^rr^ia rov
xwroov rils Gxiag ri\v tor][ivr]v %ovros Ttobg avrb
10 frfaiv, rb r^LLGv ptgog dg fr\v Gxiav ipitiTtisi rqs 6-
K, sav {Lev 0" y' poioac; aTcfyr) r&v
litl rov Aooi> xvxAov rb KEvrgov ri\g <?At?V>?, ^ /.'
^xo6ra {nag [lOioag onti^i rov dia {ifacov sal rov
15 nabs oQ&as r<p Ao|w di? avrov
xvxAov, orav d g (loioas xal r66aoa
rcbv 6vvd6[ia)v 7tl rov Ao|oi) xvxhov, jlxal ri %q-
a rov dia ^i6csv anfyfi fuag poioas 7tl rov nobg
Ao|w dC avrov yoa(po^ivov [ifyfarov xvx-
20 Aov. sstel ovv rj ^lev rCbv dvo &ctefy$tov vjtao%ri rb
2. 7ti%v] -av e corr. D 2. 3. id] corr. ex m D 2
. cctp-
D 2, acpiavrjusi, ABCD. xca] comp. supra scr. D.
7. &itexij] D, cLni%Ki ABC. 8. yiiyiGTov] corr. ex M9. KKVTQOV] H- D, Tt-p D 2
. 10. rj^iGv] /_'
corr. ex 0eb}i7<ftt* D 2. 12. all' CD. y'] 7 A, xal y BCD.
ftotpag] corr. ex jitoD 2
. 13. lo^oti] I- corr. ex /7 A. 14.
rov (alt.)] rbr A. 15. Si' avrov'] dice rov CD, corr. D 2.
16. fe'] comp. ins. C 2. riccaga ni^nra^ J fV B, J E D.
17. r*~\ r ABCD. s^oora] g B, | D, H D 2. 19. Si*
avrov] dia rov CD. 21. d'l supra est ras. A, 4 D, A' D 2.
-lrr supra scr. D.
MA0HMATIKHS STNTASE&S E'. 421
rov xevroov avrijs dvo diaGraGecov ebro rov dia
r&v Jcodtcav, rovretinv anb xevroov rijs Gxiag,
e%r}xo6ra pices [lotgas /.' ?>', yavegov^ on xal oky rj
rijs 6eA.tfvrjg vnoreuvei peyCtirov xvxhov
efyxodrcbv [lias ponces Aa y'.
6i>xarav6r}Tov d' ccvto&sV) on, xccl % ex rov XEVTQOV
Tys 6xt,as rils XCCTK rb avrb ineyiGrov dnoGtrjiia rr\ 6^-wrjg vitotsivsi, (iv [lias [IOLQCCS ^xo6ra ji
xccl ri,
3tQ, ore ra ro6avrcc e^rjxodra rb xsvroov rrjs
rov xsvrgov rijs Gxias <XTtt%v, tqnfar&eo rov xvxAov rrjs 10
& rb rb rjpidv rijs teArjviccxijs dccc^froov fxfoAoi-
diacpoQco d\ &drra)v 6rlv ^ diitAcc6iG)v xccl srt,
rots y 3t[i7irois [iitov rijs & 'Pov xdvrQov rijs 6A.rjvr]s
xal dia itfaiov&v d roiovr&v
rcc ra$ xxi[ivas Jtrjhxo- 15
rrjrccs xaraA.a[i(lciv6[jivot, 7tg6$ rs ra aM.a ra Ttfyl ras
&G)Qoviiva 6vyx%Qijii&a avrals xal vvv ye
t$\v dei&v rov fjhiaxov aito6rrj[iaros xara ra
avrd etioiievriv , ftxal 6
r
'l7trtaQ%os r}xoAov&r]6v ,xal
cos f&v iteQihaiifiavoiievcov vitb r&v x&v&v xvxh&v 20
fjMov xal Gehrivris xal yijs adiayooG) elarrov&v ovr&v
3. ||7j%o<rra] comp. BD, ut saepius. rj]e corr. A. 4.
-si corr. ex i in scrib. D. 5. UK] I- e corr. in
scrib. D. 6. EvnaraVOTJTOV ] fu- corr. ex a- D. xiV-
TQOV~\ comp. ins. D, corr. D 2. 8.
ftj corr. ex (iD 2
. r'*]
lo ABC, Fs D. 9. ore] supra scr. D 2. 11. TO] om. CD.
jjfpurv] /.' B. cshriviuy.fis'] corr. ex cs^vrjs D 2.
dimid. eras. B. 13. 7] TQLGL in ras. minore D 2.
tsuntois] corr. ex I seq. lac. D 2. 14. r*] r ABC,
D, Pa D 2. roLovtcov] -i- corr. ex v D 2
. 16.
-KV- renouat. D 2. rs\ corr. ex TO D 2
. TO. (alt.)]
om. D. 17. ZMsiipis D, sed corr. 0v*Mg$ifaie4ta D, corr. D 2.
19. i]y.olovQ'r}6v~\ -v eras. D. 21. y^g] corr. ex T?)g D.
D.
422 KAATAIOT HTOAEMAIOT
TWV v reels GgxtiQcus avTcbv yQKtpo[iVG)v
KVT&V TS xal T&V di,a[iTQG)v.
if
. IlQl TOV fjAiaxov anoGTiJiiaros xal T&V
5 TOVTOV TOIVVV dedopsv&v, xal OTL TO xaTa ras
tivtvyuag neyiGTOv cbrdtf-n^a rrjs 6kijvr]$ TOLOVT&V
6T\v |d T, OLOV <5xlv vbs r\x rov XWTQOV rr}s y^j,
dia rb TO fitv yi6ov ddt%ftai TCOV KVT&V i/O1
, TTJV d'
K TOV KSVTQOV TOV 7tlXVXA.OV 7, l'd(Q[lV)
10 6vv(x,yTai xal TO TOV i\KCov aitoGTrjpa.
6Tco6ccv yaQ oi piyiGroi xal iv T<p avTcfr
vxhoi rfjg [iv fjhaxfis 6 ABPTO ^/, TtJ df 6A.r}VlKXiiS XCCTK TO
<xtto6Tr)[jiK 6 EZH 7tol XWTQOV TO, Trig ds
15 XKTCC r^v yi\v 6 KAM itsgl XWTQOV TO N^ T&V $ diu
TG)V XSVTQCOV 7ti7Cd(OV TO [lV TTJV y^V XCCl TOV ijAlOV
TO ABF, TO dl TOV ijfaov xccl TJJV 6-TO ANT, xal a%cov pv xoivbs 6 4N&, ccC
de dia T&V 7tcc(pa)v v&ia,t, TtaQcckkrihoi,
20 yi,yv6^vciL xul Tcclg dtK^TQOts facet, nobs
TOV plv yhaxov xvxhov3} A4F, TOV ds
fj E@H, TOV $ Tils yn$ n KNM, TOV ds rijg
1. GcpaiQuis] ^9' D, -QUI$ add. D 2. 2. tf] om. BC. 3.
te'l mg. AC, B, om. D. 5. TO] ins. C 2. xara] corr. ex
v.K\A 4
. 6. Gvvytas] GV- ins. D, supra -as add. rd, sed del.
8. TO ftsV] ins. C 2, ptv B. 9. ?] post ras. 1 litt. D. 11.
lisyiGToi] corr. ex M D 2; supra add. rgsig, sed del., mg. oi
(ifyiGTOi D 2. tntiTtsdq} C, sed corr. 12. GcpatQ&v Kvyikoi]
corr. ex op v,v D 2
, mg. cycciQ&v. ABF] corr. ex ART D 2.
19. incttp&v A4, S7ta(p&\v A. 20. yivopsvai D. diccpe-
T^otg] corr. ex ^ D 2, mg. OTO D 2
- 21. A4F~] corr. exAAT D 2
. 22. rov (alt.)] in ras. D.
MA0HMATIKHS STNTABE&2 E'. 423
M
o
ig 7Ji> ipitCTtrsi Kara TO
(5TOV aTCoGTrjiia v\ Gektjvrj, r\ OJZP,&6T farjv elvai xr\v N TVJ Nilxal exarsQav TOIOVTCW %d 7,
OlOV 0TLVfjNA X TOV XV- 5
TQOV vfjs yij svog.
dst drj evQsiv, bv %SL Aoyov
TOV fjfaaxov ano-
agog Tyv NA sx TOV
XEVTQOV Trjs y^g. 10
sxpsp^ci&G) ToCvvv riEHS.
xal eitfidJi edsfi-apeV) on ^ rfs
di^d^iSTgog xaTa TO ex-
v Tats 6vtvyiai$ [i-
66Trj[ia vitoriVi TCSQI- 15
tpQiav TOV xaT avTyv yga-
CpO[lVOV 3tQl TO XVTQOV T1JS
yf\S xvxkov TOLOVXOV o Aa ~%,
oiW 6Tlv 6 xvxlos T%, sir} av
VTtb ENH ycwta TOL- 20
1. els] e corr. D 2, supra scr. C 3
.
crsi] -Imsi renouat. D 2. 2.
rj OnP] -f]O- e corr. A 1
,O- reno-
uat. D 2. 3. were] a>6t8 Y.ul C, yidC
supra add. D 2. rf?] xj\i corr. ex
rr\ A 2. 5. oiov~\ -i- supra scr. C.
NA] corr. ex NJ A. yie TQOV D,corr. D 2
. 8. N4~\ corr. ex NA D 2.
9. NA] corr. ex NJ D 2. 13.
$ D, OTO mg. D 2. Jx-
-i- corr. ex v in scrib. A.
14. [isyiGTOv] corr. ex M D 2. 18.
xvx^ov] corr. ex HV D 2. x] corr.
ex x- D 2. 20. ptv] corr. ex (i\ D 2
.
ENH] -H e corr. D 2.
424 KAATAIOT IITOAEMAIOT
OVT&V o Aa x, oi&v at d ooftctl r? ^ df fj[ifai,K ccvrfis
VTCO 0NH roiovr&v ncttiv o Aa x, otW sfalv aC
r* (btfte Kttli\ [iev sitl r^g H itQi(pQi,a roiovn
6rlv o Aa x, ol'cov 6 jrspt TO NH@ dgftoy
5 xAos r|, ^ d5
Sri rr^_@N r&v tont&v [Eucl. III731
els to fiiiwvKkiov QO& m} ft. xcu t&v viC avn
KQK V&l,G)V1} [LV H 6tai, rOlOVHCOV O
/ fl, OLG)V
6rlvriNH SiapsrQOS ^x, fj
$ N rcbv KVT&V
fyyitfrct' &6t Ko,i, OLCOV edrlv ^ ^ v&ia %d
10 roiovr&v xccli\@H k'tircu o tj A^. rov d' avrov
xalYINM ax rov xsVrpou rij? yi}g fVdg. AA'
Myoc; 0rlv rijg UP nobs rr\v ff, ov fyst, rcc
/3 Ag i
yi
yiGra xobg rb V, yivtxai ncclf]
IIP rcbv
avt&v o^i &rj. 6vvayi(p6tQKt, aga ij
r H xccl
15 IIP TOiovt&v i&lv a y Ta, olov 6rlv 17NM
AA 6vvtt[i(p6TOcci, ijT IIP xal fj
027 6'A^ rcov
avrcbv ffaiv ^ dice rb faces avrag dvai dval rcctg
rjhoi r yda, cos scpa^m, i&lv Jt
Nil rri N' xal Aot^ aoai]HZ
1. at] ttalv at D. rjpfafHx] mg. D 2, t' D. ^ vno\
v- e corr. D 2. 2. (3]
^vo CD. 3. &r] -TT- corr. ex c
scrib. A. 4. 6] ^riv 6 D. 6. ^tHvxAtov]-^
D, a D 2,
mg. ^ixy_D2
. 7. H] 9H D. Supra oreov add. *r]
$s
&N QI& v& /A7JD 2
, supra I'yytffta lin. 9 adp. D 2. 9. F]
corr. D 2. 10. roiovrov] T- e corr. C. OH] H& corr. 62
IV D 2. Jly] corr. ex It D 2
. 11. I-GXIV\ comp. B, -v del. D 2.
xca] om. C. JVM] -AT e corr. D 2. <iUa D. 12. &
comp. B, -v eras. D. oV] corr. ex o D 2. 13. ^ Is] ^ AC.
TO] corr. ex TOV C 2. ytvsxai] y
+D,
*supra add. D 2
, rx D 2.
15. flciv} ins. D 2. 16. ccUa] om. C. 17. f^iv] comp. B,
-v del. D 2. dvaiv D, corr. D 2
. ratg] corr. ex xoig in
scrib. C. 18. tlaiv] comp. B, -v eras. D.
MA0HMATIKHS 2TNTASE&2 E'. 425
roiovrcov o vq fi-fr,ol'ov stirlv
r\NM sv&sla vog.
xaC tGrw, fog % NM agog ri\v H, ovrcog ^ ftev NT3t$bg rqv HF, j]
de N4 ngbg ryv 4' oiov KQCC tiriv
og, roiovr&v xctli\ pm 4 stirou o vg ^9-,
dsf]
N r&v avr&v o y la. (Dd-ts xcct, oi&v
fj ply N@ sv&Sicc |d 7, j] de NM fVdg, roiov-
t&v foiv xal trv N4 rov
d' msi, olov farlvi\NM sv&sicc
Toiovt&vv\IIP dsiy%"Yi o
^JTs A^, cog ds ^ NM agog 10
ryv TIP, ovr&s y NB XQOS rrjv ^77 [Eucl. VI, 1],
Kttl OLOV ago, rj N& sv&slu svog-, rotovzcov ^ [isv ^776rca o
fie Arj, Aomri ds % IIN tcov ccvr&v o id x/3.
Kal otcov farlv aoa 17 plv TIN sv&sta p 7, r\ds NM
sx rov XSVTQOV rye; 'yijg evdg, roiovrcw KOIv\ plv &TL 15
v fyyiGrcc, 17ds &N (ttrj 6%r].
i\iitv agu^ on, oiov 6rlvfj
IK rov xilv-
rgov ryg yrjs fvog, roiovr&v stirlv rb [isv ryg GsA.rjvqs
sv rccig 6vvyais [i0ov ccTto^ry^a v&, rb d rov j]Mov
jutfi,rb d' anb rov nevrgov ri}g yv\ ^X9 i tijs XOQV- 20
rov Ktovov r
1. o] o D, ut saepe. i6xtv\ comp. supra scr. D 2. 2.
7) (pr.)] supra scr. D 2. NM] renouat. D 2
. vrjv] supra scr. D 2.
H2] corr. ex Hr_D2
. 6. N@] N- in ras. D. 7. N4]JN, N e corr., D; 8v mg. D 2
. 8. OGL] corr. ex fif D 2. 9.
OLOV] corr. ex ov C 8. evos] post ras'. 1 litt. A. 10. i] (alt.)]
seq. ras. 1 litt. D. w^dp] ^ D. 11. nqog 12. N8] suprascr. D 2
. 12. #77] mg. D 2,IT D. 13. &?']
<?e' V- D. 16. cy]
6y D. c|7]] -T] corr. ex N C 2. 17. &$a J^LLV D. 18. lariV]
om. D, comp. JBD 2. cslrivri?] 6f- add. D 2
. 20. OGL\ &6t D,
fai D 2,act mg. D 2
. 21. 0|rJ] corr. ex |ij D 2.
426 KAATAIOT HTOAEMAIOT
tg'. Ilfol [isye&cbv rjMov xal Gfkijvrjg xal yijg.
Evxaravorjrog d' avr6&v yivzrui xal 6 r&v 6rQa)v
[iy&G)v AOJ>O ano rov rCbv diapdroav r\^Cov r xal
6hrjvr)g xal yfjg.
5 sjtsl yao dsdewtui piv, ort, OLOV vog eGtivijNM
lx rov xevrgov r^s yijg, roiovrcov BGrlv y [ifv &Hsx rov XZVXQOV rrlg af^vrjg o tf Ay, ^ $ N@ v&ta
%d t, l6nv ds uai, (bg r\N nobg H, ovr&g ^
itobg x^v 4F [Eucl. YI, 1], xcbv ccvr&v xal ri^g
10 $$i,'yiivr]g ya<?t l~o[iv xal rqv z/JT % rov XWTQOV
rov riUov r&v avr&v /.
r
fyyiGra' xal rcbv dift-
^ 01 avrol 6ovrai koyoi. &6T xai, OLOV 6xlv
lg 6krjvr]g didpfraog fVdg, roiovr&v xalf\ plv rr^g
fGrai, y xccl dvo TtsiiTtrcw fyyiGra,, 17df rov r\Mov
15 vq xal d TtepTtrov. r\ [iv rrjg yrlg aoa did^ifroog rrjg
6A,r]viccxrlg XQiTtkaGittv 6rlv xal k'n rotg dv0l niyat-
roig [i%G)V) i\$ rov Y\^IOV rrjg [lev tifhyviaxrlg oxrco-
xal h'ri rolg d Jtfyjtroig [iicov, rr]g
1. tg'] mg. AC, si B, om. D. nsQi yjfe] add. D 2. 2.
6 T&V] 6 t- absumpsit lac. pergam. D, xal 6 T&V OTSQZWVmg. D 2
. 4. %at] ins. D 2. y?)g] e corr. D 2
. 5. ot'ov] corr.
ex ov C 3,ex OGOV D. 7. Mg. o ^ 5t >ty D 2
- 8. r] corr. ex
p D, mg. l-tft' D 2. fWiv] comp. B; s- e corr., -v del. D 2
.
tif\v D. 9. TTJV] supra scr. D 2. 10. JKGI] /act B,
corr. ex &ort D 2. 12. orov] post -t- ras. 1 litt. A, -ov e
corr. D. 13. xca] om. B. 14. <Wo] B B. itepnTcov] E' B,
supra scr. D 2. 15.
<?]A D, corr. ex ij ABC. n^iiTcov]
s' s B, e D, s" D 8. 16. T^tTr^aorteov] corr. ex . TQinldcio] D 2
.
lartV] comp. B, -v eras. D. #rt] corr. ex fjrt D 2.
it- e corr. D, t-' s B. 18. d] mut. in TSTQGI D 2.
s's B, D, f' D 2. pe#o>v] A B, M D 2
.
MA0HMATIKHS STNTASE&S E'. 427
itsvrankatii&v xccl ETI, rc5
xard ravrd d\ sjtsl xal 6 {lev djtb rov vbg xvfiog rov
ccvrov 6nv VO, 6 <T dnb r&v y tealft XS^ITCTCOV
avr&v k'yyiGra A-9*<?',
6 d' KTCO rcbv Irjxccl d
pofas ,$%y>d (1 zyytftcC) GvvijxTai, [Eucl. 5
XII7 18] JifitVi on xai) otov ev6g i<5tiv rb rife
6rQsbv iifysd-os, roioritcov sd-dv TO pv rye;
dr
,rb df rov r\Mov ,<5%[i8 {!
rccitA,tt6i,ov aQa, fyyiGra rb rov o^Atov rijg
it,'. TlEQi T&V xccra pEoog xccQaM.dt.E&v ^Atov 10
xccl
Tovrcov roivvv ovr&g vTCOKEipsvcdv axokov&ov civ
stv\ itQOGcatodEi^ai itukw 8ia j}Qct%Ea)v ,riva ccv rig
TQOitov EX rqg rCbv aTto^rrniccr&v itrjfaxorrjrog yMovT xccl GEktjvrjg xccl rag xccra [tEQog ccvr&v yivoiiEvccg 15
itccQCcMd&i'g sitikoytf^oiro xccl xa&rov rag EJtl rov did
rov xard xoavcprjv 6r}[iEiov xal avr&v
6rc3<5av di v rc5 rov ftriEvov Efarov xvxhov
1. srt] corr. ex litl D 2. TW] corr. ex to C 2
.
-s- e corr. in scrib. A, r](ii6i {LSQSI D. [ii(av] M D, et
similiter saepius. 2. ravtd] mut. in ru ccvrd C 2,
rcc ccvtd D.
8'] Ss wi D, di D 2. xat] om. D. , 3. d'] 8s D, -g e
corr. D 2. ntpnimv'] is B, f" D, ut lin. 5. 5. ^zftd] ,s-
e corr. D 2. 6. ort xat] %ai ort D. SGTLV] comp. B, -v
del. D 2. 7. JffrtV] comp. B, -v eras. D. 8. g^ D, corr. D 2
.
O.QCC] corr. ex SKCcrovtaytcci,-' D 2
. 10. t'] mg. AC, t B, om. D.
14. TCOV] corr. ex r D 2. 15. avrwv] avr corr. ex ccvt D 2
.
16. dta TOV] om. D. 18. pvyfatov uMov] corr. ex ft KVD,
et similiter saepius.
428 KAATAIOT HTOAEMAIOT
6 [iV rrjs yijjs ndkiv [ifyitiTOS xvxhos o
o $ xaTa TOV ijAiov $ xv\v 68A,tjvrjv 6 -Tz/, Jt^bs ov
$ fj yr] 6r][itov koyov %i>) o EZH, xal x
Jtdvt&v TO K) fjds dia rcbv Kara xoQvcprjv
xal
TOV F Kara
trig T/i
cro
fav
10 VXV V7tOXi,[lVr]S &>
oicav 6Tlv 6 JTz/ xvxkog
'av {iv Jtd-
KJH xal %
$ TOV A15 JtaQdA.krjA.os plv ij^cs
TTJ KH i\ AZ,, xd&Tog d5
iit avTTjV 07A A.
TOiVVVILY] [18VOVTOS dfl TOV aVTOV
tl XaTQOV TG)V (fG)TG)V r\ [lV TtS^l TOV
60[ivrj dia TOVTO T&V naQaA.hd&cov
20 JtavTaitaGi, xal dvitai6&rjTog 6Tai rc5 xal Tr\v XXv-
TOV xvxAov avTov yuxQav dvai xal TO dno-
\iiyd, TJde Ttfgl Tr\v GfA.ijv'qv xal Ttdvv av
ysvoiTO aitiftviTri xal T^S XKTK TOV zitixvxkov xivrJ6G)s
avTi]is VXv xal Tilg avTov TOV fiuxvxkov xaTa TOV
25 XXVTQOV OV ^HlXQCiV TtOLOV^g 7CQtl Tag dtt06Td6l,g
diacpoyav xaTQas, Tag [ilv TOV VI^LOV
4. K] renouat. D 2. 5. KATE] A, corr. ex KFE D 2
,
xa r F BC. 8. FJ] corr. ex A D. 9. zoiovtmv] -i- corr.
ex o in scrib. C. 11. 6] add. A 1. 17. ale D. 19. TOVTO]
corr. ex TOV D, TtKQcdu&otv D. 25. iiiv.Qav~] -i- corr.
exTJ
A.
MAOHMATIKHS 2TNTASE&S E'. 429
l \JLQVQV TOV vbg hoyov dei%o[ieV) Afyco ds TOV
^i Ttgbg TO v, Tag $ rv\$
dfao'Ta fig tag f|^g (podovg
vcw. lhriq)a[iv 6s TK>V T6<5aQG)v TOVTGJV
{LKTCOV TtO&TCC [lV SvO TCC 'yiVO^lSVCC TOV 7tMVXkoV 5
MCCTCC TO CtTtOySlOTCCTOV TOV XXVTQOV TVy%aVOVTO KCil
TOVTCW 7tQOTQOV [lV TO p%Ql> TOV KltOyeiOV TOV B7U-
KVKkoV, O GwrplTKl 8iCC T&V JtQOCi1toddl,'y[lVG)V [p. 422, 7]
TOIOVTC3V |d 7, OI'OV 0Tlvfj
K TOV XVTQOV TJ]$ yf\
l/dg, $VTQOV d TO fl>%QI> TOV TCfQiyflOV TOV 7tl- 10
xvxhov (Swccyo^ifvov xal TOVTO T&V ccvT&v vy v
[p. 416, 5], TK dl koma dvo ywopwa TOV
XCCTK TO Tteoi'yfioTaTov TOV xxVTQovXCll TOVT&V df TtttklV 7tOOTOOV [lV TO [l^Ql TOV UTIO-
yLOV TOV 7tlXVK&OV GWCCyO^VOV dlK TK TtQOaTtodf- 15
deiyyilva [p. 416? 6] TOIOVTMV ]ny vy, oiov 6tlv ^
x TOV xwTQov T^g y^s fVo, dVToov de TO pfyQi
TOV TtQifyLOV TOV 7tMVXA.OV 0VVK'y6^lVOV KCtl CiVTO
T&V avT&v ty Ay.
Jtfl TOIVVV fjTA 7tQl(pat,Ct VTtOXMTCCl, [IOIQ&V A, 20
sli] av noil $1 VTtb FK4 yewtec,
oicov \iiv eltiw ai d
daftcd rj, TOIOVT&V A, oicw d' KI dvo oa&al T|, TOI-
OVTG)V f. &6TG KK\1] [lV 1tl T^g AA 3tQl,(pQia
TOIOVTG)V 6TLV,
OLG)V 6 7t()l TO AKA
1. S\ corr. ex <fy' D 2. 2. KGL] ac i A, &GL D, fai D
2.
sv\ BC^D, sv AC. 6. xara] post ras. 1 litt. D, infra %-
add. ^ A. 7. Mg. a BCD 2. itQo-cv A. 10. Mg. u
BCD 2. rov (alt.) 18. negtyfiov] bis D. 12. dvo] 3vo rd D
utroque loco. 14. y mg. D 2. rov] corr. ex ro C 2
. 15.
TiQodsdfLyntvcc B. 16. ol'ov] -i- in ras. C. 17. d mg. D 2.
dsv\
dfvreQOV D priore loco. 22. roiovroav ri-] supra
scr. D 2. $'] 8s D 8
. dvo] p BD 2.
430 KAATAIOT DTOAEMAIOT
KVKlog r\, ijd' iitl t% KA rav Aout&v [Eucl. Ill, 31]
sis t<> flpiKVKkiov ~QK. Kal TGJV vit avrag aga v-
r\ [ilv AA roiovr&v 6rai f, OLCOV 6rlvr\AK
QOs ptt, fjd K4 r v ccvrcbv ~gy v. KOI oiov
5 CCQCC 6rlvi\AK vos, toiovtcov xal
fj pv AA sGtat,
o A, i5$ KA evftsia, o
vfi. rcbv d' avrcbv 6Tiv xal
f\KA4 V&tCC iltl [lV tOV fjAlCiXOV
/ o^Z, ml $ rcbv tifhyviaxcbv teara [iv rbv
OQOV |d 7, xccra $ TOV dvtQov vy v, Kara dl tbv
10 rgitov ^/y vy, Kara $ rbv rdragrov ty ky xal homyccpa i] Ad, rovrstiriv ^ Ad, jtd adiayoQcp i6iv
avitioi, iitl [ilv rov fjfaaxov aTto^rtj^aros k'tirat, a6&
^, 7tl de r&v 6^vLccx&v Kara [iv rbv nocbrov OQOV
fy Z^, Kara dl rbv vrQOv vfi vvj, Kara d rbv TQITOV15 jHy a, Kara dl rbv rtragrov A/3 pa. &6r Kai, oi&v
6rlv r\AA vitoreCvovGa OK, roiovr&v 6rai ^ AA
vnaxovo^vr}s^ iva ^ ravro^oycb^v, rijg avrils
o/3v& Kal o vg v($ Kal a VTJ xal a ivy ^ia
Kal a v &' Kalrj pv 7t* avrri$ aga 7tQi,(pQi,a roi-
20 ovrcov k'Grai o/3 v Kal o vd Ij] Kal a d vd Kal a K
Kal aji fyyitira, OLCOV itirlv 6 7t$l rb dAA OQ&O-
yaviov KVK&OS T|, 17d' bitb A4B ywvia, TOVT&TIV
2. r^iiY.vv.'kiov^ comp. macula obscur. D, corr. D 2,o n
mg. D 2.
5. A A} corr. ex Ad D. 6.J] seq. ras. 1 litt. D. d']
supra scr. D. 8. CCGI\ &ci D, t&ai D 2
,ut saepius. litl~\
-i
in ras. A. 9. de (pr.)] ins. D. 'Tor(pr.)] supra scr. D. vy]
corr. ex fiy D 2. 10. r^raprov] j seq. 1 litt. deleta D.
Ay (alt.)] e corr. D 2
^11. slew] ft- ins. D 2
. 12. aviaoi]-ot in ras. A. 13. OQCOV C. 17. TawcoHoy&iLfv] -o- pr. in
ras. C. 18. xca'(pr.)] om. BC. o (alt.)] o seq. ras; 2 litt. A.
xy] mut. in xa D 2,sed rursus corr.; xy mg. D 2
. 19. v -91
]
corr. ex v& A, ex vri& D 2. TtSQiytatia] comp. postea ins. D.
22. d"\ $t D.
MA0HMATIKHS 2TNTASE&S E'. 431
v\vjtb ZA [Eucl. I, 29], OLCOV piv d6iv ai dvo OQ-
&al r|, roiovrov oft
v xal o vd TTJ xal a d vd xal
a x xal a |it, OLCOV d' ai d oo&al T|, roiovrcov o a x
xal o xt, -9- xccl o A/3 x xctl oji
o xai o vfi L &6r
sjtsl xal TO [isv A Grjiistov adiacpogst rov K XSVTQOV, 5
% de ZH& TteQiysQsicc adiucpoQG) [i%a)v 6rlv rijs Hdice rb rr}v yijv okqv 6r)[Liov Aoyov %sw TCQOS TOV
EZH& xvxkov, xccl % H rijg TtccQccMd&cog TtEQicpz-
oicov 6rlv 6 EZH xvxhog T|, rotovT&v enl
rov f}A.i,ccxov ayto^r^ccros Ititai o a x, iit\ dl 10
6A,r)VLCCXG)V XCCTK [lV TOV TtQ&XOV OQOV O X% ^,
xara d TOV devrsQov o A/3 xg, xccra $ rov rgurov o
ft o, xccra d$ rov rtragrov o vfi ~K' aitey 3tQOXi,To
rov avrbv d rgonov xal iiti r&v koiTt&v anoGra- 15
rov xara xogv(pr}v (ftftisfov rag yivo^idv
Zxatirov OQOV 3taQaMd,i,s ^L^oy^d^voi, dta
g ti%Qi> roov rov rttagrrjiioQiov {IOIQ&V 9
xavova Jtgbs rag bucxQitistg r&v itaQakka^s&v 7tl
t, 6Mdia $ ^, obv v [iv ro5 20
rag rov rraQrr^io^Cov [toiQag 9
1. dvo] B B. 2. o vd ITJ] corr. ex ov 81, (i in ras.) r\ D,
et similiter saepe. 3. T|] supra scr. D. 4. o (sec.)] in
ras. A. o (quart.)] eras. D. 5. ccdicicpoQei] corr. ex dia-
cpoQSL D. 6. adiacpOQco] corr. ex dicccpOQOJ C 2D 2. JortV]
comp. B, -v del. D 2. 7. G^SIOV'] cg D, ^p D 2
,et similiter
saepe. Tcgog] fl D, ut alibi. 8. H~\ N B. 10. IWca]
1<J B. 13. &7t8Q nqoiv-sito dit^ai] D 2,
:r>j D, supra add.
(uel OTtfp) I'det dftiat D 2. 17. Tta^a^a^ts D, corr. D 2
.
18. rcbv] om. C. Tfra^TTj^ot^tov D, corr. D 2. SisyQutyev C,
corr. C 2. 19. xavovia C. 20. ncd.iv\ om. D. 21. 9] corr.
ex b<? C 2.
432 KAATAIOT HTOAEMAIOT
dia dvo drjAovori, xv\v TtaQav^rjGiv avrcbv
iv ds ro5 dvrQG) ra impdkkovr
^rjxo6rd r&v j]faaKcbv itaQaMd%(ov ,iv de r&
rag xara rbv itQ&rov OQOV ryg GEh
5 iv $ r<p retaQtcp rag vjtQo%ag r&v TOV
OQOV JtCCQCchkd&MV ItCCQCC TKQ TOV JT^COTOV, V $ TG)
rag Kara rbv rQirov OQOV 3rapaAAag, iv de
rag VTteQo%a$ T&V rov TMKQTOV OQOV TCCCQK^-
itKQa rag rov tQirov, oiov &g 7tl t^g x&v A
10 ILOLQ&V 7taQa&6G)g ra o a K rov ^At'ov, 7ti,ra |^g
ra o K & rov TtQ&rov OQOV rrjg GfA.tjvrjg xal f^g ra
o t^, oig vitQ%i 6 dvrQog OQog rbv jtQcbrov,
ira Tiochiv ra, o^L rov rQirov OQOV KCCI flijg ret o
t/3 A,
olg vitQ%i xal 6 rraQrog OQog rbv rQirov. VXv15 d rov xal rag iv rotg iira%v rcbv anoyCc3V xal r&v
KBQiysi&v a7to0rt]^ia6i 7taQaM.d%i,g avahoyog rolg xara
[iQog r[nj[jia<ji,v dnb r&v Kara rovg MXfipwovg ti(5-
GaQag OQOvg itQo%iQcog {i&odvi,v dia rr^g r&v
xotfr&v jtaQa&(5G)g ra Aoma ^Iv rQia 6kidia
20 i^Tcrai JtQog ri\v 7taQa&6i,v r&v roiovr&v diacpoQ&v,
2. IxaffTco] |a
(|4 D 2) stidcrcp D. r^fiari] T[ir][idTG>v D,
T(OV D 2. 3. S^TJKOGTCI xwv] om. D. TW r^troa] rwt
D, t- eras. 9. -tgixov] T' B, y D. oiow CD, corr. D 2.
om. B. rcbv I] corr. ex ^ D 2. 10. rd] supra scr. D.
Post STtsiTa del. TC D 2. e&jg] inut. in |f ? D 2
. 1 1 . ra (pr.)]
iav.f? D 2.del. D 2
. Mg. ra o a. xs D 2. 0e^7jV7]g] corr. ex G^r]viav.fj?
12. dtvTf^og] corr. ex ^ D 2. OQOS TOV TIQ&TOV] corr. ex
rov a D 2. 13.
ft]corr. ex jto D. TOV] corr. ex TO D 2
.
rgCrov] y D, ut saepe. |r?s rd] || B, f^rjxoffra C. 14.
rov] corr. ex TOV D 2. 15. |u.Tav] comp. D, corr. D 2
,ut
saepius. 16. anoGrripaGiv D, -v eras. Supra avcdoyws scr.
ov D 2. 17. TWV] T D,
vadd. D 2
. lisi^svovg C,
vov? D. 18. f^rjTtoffTwv] || BD 2, | D, ut saepius.
MA0HMATIKHS STNTASESS E'. 433
XCCi CCVT&V TOV 7tt-
TOV
BH
TQOTtOV TOVTOV.
GTG) yao 6 6e-
7tol xdvTQOV TO JB, TO $
TOV diCC {1<5G)V TG)V %O)diG)V
xccl Tr}g yfjg XVTOOV TO
AE4Z dt^O-to ^ ZF5, 10
Xdl 7tV%&G)6CClT BE xccl
1} FE,Guv itl TJJV AdTOV B
f}B H, ano
d TOV Ffj Fid, XCCI V7CO- 15
TtQGOTOVr\
AB 3lQl(p, ^
0TG)6a TOV XCCTCC TO AaxQi/Sovg xccl agog TO Z
KBVTQOV &G)QOV[lVOV CCTtO- 20
ysiov [loio&v Aoyov VXVOIHJCCV I",
G3<JT XCcl TJJV VTtO
BEH ycovCav, oiojv [iv101V CCi d OOd'Ccl T%, TOi-
OVT&V LVCCi 1, OiCOV d' CCI 25
/3OQ&Ccl T|, TOIOVTOV QX^
XCcl diCC TOVTO TT]V [LV
TOiOVTCOV yCv<5&ttl OX, OiCOV
1. oov] supra scr. D. 12. xa-foroi ds ij^&coaav'] v.ccl
D. 25. elvat] in ras. B. 28. yivsa&ai] corr. ex
Ptolemaeus, ed. Heiberg. 28
434 KAATAIOT IITOAEMAIOT
edrlv o nsol TO BEH oQ&oycDviov xvxhog T%, rv\v d' enl
Trig EH TCOV AOLTC&V [Eucl. Ill, 31] sis TO rj^ixvxhov .
xal T&V V7toTivov6G)v aga avTag sv&ei&v ^ pv BH6Tai, TOLOVTOV (Vy VS, o'lOV 6TiV
fjEB dldflSTQOg ^
5 r\ds EH TOV avTov f. AA' OTav TO E XSVTOOV rov
tl TOV CMOySlOV fjTOV ZXX8VTQOV, A.6yog 0TLV
ZE yfQog TVJV EB 6 T&V % ngbg TK T' xal oi&v
6Tiv fjEB sv&sta LS, TOIOVTCOV xal
fj [iv BHfarcci d Ay, r\
de EH ev&sia ~0 A^, ^ $ HEZ oAi?
10 |/3 Ar?. xal itl TO aito trijg ZH [iTa TOV anb Ti^g
HB itoi,i TO ditb 1% ZB [Eucl. I7 47], h'tiTai xccl amy
TOIOVTG)V %fl JU/J7,O
f
lOV 0TIV TO [lV ZA TOV TtQ&TOV
OQOV CCTtOGTrjlLCC |f Zf, TO d$ Z^t TOV dVTOOV OQOV
vd'pf,
TO d A/l didyoQOV T^g T&V dvo TOVTCOV
15 V7tQO%ilg ~i A. xal TO xaTa TO B &QK didtpoaov
TOV TtQ&TOV OQOV TOLOVTOV 0TiV ft f, OiG)V oAoV TO
didyoQOV ~i A' co6T xa^ oi&v fatlv TO ohov didyogov
1, TOLOVTKtV (5TKl Xal TO TOTS dld(pOQOV id O. TttVTK
uoa 7caQad"t]6o^v sv T& % <?fAidtc? rc5 ^rt%C3 TW TISQIB-
20 %OVTl TO iJlllGV TOV T&V | KQi&llOV, TOVT<5Tl,V
Tolg A, dt TO xal oAag Tag xxsi,^vag v TK>
1. d'] 6*8 B. 4. di.d[iTQos] comp. in ras. D 2. 5.
mg. C. 6. 77] corr. ex j]v D 2. IGTLV] comp. B, -v eras.
7. EB] corr. ex ES C 2, tJ3"mg. C 2
. 9. EH] HE D."J3
"
plri AC. 10. TOV &7to] post ras. 6 litt. D, -v a.- e corr. 12.
icTiv'] comp. B, -v eras. D. 15. rl] corr. ex Tj A. 16. TOV]
corr. ex ro D 2. TOLOVTOOV] corr. ex Trotovvrcov D. SGTIV]
comp. B, -v eras. D. 17. I] corr. ex 4 A. ro olov] 67ov
ro D. 20. rovrf'dri^] comp. B, -v eras. D. 21.
a BD.
MA0HMATIKHS STNTASE&S E'. 435
rov xavovog 9 [101001$ TO %u<?t> 7tQi%LV r&v
Kitb rov A inl rb 4 [IOIQ&V ~Q%.
xara ra avra de, xav r^v .Tz/ 7tQi<pdQiav vito-
ftcctusd'cc r&v avrcov, ^ $v F dsiffiijtietai, roiov-
rcov d ky, oiwv 6rivfjEP en rov nsvrQov ~s Ts^ i\
5
ds E@ biotas ft Ii?, toutti dsr]Z r&v avr&v v
%/}' xal dia ra ccvra 17ZJT vnorsivovGa v Ay. aitso
dAiv catb r&v rov Ttacbrov ooov %s Is ra
p/} svQTJGonsv %rjxo0ra ovra rov oAov diacpo-
oov ^d o- a xal avra 3tccQad"tJ6o[iv iv r& avrcp 6- 10
Aidtcj Ttgbs r& r&v | aptttytcd dice rb xal rqv ABF7tQiy>Qi,av fivai {lOiocbv ^w,.
TtdklV VJtOXl[lVG)V r&V aVT&V 7tQHpQ(,G)V V0l-
6&G) rb E xvraov inl rov itSQiysiov rov XXvrQov,XCC& V &0LV T rQlTOS OQOg 7tQl,%Tai, XCtl 6 T- 15
raorog. Jfd ovv xara rqv roicivrrjv frfaiv Aoyog
6rlv rrls ZE Ttgbg rr\v EB b r&v \ Jtobg ra y, xal
olov CCQCC fjBE yivtrai r\, 6vva%&ri<5ertti, KOI xccroa
yisv r&v BH xal F vd~iS)v^ orccv xal xarQK r&v
AB Koi Pz/ yrOi(pOicjv | {loiativ vTCOKBrircci^ roiov- 20
1. rt^LGv] mg. D 2
, t> D, [_ D 2,ut saepius. 7tQii%u D,
sed corr. t&v] bis D, corr. D 2. 2. A] akcpcc AC. Q7t] corr.
ex QN D 2. 5. $ ty] B, corr. ex Lty D^^y AC. 6. E
] corr._exE2 D 2
. 6(ioi<og~] corr. ex o D 2. ZTJ] corr. ex Jr\ D 2
. i/J]
corr. ex f D 2. 7. ZF] Z- corr. ex F in scrib. C, TZ B.
8. aqpf^ovTfff] -16- e corr. D 2. 11. n^os] om. D.
ins. in ras. 1 litt. D 2. 12. dvai\ om. D. Post
ins. ~ D 2. px] Q- ins. D. 13. K mg. A. 14. TO] TOO A.
E] in ras. D 2. 17. ltnv] comp. B, -v eras. D. 18.
corr. ex F D 2,ut saepius. 20. KCCI] om. D. vno-
D, ante t ras.
436 KAATAIOT HTOAEMAIOT
rov g vg, olcov e<5rlvi\ZE sv&elcc |, xaroa $ r&v
EH xal E r&v avrcbv 8 o- &6r xal rijg plv ZHyivousvys rcov avrCbv <?, -rijfg
ds Z bjioicos vg, dia
roc avra xal xv\v {isv ZB vjtoTivov6av
5 %d %y, tr\v dl ZP roiovrcov v$ scg, OLOV
rov rgfaov OQOV ^ ZA ev&eia %rj, % ds rov rov TQL-
TOV TCQOS rbv reraQtov diacpogov *YIAd sv&sicc tg.
sav [isv KQCC ra |d ocy cupeA&nsv anb TCOV |^
fotipfhfosTffi f][jilv y Af, artsy rcbv tg TOV oAov
10 901; efyxoGta yivo^isvcc 1/y Ay T
TO) rcbv A aQi&{i(j) iv rep oydoq) 6'skid LG). E<XV de ra
v$ K$ dcpA,G)[iv anb r&v avr&v
~ia A^, a xal ccvra r&v Ig rov o'Aov diacpogov
yivQptva, \iy xd jtccQcc&rjdoiLSv O^LOLOS rq) r&v a
15 v TW KvrG) 6ydOK) (jfAt^tw.
ra v ovv dia xrt iv r
rovrov
rov rooitov xr&iJ6rai,) ra ds dia rqv avrov
rov Bnixvxhov xara rbv xxvrQov ndoodov
20 <?ofti> ovr&$.
6t(D ydo 6 xxvrQo$ rrls G^tfvrjs xvxhos 6
1. g] S 4 B. 2. EH xat] HE e corr. D 2. E&] seq. ras. 1
litt., E- e corr. D 2. 3. o^ot'wg] corr. ex |Vl D 2
, mg. ofiotcog D 2.
6. rov TOV] scrips!, roi) ABCD. 8. ra] supra scr. D 2.
xara^ftqpO-Tfcfrat] -^tt- corr. ex dw D 2. 9. roi)] corr. ex
TO D 2. 10. iy iy] in ras. D 2
. 11. I apt^w] supra scr. D 2,
infra est ras. 3 litt. 12. v$\ corr. ex re in scrib. A. 13.
corr. ex H D 2. 14. ofiot'cos] comp. D, corr. D 2
. f a^fO-f
corr. ex 1? D 2. 15. avrw] om. D. 18. avtov] om. D.
19. tTrtxvxP.ov] post -t- del. nedov? D. 21. ABTJ]AEP C.
MA0HMATIKHS STNTASE.QS E'. 437
xvx-
7tol Kvroov rb E Kal did^roov rv\v AEF,vositi&G) rb Kvroov rov dice [ifawv r&v
Aov TO Z, Kal dia%&i6r]<:; ri\g BZ4 v
KarQcc r&v vjtb AZB KCCL JTZz/ y&vi&v roiovrcov
,otwv efalv aC d ooftal T|, ortQ ^v^ccLvei rri$ cbro- 5
?,orav nv iitl rov B y rb Kvroov rov sjtiKvxkov,
V7tCCQXOV<Srl$) rav $' 1*1 rOV ^/, [lOlQ&V ^K.
Kal S7tit> V%&l<5G)V r&V
Kal E4 xd&roganb rov E jtl r^v 10
fi EH.roCvvv
r\vitb
BZA ycwtcc roiovr&v
0rlv o%, OLCDV ai/3 6^-
T|, ty av Kalfj
15
7tl Tij? EH 7CQi(p-
BE
QSLK roiovrcov x
farlv 6 XQl rb EZH
TO
d' M rrjs ZH r&v Kout&v [Eucl. Ill, 31] i? 20
v I' xal r&v viz avras Kocc zv&si&vi]
1. Sidpfrgov] corr. ex ^ D 2,
ut saepius. 2. Supra vo-
add. f^V^co D 2. 4. AZB] corr. ex BZA D 2
. FZJ]corr. ex FZA D 2
. ycovw5i>] corr. ex ycovfa D 2. 5. 60<9m']
supra scr. D 2. 6. ^] corr. ex r\v D. 7. I] corr. ex a in scrib. C.
9. %ca] oin. D, comp. mg. D 2. E4] corr. ex E^f D 2
. xatff-
ros] corr. ex T D 2. 11. BZz/] in ras. A 1
.i] EH] add. A 1
.
12. ITTFI] corr. ex inl A. 14. at] t^fflv at D. 18.
J<mV] corr. ex stair D 2. 20. ^' ITU] ^a Ttf^t D, ^s
litt D 2, 19 d
j
Iwt mg. D 2. 21. >tat] om. D (macula obscu-
ratum?).
438 KAATAIOT HTOAEMAIOT
[iv EH 0TaL TOIOVTGOV Qy vl, oiwv sGrlvf)EZ
v7toTLvov6a px, fjds HZ T&V CCVT&V |. &6T xcct,
o'icov 6tlvf) iilv EZ iisra%v T&V XSVTQ&V 7 #,
^ (f X TOV KSVTQOV TOV XXVTQOV [& JLUX, TOl-
5 OVTWV i(frai xalfj per EH ev&sta y vg, ^ df Zff
T&V avrcbv 7i 7. ^al exel TO KTCO Tys BE hsltyccv
TO KTtb Trig EH 7t0i t anb T^S BH [Eucl. I, 47],
SGTCCI, xal exaTBQK [Eucl. Ill, 3] T&V BHxal AH t&v
KVTC3V^I/rj wy' KHSTS xal oA^ {lev r\
ZB TOIOVT&V i<5t\v
10 vd y, olcov IGTIV % [isv ZA r&v itQ&T&v OQCW ^, v\
ds ZF T&V dsvTSQ&v OQCOV A-01
Kfi) rjd' v7tQO%r) av-
T&V K A^, AoiTtr] dfj
Zz/ T&V KVT&V ^/y jtZy.7td
OVV TK I T&V [lV V$ y V7tQ%Sl v, CC7tQ TG)V X A^
TOV o'Aov dicccpdoov ^xo6Ta yCvsTai, i^ !/rj,T&V d
15 Ijiy [iy Tolg 7g tj? KTISQ xccl ccvTa TCOV K A^ t,r]xo6TK
yi'vTai, {i xa, ra ^v tf 7^ d^Aovdrt xaQOCJhltiopev v
T& vaTG) ^eAtdtcj TOO T&V A KQi&iup Tvjg ajro^g, ra
df fij jftt TG> T&V ^3C, TOVT0Tl,V TtdklV TCS T&V | dttt
TO tfpos Tatg 9 ovro^ roi) TtzgiyeCov i<Sodvvcc^iv XCCTOC
20 TO KTtOGTrilLtt TYjV T&V 1 aTtO^V Tfi T&V ~QX.
1. py] in ras. C. EZ] -Z in reparat. D 2. 3.
corr. ex H0 D 2. 4. 5' x] de|x A, ds\t* A 1
.
TtfcVrov C. 5. ftftca] (7^ D, -v del. D 2. 6. BE] EB D.
8. BH 9. ccvr&v] om. A, BH H4 mg. A 4. 9.
jZrj] corr.
ex (I7r C. olrj] -A- e corr. A. 19] supra scr. D. ^rtV]
comp. JB, <'D. 10. Z^] ZHJD. |" 20. px] mg. D 2. 11.
ZT] corr. ex ^P A. Ante Hd- del. Toto-yrcov D 2. 12. ZJ]
corr. ex Zz/H C 2,J Z D 2
. 13. ovv] comp. ins. C 2. 15. fly (alt.)]
supra scr. C 2. ansg v.ai~\ supra scr. D 2
,KKI etiam in textu.
16. iv] ins. D 2. 17. ^i/arw] AC, $ BD 2
. 18. waiterw] A,
cornp. BC, r;'rot D 2, supra scr. yg. r
f D 2. 19. -tuts] 9 D 2
,/' supra
scr. D 2. 6Wog] -TOS supra scr. D 2
.
MA0HMATIKHS 2TNTASE&Z E'. 439
TOV KVTOV dfj TQOJtOV XCcl 7tl TG)V akhcOV 7tQL-
ra ywopsva sfyxoGTa r&v diatpogcbv iiti-
Kara rag>
xzsd'i,[i8vcc$ TQSIS vrtQO%<xs
7tl
TG)V V TG) XKVQVl KQl&[lO)V filCt TO KCCl Xtt CCTtO t&V 5
7tl TK 7tQiyLa polkas ^7t TtQOs talg rov
c, [loiQcug KTtagxi&Gftm, Jtags^'na^sv (p'
TG)V
dice
- 10
ra
tit avr&v rcbv
r&v dia rotiovrov
7tl r&v QrjxoGr&vW. xaC itinv 6 xccvav 15
Na
Y.U- mg. A 1.
comp. AC, corr. ex
e corr. D 2.
2. yn/d^fva] yiaD, et similiter saepius.
-craft- corr. ex Gaiy, D 2. 4. T^Tjftara 5. nuv6vi\
5. &Qi&ii(bv\ corr. ex g D 2. 6.
D 2. gn] corr. ex QN D 2
.
9. [IVZOL] corr. ex ftfWoo D 2.
D, 8- e corr.; mg. y(>. s<x(jiOi-
D 2. 12. yivo(isvr]s a^ioloyov D. 14. vnsgo^&v] in
-Q- inc. fol. 117V B. fiijrs D.
OVTOS add. B fol. 117V :
^irjrs D. 16. Post roi-
v.a.1 tnl T&V 8C ccvr&v xat TOV
a'. 01 Hoivoi ccQi&noi ot sv TOO a. OEhiSifp inl [lev TOV B*a! r J f Z cefodLov nQi%o<vGi Tag WQIGKOHEVCCS &v TO> B ctU-
diat TOV T&V ycovi&v navovog l^affrotf sni TOV KCITO. KOQvcpi]v ini
rbv TJI.IOV T) Tj]v G&r\VT\v otxfi'ooff 7fQL(pQeLccg T&V di' KVT&v yqcc-
cpO[iva)V
440 KAATAIOT nTOAEMAIOT
snl de rov'
nal rj
f
GsUStov rag anb rov angifiovg
anoysCov rov sniY.vY.kov snl rb Y.svrgov rfjg tff/bjvrjg i}u,iGsiag
polgag :
snl ds rov -91
'
Gski8ov rag rfjg pici^g &no%f]g [loigag rfjg
Gslr\vr\s tfroi anb rov fjMov 7}rov Kara Sidpsrgov avrov Kara
rr\v syyvrsguv SidcraGiv :
B. 5rorpaHa|ftg ^Mov inl rov diu rov nuru xogvcpriv ncti
rov nivrgov rov rjMov yQCCfpopsvov ptyiGrov Kvyikov :
T. rov GTtwvY.'kov rfjg Gefajwrig uccra rb anoyeiorarov rov
iwsvrgov ovrog v.a\ rfjg ce^vrjs nccra rb anoytiov rov sitiY.vKl.ov
ovarjg TCKQKMct&Lg lit\ rov diet rov Kara. xoQvcprjv cr]^itov v.ai
rov yiivrqov rrjg Grtrjvrjg yQcccpopevov [isyicrov *v*%ov :
A. rov 7iLHvy.l,ov rfjg Gfhijvrig sni rov anoysiov rov
ovrog, rfig Ss Gf^vrjg Inl (rov eras.) TttQiytlov rov
ovGiqg, r&v ywopivcov rfjg G&r\vr]g naQaM.df(ov naga rag T
ijrot rag anb rov anoyBLOv vnQO%dg :
E. rov iTtwvnkov ri}g ce^vr]g enl rov ireQiysiov rov
rgov bvrog, rfjg ds G6^i]VT]g Inl rov anoyeiov rov
g. rov 7tiKvy.l.ov inl rov Ttsqiysiov rov iy.y.ivrQOv bvrog,
rfjg Ss G^vr]g enl rov neqiyBtov rov smy.vY.'kov,r&v yivo-
[itvcov 7taQuM.d,(ov viiSQO%ag Ttgbg rag rov rgirov OQOV nag-
Z. rov tiiiy.vy.'kov rijg Gtlijvrig Kara rov anoyeiov rov
uivrgov bvrog, rfjg de GfX^V7]g ptra^v rov anoystov v.al
yeiov rov fitwvKlov ovGr\g, diayoQai r&v roiovrtov anoGrr]-
[idrcov rrjg Gf^tjvrjg ngbg rb peyicrov ccnocrrjfia, ol'mv ecrlv
T] rov [ifyLGrov anoGr^fjiKrog ngbg rb &d%iGrov v7tBQO%T] f rl'
H. rov iniY.vv.\ov ri]g GS^vrig Kara rov nsgiysiov rov SK-
ovGr\g, ri]g 8s Gsl.r\vj\s inl ra [lera^v rov anoytiov noi
rov STtiy.vY.kov ovGrjg, diacpogai r&v inl rf]g roLavrr\g
nagodov rfjg Gf^vr^g anoGrr^idrcov nqbg rb snl rfjg rov nsgi-
ysiov rov SKKSvrgov ftscscag rov iniY.vY.7.ov psyiGrov
ol'cov scrlv i- T) rov psyfarov ccTtoGrrjfiarog snl rfjg
ftsGstog rov sniKVY-'kov ngbg rb s7.d%iGrov dnoGTri^ia Siacpoga
ovca :
MA0HMAT1KHS 2TNTASE&2 E'. 441
&. TOV STtiy.vY.'kov rf]g 6li]vr]s snl T&V peTa^v irccgodav OVTOS
rov anoysiov v.a.1 itSQLyeiov TOV KKVTQOV diatpoQtxl xo*v yivo-
[tsvcav UTioGTrjiicizav snl T&V st^rifisvcov [isrcc^v nagodcov rov
STtlV.VY,l,QV TtQOg TO TOV KY.ivtQQV KCLtO. TO K7t6yLOV CCVtOV
GTOV anoGTTHLU, oRov IGTLV r) v7tQO%r) TOV psyiGTOv
fiaTOff TOV IY.V.VTQOV TtQog TO &d%i6TOV CCVTOV anoGTripK ?c "kr\'
OVGCC : (des. fol. 117V).
tn^OX^K-
X
*x:
-<
5i
cy5S
^>-3St
a^
442
Tl
MA0HMATIKH2 STNTAgE.QS E'. 443
SfW
i-f i i. i if^r^ri 11
,-V o*S-5-x3SS 53 ?<" .
baaaaaaaeaaa
DOC 000
ite-lfejiiSJIIPISlsll
ooooooooo
>! s- o '>5_\<^> i/> a--
|JJ/. O O O O
-s
<'~3;^5p< Si^ '3.
<! i^:c>*' ^ fl ^= ^.
S IHii r.
444 KAATAIOT IITOAEMAIOT
yg rcbv itaaaA.A.d&cov di,axai6G)g.
f
'Orav ovv TtQoaiQ&yisQ'a, hapfiavsiV) noGovf] Gshijvr]
xa& xa6rrjv r&v naoodcov 7taoaAka66i, nacbrov eni
rov di ccvtijg xal rov xara xoovcpyv 6r]{iiov yaacpo-
5 [ifvov peyitirov xvxkov, 7U6xil>6[id'a, tt60a$ farjpsQL-
catfysi, rov [leGrjiiflQivov Kara rb V7toxi[ivov
xal rag VQ&foas ffawfyxovrfs ig rov r&v
y&vi&v KKVOVK rov ofasCov xMparos xal rov
dodeKarr^iOQiov rag 7taoaxi,[ivas ry &Q10 rd5 dfvrQG) GffadiG)
7} oha$ ^ rag 7H,^a^
[iQi, rrjg aoag f|oftv, ag K7tt%si rov xara
6r){iiov i\ 6krjvr] 7tl rov di avr&v yQayo
yfarov xvxkov, ag i6Vyx6vrg fig rov r&v Tt
kd&av uavova 6xty6iid'a.>xara Ttoiov 6n Grfyov
15 rov tto&rov Gekidiov, xal ra 7taoaxc^iva rc5 aQt,&iiG)
v rotg cp%rig [ira rb r&v fihiax&v 7taoa^d^G)v
r66ao6i, skidVotg ,rovr<5nv r& r y' xal r& d' xal
rd)f
xal r& $\ X^Q^S xa6rov aTtoyoa^o^i^a' 7tira
rbv xar' Xtvrjv rqv coaav diaxexQi^iBvov ri]g avco-
20 [laMag aaL&iibv nobg rb axoifog anoysiov hafiovrfg rj
avrbv ^, lav vjtfQTtiJtrr] rag ^t iLOioag, rbv fainovra
1. i-O1
'] C, &L B, om. AD. SICCKQIGSCOS] SmcpOQ&s D. 2.
iQ03{ie'Q'K] corr. ex TtgocaQOVfif^cc D 2. [email protected] iv ] GY.O-
D, yg. kct[ificcv" mg. D 2. TCOGOV] bis D, corr. D 2
. 3.
. 4. criptLov] supra scr. D 2. 8. ofasi'ov (alt.)]
-- ins. A. 11. xi]g] corr. ex rccs C 2. 12. di' avr&v] corr.
ex dia. r&v D. 14. navivas D, sed -g eras. 15. c^tofyiw]
g"* D, q D 2, mg. KQL&IKO D 2
. 16. TO] add. C 2. 17. TOVT-
6Ti D, comp. B. 18. ^TTftra] corr. ex EHITK in scrib. A.
19. tov\x5>v C. 20. KQiftpov] sov
D, et similiter saepe.21. rag Qn] TCC CQTC C. Supra" rov add. a D 2
.
MA0HMATIKHS STNTASE&S E'. 445
ig rag r% TO r^iiGv Jtdvrors rcbv ovrcog
i0Vyx6vrg eig Tovg avrovg doi&iiovg 6x-
a, notice ^rjxotird icaQaKZirai ro5 aoi&iHp x&glg'
xalv\ o^AtdtG), xal o6a yfsv av v TGJ %
Q&f}, TK ro6avTa %rjxo6Ta 2,afl6vrg rov 5
sv rc3 d' GfhdiG) dioxpogov 7tQo6&ri<50[iv aid Tr} rov
TOLTOV Gskidiov 7taQaMd%i,, o6a d' av v rco r\<5z-
ra rodavra Qrjxotira Aaflovrfs rov iv
diayooov 7too6&ri6o[iv aiei rtdhiv rfj
rovf
(3^idiov TtaQttkkd&i nal r&v ovrog ysvo^iBvcov 10
dvo 7taQaA,A.d,G)v xd"rj06^^a ir\v vTtSQOj^v ^i]g $
&apovrg, o6ag UTtiisi {leGcog r\ <3A.ijvr] {loiQag r\roi rijg
rihianrig 7} rr^g ravrrjv dia[jirQOv6iig Kara %v\v iyyvri-
oav bnorsQag avrcov didtiratitv^ i60L6o[iv xal ravrag
fig rovg v r& a 6kidC(p doL^^ovg^ xal o6a av 15
ai, ita^uv QrjxoGra v r<p &' xal
ra rotiavra ^xo6rd hafiovrfg, rjg
rcov dvo TtaQahka^E&v VTC^o^g^ ra yevopwa 7t
60[iv atel rt] ha66ovi,) rovretinv ry x rov y' xal
6' tifkidiov diaxxoiiivr]) xal ra 6vva%&vra ,o(iv, 20
a 7taQakkdo'6i, 3] Gfkrjvr] 7tl rov di? avri]g xal TOV
%ara xogvcprjv 6r]{iiov yQacpo^isvo
avr6d'v artkcbg xal
1. rag] corr. ex td\ D 2. r^] e corr. D 2
. Travrort] -v-
e corr. D 2. 2. iGe\vyv.6vTSs A 1
, 6ia|fi;fyxdvrfff A. 4. rf]
supra scr. D 2. 5. ia^dvovres D, corr. mg. D 2
. 6. ctki-
Stuv B. 7. TQLTOV] 7 BD. aelidfov] supra scr. D.7;']
dydoco C. 8. ra] supra scr. D 2. 10. ovr(o>| D. 12. TJTOI]
Om. B. 15. a:'] Trpcbroot C. sdv] &v BD. 16. Ttagd-
D. jraltv] supra scr. D 2,ndhv C. csfodLo) KCU
oD. 17. /La^tovrfg A. 18. ywopsva D, corr. D 2
.
19. lld.G6ovC\ corr. ex g mg. D 2. TOVXSGXLV\ comp. B, -v
del. D. 21. jraeodaget D, corr. D 2.
446 KAATAIOT IITOAEMAIOT
Kara rqv bpoiav &6iv f'vfxa rcov
fx rcbv iv rc5/3' tiehdiG)
rfj TtrjAlXOrrjri, rfjg djtO TOV KCtrK XOQVCpYjV
5 Lva ovv xal rqv xobg rbv dia {isG&v rcov
rots yivojisvrjv TtaQKhkafciv diaxQivoyiSv Kara rs [ifjxo$
xal Kara nhdros, rag ccvrag xdfav far)[iQiva$
&S aitfysi, rov [iftiypfigLVOV % 6hijvr]
sis TO VTO [ifyos rov r&v ywvi&v xavovos iti(5K-
10 il>6[id-a rs xaQaxi,[ivas r& apt-fruca r&v &Q&V ftot-
gaS) av plv TtQO rov n<5rnifiQivov fj % ^fA^V^, rag
iv ro5 y' tiehditp) av d [ira rov [isGrjupQivov, rag
sv r& d\ xav yiv dvrbg r&v Q poiQ&v &6w^ avrag
ajtO'yQaip6{id'a) iav d' VTISQ rag 9, rag tentovtiag ig
15 rag ^Mt' roGovrcov yap k'tiraii\
ka66G)v rcbv itsgl rr\v
KKL^Lvriv ropfjv ycovi&V) OL&Vj] fiia 6od"?i 9. rag
a7tO'y'yQa[i[ivag ovv poiQag diTtk&Gavrsg sfaofaopEv
fig rb r&v iv xvxhG) SV&M&V xavoviov avrdg rs xal
rag ksntovtiag lg rag ^JT, xal bv av %r] Aoyov rj rrjv
20 r&v dfdiTthioiiw&v poiQcbv itai(pQiav vitorsivovGa
vd-ta Ttobg r^v vitoruvovGav r^v teiitovtiav fig rb
v,
rovrov | rbv Aoyov ^ xarcc itkdrog
g nobg xr\v xara ^tijxog, f7tfi,drJ7to ai xr^'ki-
1. fVtxfv D. 2. iv] s A. 5. iitccov] corr. ex jwf'dca D_2
.
7. Kara] om. D. 9. ycovi&v~] corr. ex yco^ico A 4. 11. ??]
corr. ex T\V D 2. 14. a.TtsyQutydyisQ'cx. B. d
J
] $s D. VTZSQ] -E-
e o6rr. C. 15. git] Q7t polgctg D, -n e corr. D 2. sldcoav]
I D, corr. D 2 et in mg. 16. Post ofav add. av D 2,sed del.
17. flaoico^isv diTtiwcccvreg D. 18. x-yxAra] nv D. 19. avcorr. ex &it%'fl D 2
. 20. vnoTftvovcas fv&tias D, sed
corr. 21. rag Hfinovcas D. 22. r}pwvKhov~] o_ D, dcorr. mg. D 2
.
MA0HMATIKHS 2TNTASE<> E'. 447
Kavrai rcbv xvxAcov itEQtylQSiat, adiayogovGiv
itokv7ika6idt,ovr<s ovv rov aQi^^ibv r&v
v&icov 7tl rr^v VQi6xoiivr]v cog && T v diet rov
xara xogvcprjv Giftitf&o yQacpopilvov xvxAov Tt
xal tec yLvopfva pQ%ovrg lg rov
rov iLQt,Gpov Gwayoiifva police Qopw iv\
xara
OTttV (iV TO XCCrd XOOVCpYjV 6r][llOV 7t rOV [l6r)[l-
r rov ror 6ovttvovvros rov 10
TG>V
nobs ii0r][if}Qiav avrov, orccv dl vori(brQov $ TO XCCTK
xoovyqv rov [i6ovQavovvToS) ngbs rag KQKTOVS fj
arog 6rai 7taQccM.ais, iitl $ t&v Kara ftijxo^,
at ytrj^t,x6rr]Tg rear iv TG) xavovt, TtaQaneiyid- 15
v&v ycovicbv rv\v ait' KQXT&V 3tQt,d%ov6i T&V dvo rcbv
vnb rov 7to[ivov r^tjfjLaros rov diet [i6&v xccrQO)&v
TtQi%oyiVG)v, Ttfc plv Kara itAccrog TCaQaMd&cog itgbg
CCQXTOVg yiVOlLSVYlS, <XV [lV [1%G)V % 6^0-i}g ^ XXl-
ycwia, ig ra TtQoriyov^va rcbv fydicov f)Kara 20
TtaQaMa&g, iav de &a66G)v OQ&ijg, ig
rd 7t6iLVK) rrjg $ xarcc nhdrog Jtaoa^^d^fcjg agog
yivo[ivr]g avuitaKiv, eav [ilv [ififav r}
r\ xxL^ivrj yoovia, fig rd jto^ivcc r&v
4. orjjLtftoi;] D 2, comp. D. 5. Y.CU TK] supra scr. D. 10.
97] corr. ex r\v D. TOV (alt.)] TOV\TOV D, corr. D 2. 1L Supra
7) add. g D 2,sed del. 12. vorsiOTfQOv D, sed corr.
r]] corr.
ex r\v D. 13. rag] om. D. 14. itctTog] corr. ex nldrovs D 2.
^f] supra ras. 3 litt. D 2. Kara] v.ar- D. 15. Y.O.VOVIK> D.
16. 7t8QL%ovGr) D, corr. D*. 17. *enfya&ev] -ftsv corr.
ex ve[i D 2. 18. n^drog] corr. ex nldrovg D. 21. sidecar]
S D, ttdrrcov D 2. 24. OQ&TIC] corr. ex oQ&rj D 2
. yoovicc]
comp. D, ut saepe.
448 KAATAIOT IITOAEMAIOT
rj XKTK [if}xog <5TKi TtKQccMa&g, eav d skaGGcov OQ-
'a fifVrot rots
i TOV tfhov G>g p?#v ccfad-yrbv KVTOV
5 (SovTog ovx ayvoovvTsg, on rtouJGfi, TLVCC TCZQI avra
xciravvor][ivr] xal TCBQI avrbv x t&v
tt&s ,aktf 7ti pi} ovr&s c^rfkoyov
ra (pKiv6^VK dice rovto 7tccQaxoA,ovd"ij-
nvcc
10 avv rijs roiavrrjg 7ti6Td6G)$ $$&%&$ ye
o^uotog d xal agog rccg
rjQX6frr][jLv ratg agog rbv dta {ifaov rcbv
xvxhov yivouwcug vitb rov dice rear 3t6ka)v
rov oQ^ovrog yQayoyiwov yiyi<5xov nvxhov ytQt,cp-
15 Qffaig r xal ycovicug ccvrl rfbv ngbg rbv Ao|6v rijg
6^YjVrjg &O)QOVlt,VG)V ,1ti TO {lV V rctlg fXfolTtTl-
xaig GvQwyCttig (S6^ivov itaQa rovro didtpogov avsit-
afa&rjrov i\v, TO db xccl TavTa
T Tcclg di%6i,v xccl Qi
yc)dg iv Totg
20 G)Ql6[lVG)V Xtt&' Xa6Tr]V TG)V TCi TOV
d&v T^g ^^vrjg xccl T&V aTtb TOV tfwdfap&V
)akka xal Totg pzyi&sGiv xal Talg &<5<5iv ccvTCitg
iva d' vxaTav6rjTov yivr\rui TO teyoiiwov, IxxsC-
1.|u.7)xo?] supra (i- macula A. 8s] d' B. &dGa<ov~]
^ D,
V) D 2. 5. &yvoovvTs] &y- in ras. 1 litt. D 2
. 6. avr&v D.7. s^S D. 8. TtsQi] supra scr. D 2
. rovro] corr. exrovrov D 2
. 9. OJGTE D. nvcc] -v- mut. in ft C 2. 10. yf]
AD 2,TS BCD. 14. OQI^TOS D. TifQLcpSQSiais rf] -SQSIKIS rs
e corr. D 2, neQicptQicpsQEictis re C. 18. Post TKVTKS del.
auras D 2. 19. deit-toi D. 22. utys&eGi D. d mg. A.
24. d'] 94 D.
MAOHMAT1KHS STNTASE&S 449
to filv TOV diK pfacw T&V tydiov xvxkov
TO ABF, rov ds Ao|oi) Tyg Gf^tjvrjg TO
xccl 6vvd6{iog {Lev v TO A Grjpetov, Trjg
TO
z/, xccl
dnb TOV
dux
sill TOV
TCOV ca-
TOV
ds itokog
TO E 10
KOI ys-
di CCVTOV [ie-
TO E4 Z, dice ds TOV B
qv4H TtsQKpeQSLccv, 15
dia ply TOV XWTQOV trifc
TO EB, 7taaaMcc66sTG) TSi\
xal 'ysyQccy&GxSccv tit,' avTov nobs Tag B4 xccl BZ oofrccl
CCL H KCCl HK, &6TS T&V [lV KKTCt [1^X0$ d,7tO%(bv
TOV GwdEGpov xr\v ^LSV ccxoifiii yCvsti&ai TY\V AB, Tqvtie <pccivo[ievr]v TTJV AK, T&V $ xaTa xhaTog anb TOV
dice ii6(ov TV\V plv axQiftfi TV\V B4, Tqv df cpcavo[ie- 20
vyv tv\v KH, xal T&V axb T^g 4H Ttobg TOV fe
&G)QOV[lVG)V TtaQCdhd&GW XCCTCC ^XOS 1*>V TT}V
rri H, xaTa nbaTog df Tqv foyv TTJ
1. rb (Jilv rov] rov [t,ev D. 2. r(ifj(iu TO] corr. ex
TO$ C 2. 4. KSVTQOV] x/ D,
ovadd. D 2
. 12. 81 UVTOV] corr.
ex dice rov D 2. 14. did (pr.)] corr. ex rt D 2
. EJZ] corr. exW txy
EAZ D 2,mut in EJ"Z' B 3
. 15. nsQLcpEQStccv] t, D, 7 D 2,
nag. n D 2. 16. 8C avrov] corr. ex SLU rov D 2
,6Y uvrov H
Halma, fort, dice rov H. B4~\ corr. ex BA D 2. BZ] ZB D.
17. xca] om. D. 21. r&v] corr. ex tr^v D 2. 23. &H]
"H0 B. fojjv]'
M D,^ add. D 2
.
Ptolemaeus, ed. Heiberg. 29
450 KAATAIOT IITOAEMAIOr
fad ovv fj pV AH xaadMa&g fvafaxfrai, dta
7taoxr&i,[iVG)v rijg EA 7tQi(pSQiag doO-ft'tft?^
xarf
oa $ r&v A xal H TtaoaMafeov rrjg vnb
PZE y&viag Sofafays 9 ftfiflg d' v rotg [i7tao6d'v
5 aitd%aiiv rag itobg ra do&wra rov tydiaxov Gq-
[iia yivopevag rov did rov xard
r xal ycoviag^ [i6vov d' %o[ii
rov did [i6(ov GYjpftov rb 5, tpavfoov, onrift
EB 7tQt,(paia 6vy%aG>nd'a avrl rijg EAy rr\ $ VTCO
f 10 FBE y&vta avrl rijg vnb FZE.b [iv ovv
r
'l7t7iaQ%og 7te%CQri6e [iv xal rqv roi-
avryv diOQ&cotiiv TtoiiJGaG&ai, ,Jtdvv d' dvfrtiGrdrwg
xal Jtaad rbv Aoyov avry <paivrai
jcocorov [ilv yag pia diaGraGft, rrjg Ad15 xal ov%l Jtdtiaig T) stA^to^fcv, ortQ %v dxoAov&ov r&
xal xegl r&v HIXQ&V dxaif$oAo'yi6d'ai,
iti,ra xal nfaiotii rotg droTt&rfyoig fAaO1
.
itd yaQ xal avrbg rag r 3tQig)aiag xal rag yoviag
rag jcobg rbv did pfe&v r&v a)diG)v
20 rvy%avv 3rQoajeoddi%(bg, xal on rrjg
fiAH hapfidvfrai,' rovro ydo iv rw nacbrG) r&v
3. &H~\ corr. ex 01 B 3. 7rapaHa|fcor] pr. -a- eras. A.
4. TZE] corr. ex IZE D 2. 5. r. do&evr. D, ut saepius.
crjfitlu ywopsvccs] compp. in ras. D, corr. D 2. 6. rov (pr.)]
in ras. D. dia rov\ bis A extr. et initio pag. 8. 6r]^toov C,
c?D, CH D 2
. 10. i,no] v D, add. D 2. TZE] corr. ex
ZE D 2. 11. fwf^ft^rjdf] seq. ras. 1 2 litt. D, corr. ex
cnts%KLQr]G B 3. 14. Ad\ AE D. Gvy-AS^grixai] -y- corr. ex
v D 2. 15. nlsioGiv] -ft- in ras. A. 17. nteloGi\ corr. ex
itteCoGiv D 2,mut. in nteioGi C 2
. rots'] om. C. aroncorsgoLs]&- add. C 2
. !&cc&8v] -v del. D, Hafts B. 20. trvyXuvi- BD.
7fQoanoSdi%o)g~] -to- corr. ex 3 litt. D. try?] A, anb rri$
BCD.
MA0HMATIKH2 STNTAEE.QS E'. 451
Qb$ rr\v T^S
7tQl(pQlCCS $6(5LV TTj T EZ 7tQl(pQia Xttl 11]
vnb EZF ycovfa &s ddo[ivais' ovr&g yaQ iv rat
dVTQG) TYJV Zz/ 7tl,A,0'yi,Gtt[lVOS KCCi
vnoTi&Tai,. nagriyaysv ambv ptvTOi TO
diori TO B xal ovyl TO Z 6rj^t6v i$ri TOV dux
TO dfdoiiwov, xal dia TOVTO T&V TS
EB dfdoTat, Kal ovyl f}EZ xal T&V ywvi&v fj
VTCO
EBF xccl oi)%l r)vnb EZF. k'v&sv KVL\ ngbs to 7toir[-
TLVK xav [iQMr}v didgftcoGiv KeuivriTcci nob- 10
yi,vo[jivr}s afa&rjTfis itavv diacpoQag T&V EATCCS EZ dltt TO 7toAi> H&M.OV KL-
v&v avTccs ^ dfdoG&ai,) Tijg d BE Tijs t& ovn ds-
donwrjs -Y\ XQOS xr\v Ed dicctpoga TO nkei^Tov dioitist,
[IOVG) TG) TijS B4 XCift' XCC6Tr]V T&V CCTfO TOV 6VV- 15
TO pvrQi Tils Math fbv vyii] TQOXOVaxohovfi-ov ysvoiT* civ fjjilv VTC
<5TK> yag c3diaxb$ 6 ART KOI TtQog byftaq CCVT& 20
6 4BJS, i\df Gfkyjvr] iJTOi, XCCTU TO 4
r}KCCTCC TO E
Kara nhccTos TOV ABT dia [i6cov T&V %&-
1. naQcdKY.Twwv D, corr. D 2. ccnodsfavvGi D. nqog] Ss
B. 2. Ez/] corr. ex EA D 2. 7tQupSQ8ia] corr. ex ^
at
mg. D 2. wi 3. ycovtoc] mg. C 2
. 3. EZT] E- corr. exr in scrib. C, -r ins. D 2
. 4. Zz/] -J e corr. D 2. 9. ov% D.
11. ywo{ivr]s] -g add. C 2,
corr. ex J^ D 2. 12. itoliv] -o-
corr. ex v in scrib. C. 13. tie] <? FE C et B (F- e corr. B 3),
corr. C 2. 14.
17]corr. ex xf\i D. TTJV] xr\ A. EJ~] corr.
ex EA D 2. TO iffaiGTov] TO nte?- in mg. transit D. 17.
V.KTCC] -TO. supra scr. D 2. 21. z/BE]z/-e corr. C. TJ] in
ras. D 2. 22. wra] bis D, corr. D 2
. AST] AT D. r&v
-AVV.\OV] om. D.
29*
452 KAATAIOT HTOAEMAIOT
dfav xvxkov dedo[ievqv ftfiptqp^p&at^ olov rrjv
xal rv\v BE, &6re rag pev Ttgbg rb B 6r][ieiov rov
<pdi,axov 7tQi(pQiag anb rov xara xogvyijv xal yco-
viag dfdoG&cu, fyrsZG&ai, df rag agog rb 41}
rb E
A
E
lav plv dr) roiavryv %y ftltiiv 6 fwdtaxdg,
agog ogftag ycoviag slvai r<p dia rov Z tf^fm'ov, o
rt6hog rov OQ^ovrog, xal dia rov B yoa-
vxAep, olov rcj Z5, GvimeGstrai ov-
10 rog dr]kov6ri, rfi 4E TCSQtcpSQSia, xal ^ l*<v y&via f)
ra z/ xal E fteoaovinEvrj adidtpoaog etfrai rijg
rb B vjcoxsi^vrjg' ooftal yao xal at dia rovrov
rbv tydiaubv ywopsvai' ri\g de ZB<i] plv ZJ thaGGcov fGrat, ry BJ, rj
ds ZE15 rfl BE dsdojisvaig xal avratg.
sav ds (Svintiitrri 6 ABF fydiaxbg rti dia rov
xara
2. Supra v.af add. tf D 2. 3. 7ttQicpSQiK$] om. D, 9" supra
scr. D 2,
TC mg. D 2. 4. TO (pr.)] corr. ex ra. C. 6. %ft D.
8. 8ia] supra scr. D 2. y^aqpo^vo)] -w e corr. D 2
. 9.
/nfytcrca] corr. ex neyLGros D 2. xvx^oo] -w e corr. D 2
. ZB]BZ D.' 6vv7tf6ircu ABC.^ 11. z/] corr. ex A D 2
. 14.
corr. ex 2,A D 2. skaGGcov] comp. D, s^drrtov mg. D 2
.
15. BE] corr. ex KE D 2. 16. cv^mnrr]] -vfi- e corr. D 2
.
17. yQKcpotitva)] corr. ex I^w/ D 8
.
MA0HMATIKH2 STNTASE3S E'. 453
xal V7to&[ivoi, itokov rov bgi^ovrog TO Arag Ad xal AE, xal avrat, dioitiovGi rijs AB
<pQiag xal ai vito BAd xalA
BAE y&viui rijs {irj ovdiqg
7tQorQov. didovrat, $ ai $iv
Ad xal AE rov Aoyov ovrog
G)g 7t' V&IG)V dia TO
aTfo r rijs AB xal
xal BE dfdopwcov ra
ait avr&v 6vvr&vra 10
ra ccTCo r&v Ad xal
AE [Eucl. I; 47]* axohovftog
$ avralg xal ai VTCO BAdxal BAE y&viai.
rijs ^ vov fydiaxov &tia)s yxxfa[ivr]S) &v aitb 15
rov Z jrdAov rov b^L^ovrog 7tL^v^G}^iv rag ZB xal
ZHd xal ZE* dfdouwr) u,v 6rai ii r ZBxal rj vnb ABZ ywvicc xccl itccfav d^Aovdrt at
xal BE. o(pikov(5i,v d do^vai ai r Zz/ xal
ZE TCQi(pQiai xal ai VTCQ AHZ xal VTCO A&Z 20
yovmt, didovrai, dl xal avrau xa&rcov affiziGtiv 7cl
rrjv ZB r&v AK xal EA.
7tidri ya() i\VTCO ABZ y&vi'a
2. AA *ai AE~\ e corr. D 2. 3. at] i] BD. BAJ] corr.
D 2. xa^(alt.)] xalvwo D. 4. ycovfai] rm
atD, ycovicc D 2
.
5. didovrui] supra scr. D 2, mg. dtSovrut 8t D 2
. 9. xal
BE] 8 D, p D 2. 10. &n'] corr. ex vn D 2
. 11. TWV
rf)s D. 13. at] i] B. BA4\ B- postea ins. D. 14. xat
om. D. 16. 87ct,&vcQiiv~\ -f- corr. ex | D. 19. xcu(pr.)] om. D.
oysttovGi D, -GI e corr. D 2. 20. xal vno] xal at vno C,
om. D. 23. c'jmdTf] -drf in ras. 1 litt. D 2. yap] supra
scr. D 2.
454 KAATAIOT IITOAEMAIOT
TtdvrorYI
VTtb ABE, didorcci, roc BK4 xccl BAE 60-
froycbvicc xccl A(fyo rife ZB Ttgbg ras itsgl rr\v OQ&TJV,'
tiersTtd xccl Ttgbs ras 4B xal BExal CCL Z4., ZE vTtOTwov-
do&riGovrai, did rovro
xccl ai VTtb 4ZK nal
b EZA ycovicu vit8QO%ccl
r&v STti^rovfievcov
^ ftt> yctQ VTtb AHZ ftt-
10 o>v serlv rfjs VTtb ABZtfiVTtb^ZB, % ds VTtb AZttdttav rijs VTtb ABZ TyVTtb EZA [Eucl.I; 32]. <pcc-
vsgbv d\ on, xal TtfofaTYi
15 yivsrai dicctpoQa rri$ av-
rrjg KKX& Tthdrog atfo^t
OTKV rb B GriiLslov avrb % to xat<x
Ttgbs rb B yi,vo[ivr]g ycovias KI Ttl ra
rov xccroc KOQV(pr\v ogd'ccs Ttoiovtiw Ttgbg r& Sco-
20 diccxa y&viccs' r&v d 7tQi<pQi$)v ,orccv
r\ ccvr^ &-6i<3 r]' pydfiuag yccQ Ttdfav ywopwrjg Ttgbs rb B TtQi-
<pQi'ocs CCL TtQbs roc z/ xccl E ryhxccvrcu faovrcci,, r\U-
rCbv [lev
xccl E
1. ndvcoTt] -ro- e corr. D 2. BKJ] BJK D. 69^0-
a
ywvia] ogftoyavi D. 2. ZB] EZ D. 3. rag] supra scr. D 8.
JB1 mut. in BJ D 2. 4. af] rj
B. ZJ] ZJ wi D. 6.
v.di (alt.)] yicd KI D. 7. EZA] corr. ex EZA A, ex ZA D 2.
10. HTTtV] comp. BD. 11. JZB]'J- e corr. D 2. Ss]
3' D. 12. ABZ rjj vnb EZA] in ras. A 1. 15. ym-rca] yive-
renouat. C 2. 17. 77] corr. ex i]v D. 18. yccQ~] comp. D,
corr. D 2. TO] D, rca D 2
. Y.KL] supra scr. D 2. 20. 17] A,
avrfjs rj BC, Kvrrjg C 2,
TE D. 21. ij] seq. ras. 1 litt. D.
TO] mut. in TW D 2.
MA0HMATIKHS STNTAgESiS E'. 455
av (btfiv xal aC ri}S xara itkdrog Ttagodov rr^g <5e-
xal orav dgfrbs f] rtQOS rov (pdi,axbv 6 dice
rov xara xogvcpijv' oty yap nafav rq Kara
itKQodcp diofaovGi rils ZB al Zz/ xal ZEev ds rats aMcug &60i,v tyxfavoiisvys rij$ 4Errjv ZB ai re r&v TtSQicpSQSLcbv KOI aC rcbv ycovi&v
V7tQO%al lid TO sAarrov 6vvayftri6ovxKi. &6xe xcu\
orav ILSV ILOIQCCS fj 6A,ijvt] Kara, nAdros KTttffli rov
diet [i6G)V) fj jtfafarr] diccfpoQK r&v rtccQccMd&cov 6rat
dflxcc k'yyitira, QrjxoGrcbv aC ycty rov psyfarov dicctpo- 10
QOV T&V 7tQt,CpQLG)V yiOlQai T06CCVrK TtOlOVGlV ^-xotira itaQKM.d%&$ iitl r&v ^yfat&v viCQO%G3v xal
orav $ r^v ev ral$ $\kioi-
itdgodov ait%fl' avrrj d
yivtrai [nag poiQag fyyitira xal fjpfaovs' ra l'6a %ij- 15
xotira a /.' didyogov e'Grai, rijs TtagaMd&Gos rov roi-
ovrov Gitavi&s 6v[i7tfarovro$.
% jifiWot p&odos ^ XQOS rqv roiavrrjv
rcbv T y&vi&v xal rcbv jtQi,(pQiG)v ysvoiro av
%iQog rolg f}ovko[ivois &$ & ovr&s piXQotg Ad^otg 20
rov TQ6jtov rovrov. xa&okov yccQ rov rcbv
1. <a6iv\ -v eras. D. ca] cci &no D. 2. rj] seq. ras. 1
litt. D. 3. yap] ^ D. 4. ZB] seq. ras. parua D. xat]
om. D. 6. ri\ corr. ex XL in scrib. A. TtfQifpeQSi&v] 9 D,
^5 -^2
>et similiter saepius. 9. TtteiGrr}] -i- corr. ex a in
scrib. A. 10. SSKK] corr. ex Ss <5* C 2,T D. fyyurca] ir1
*
in ras. D 2. f|r]xo0rwv] ff renouat. D 2
. psyiGrov] e corr. D 8.
14. sKlefys D, -GL add. D 2. 15. jipfaovg] in ras. 1 litt. D 2
.
d mg. A. 16. a/.']
in ras. D 2. 19. r&v (alt.)] om. D.
20. ebg iv\ cbfv B. 21. rov (alt.)] corr. ex robv C 2. rwv]
c
corr. ex rccg D 2. ycovi&v\ corr. ex YOJ D 2
.
456 KAATAIOT HTOAEMAIOT
v di7th(b6avrg Kal sfasveyxovrsg fig to r&v sv
voviov ra 7taQaxi[iva avrti r xal
TOJ tefaovn sis t&S t&v tfvo OQ^COV poiQag QX X&Qlg
7tokvnka(Sid6avrg rtl rag rov nAdrovg potQag rb QK5 exarsgcov Kjcoy^a^o^s^a xal ra IK r^g itQ&rrjs ycovias
ysvopsva a<psfov[iv psv ajtb rfjs vitoxsiiisvrjg dnb
rov Kara, KOQV(pr\v TtSQiysQEiag ,orav enl ra avra
fi
rip xar& xoQVtprjv f] 6s^v^^ 3tQ06&"iJ6o[iv da, orav
sill ra wavria, Kal ra yv6^Lva itoi,ij6avrs eg? savra
10 6vv&vrs r rolg BK rijg kencovGris y&viag ywopwoigKal avrotg r&v <5vva%&vr&v rv\v
ra x rijg keiTtovGyg yavi'ag d
KarovraKiKaieiKo6aKi, itoiri^avrsg Kal
15 ig rag fvyqiievag 7tgi(pQiag r&v rotg
itaQaKtiptvcw itQi(pQiCbv V r& Kavovi r&v
rag Ji(U<ffa$, av plv pziCfav y 17 dt,G)Q&a)[ji,vr)
<ptQia rr^g TfQcor^g^ 3tQ06d"tJ6o[iv ralg rijg
y&vCag, av dl ^d66c3V^ d(p^.ov^iv avr&v, KOI
20 Kal rqv ycwiav di&Qd-oiLwyv.
dl VXv ftfrMttltfJNo ?tl rrjg
fj pl
1. comp. in ras. D 2. 2. Y.UVOV
LOV C. 3. TOJ]
TO D, r& 1 D 2. 4. tov~\ in ras. D 2
. px'] px A. 5. yeovfog]bis C, corr. C 2
. 6. yivopEVK D, corr. D 2. 7. rov] -ov in
ras. D 2. TtSQitpegfiag] comp. renouat. D 2
. $] seq. ras. 1
litt. D. 9. eavta]- ins. D 2
. 11. zrQccya>via&i6iv D, sed
-v eras. 14. !xaTO*>raxntai(.xo<JGx mg. D 2, Q v.ul x D. 17.
ri^LGfiag] in ras. 1 2 litt. D 2
._ lav] Kaijdv AB, xat del. A 1
;
S fdv C, corr. C 2;av D. ^] con*, ex r\v D 2
.
CD, corr. D 2. 19. iKdrrav in ras. 1 litt. D 2
. 20.
CD, corr. D 2. 21. Ss ?txfv] corr. ex d' svwev D 2
.
MA0HMATIKHS ZTNTAgE&S E'. 457
i]$ V7tb ABZ ycovia roiovrcov A, oi&v
r\
9, XaTQa d TG)V 4B XO.I BE T0$ TthdrOVS [lOLQ&V .
roCvvv rats $v directs r&v A IIOIQ&V, rovr-
reels I? TtaQaxurat, sv&eta r^irj^idrov f, rats $
is t&S ^vo OQ&ccSi rovrs'tirw rats Q^t
sv&sta r^irj^idrcov yd Jtyyitira, yivsrai, Aoyos
rijs BA TCQOS AE b r&v | Jtpog ra yd. 6 d* avrbs
[Eucl. VI, 1] xal rijs BK XQOS 4K, otWvovtia ~QK. jtokvTthadideavrss ovv sxdrsQOv rcbv
fi&v 7tl ras [loigag rijs vnoruvovGrjs xal rb QX' 10
avr&v A,afi6vrs %o[iv xarQav [iv r&v KB xal BAr&v ccvrcbv
/3 A, warfyav $ rcbv 4K xal EA 6[ioiG)S
d x. ra drj ($A TtQ&rov, av ^iev xara rb E 6r][itov
i] GfAyjvr} i)itoxBrirai, d(p&6vrs rcov rijs ZB 7tQi<pe-
[loigcbv jidia rb itl ra avra rco xard xoQV(pr\v 15
rrjv xara ithdros axo%fjv rrjs ^fA^V^g, rovr6ri,v
dia rb d^ig)6rQa T) vonc&rEQa i} floQi,6rQa tivat, rov
Z&diaxov, %0[iv rqv ZA poiQ&v pfl I, ihv de xara
rb 4TI r\ &^t]vrj^ TtQOG&wrfs avrats di>a rb fvavriov
1. to'] d' D. ycovia] supra scr. D. _ 2. JE] A- e
corr. D 2. 3. TOVCSGTL D, comp. B. 4. | (pr.)] in ras. A
r
corr. ex D. (alt.)] J- D. S\ comp. ins. D 2. 5. 8vo\
ftBD. rovrtszi D, comp. B. 7. 5^1] corr. ex BJ
g (pr.)] fi D, ut saepe. ra] om. D. 8. z/X] corr.
ex AK D 2. vnorivovGK A, sed corr. in scrib. 9. SKUTSQCOV D
t
corr. D 2. TWV] ins. D 2
. KQL^&V] s D, ss I>2
- 10. 9%']
^x AB. 11. xat] om. D. 12.J3 I] pi BC, ut saepe.
J3I TCOV] mg. A 1
. xca] corr. ex x D 2. 13. Post x
litt. (s?) ins. D 2,sed del. E GTULSLOV] corr. ex SG D 2
. 14.
VTtOHflTCCL D. 16. TOVTSGTl D, COmp. B. 17. @OQi6t()CC i)
voziwTSQcc (corr. ex voreio^a D 2
)D. ftvat] supra scr. D*
18. eo<haxO'u] diet IIEGOV D, dta fif'ocov D 2. 19.
17] corr. exD 2
.
'
458 KAATAIOT UTOAEMAIOT
v tr)v ZK ftotpwv ft L Gvv&evttg ovv to outb
XcttQag t&v ZA xal ZK %G)Qlg pera tov anb excc-
tfyag t&v 4K KO.I EA, tovt6tw to aito t&v d K
perd re tov aito t&v pf} A xal [ita tov CCTCO t&v p A,
xccl r&v GvvK'ffievr&v %fogls hcc(l6vrss rqv Tthevgav
XCil %r\V [lV ZE 7tQt,CpQi,aV ILQLQCbV {lf$ fAS
[id. Aoinbv df tec 8
x KatovrccxMcci,Mo6dxi, noiKvts^ Keel
ra[i fg xa ytccQcc ta p p
10 tr^v plv EA tOLovtcov t/3 rj k'yyrfra, ol&v <5rlv q ZE
oicov Grv
{lV t&V l(l YI V&iy 3tQl<pQl,a [101,QG)V Ta XCil
ry d r&v I {_' y' rtQi<pQi,a poiQcbv I y15 &v ra riiifari kafiovtsg t& plv s xcd d
f
rijg VTCO
EZA y&vLas atpttoiLv tcbv trig vitb ABZ y&viccg
V A diCC tb Xttl trjV ZE 7tQl<pQiO,V A.CC660VCC
1. Ante ovv del. avrais 8t>u tb ivavriov D. 2. ZA~\ -Ain ras. D 2
. xat] om. D. ZK~\ -K in ras. D 2. 3. xca]
oin. D. Towcton D, comp. BC. 4. TB] supra scr. D 2. ^(pr-)j
ins.D 2. perd (alt.)] ^ D. TOV
(altOjJns.J)2
. 6. ZEJEZD.jig] v? D, [ifi py ty mg. D 2
. 7.fttf]
vd D, p pccv mg. D 2.
8. MKTovTccKMui,* D, coir. D 2. 9. ft^] N<5 B et, -s e corr., D;
fi? supra scr. D 2. pd] ^v8 D. 10. roiovrm D.
ifi]i- e
corr. D 2.
jj] corr. ex x D 2. 11. 8i] om. BC. F /.' y']
in ras. D 2. 12. Z^] corr. ex ZA D 2
^ 13. ^] e corr. D 2.
sv&ftai nsQicpfysiai, CD, corr. D 2. ta] -a e corr. D 2
. ']
A, C, ^ BD.A, C, ^ BD. 14. /_']in ras. D 2
. TtfQLysQsictiC.
y'] -v F y' in ras. 2 litt. D 2. T(alt.)] postea ins. C.
in ras. D. 15. &v ra]m ras. D, oo- corr. ex o D 2;
ante
ras. B (rav corr. ex cov B 8). ^^tVT]] in ras. minore D 2
. e']
ABD, C. 16. TWV] corr. ex rov CD 2. 17. f] in ras. D 2
.
ZE] corr. ex Z D 2. &rf<HFova] s* D, 4i
a D 2.
MA0HMAT1KHS STNTAEE&2 E'. 459
slvcu rife ZB xccl s^o^iev r^v vnb AZ ycovtav poi,-
Q&V xd \ ra ds s g' rfjg vnb AZK yoviccg
tots ccvroig A dta ro teal ti}v Zz/ :
elvai rils ZB 6%oiiv xotl r^v vitb AHZy&viav [loiQ&v A g'* outey jtQOXi,To yi&odev6<x,i. 5
1. A0Z] -0- e corr. D 2. 2. F g'] g C.
xA, "^IXD. 4. jLtf^ova] ^aD. ^/fZJ -K- in ras. D 2
.
In fine: KlocvSiov n-totepuCov ^a-d-rj^artxwv F AC,f*a-9-rjfiartx?j5 dvvralecog F B, Klctvdlov
i/ FAD.
s-
Td$ VE6uv lv rco g' rcov
a. JtQi Gvvocov Keel
5 /3'. TCgayiJiCitetcc xccvovicov [i
y''. M&etiis r&v xccvovi&v.
re JCEQiodixac; xal rag axgifletg
f
. 7tQl r&V fXfalTtTMKtV QQ&V fjMoV XCCi
10 g'. neqil rijg diaGrdGecos r&v sxfoiitTM&v [irjvcov.
XCCVOVL&V exfaiJtTM&v.
rcbv fKAeiJtTM&v xavovi&v.
15 ltt. 7tQ\ T&V V
rag JtQo6vv6i$
2. rdd' D. r<m>] rfjs B, om. D. IIroten(xiov~] om. D.
lLKQ"r}yLCiTiKa>v] \LuQ"r]^Kriv.i]<s GwrdJ-scos B, om. D. 4. a'] etceteros numeros om. I). 5. TtQccypuria C. 6. y' nctvo-
vi&v\ om. D. 7. rag (alt.)] om. D. 9. JxATjTrTixeov D. fyiovKcxl G&r)vj]<i\ compp. BC. 11. ^'] in ras. A. v.uvov(ov D.
12. r\'--
nccvoview'] v.ui comp. D. 13. SICCKQIGIS 14. ^x-
foftyfaw] om. D. 14.^lax^tctg]
in ras. D. 15. m'] ca B.
negl T&V] g nsQt T&V in ras. D. fxAfityfcrtv D. 16. t^'j
fit,B. T&V~] om. D. nqovtvctis A. diccyQucp&v] $ D.17. ty'] yl B.
KAATA. IITOA. MA0HMATIKHS STNTAgESS <S'. 461
Ilegl Gvvod&v xccl
dq rvy%ccvov6r]g rrjg itegl rag
tiv&yictg f}Mov xccl Gshtjvrjs jCQccynccrticcg,
rai itdfovfj
rcbv axQifl&g fo&Qovpwav Gvvod&v xccl
itavGskriv&v sjtfaxetyiS) attccgxeiv [ifv fiyovped'cc TCQOS 5
iv\v T&V roiovrov TtQcbrrjv xccrd^rj^iv rag aitodsdeiy-
[is'vas xu& SXCCTSQOV r&v cp&Tcov 7tQi,odt,XKS re xccl
avaiicttovs xt,vtJ6i,s dwcctov dta rovrcov yivQpivQv
rotg iifjxaroxvovGi rag xccra pfyog ccvr&v 7to%ag
xd<5TOT GvyxQivfiv fXiA.O'yt&Gd'cci, rovg re r6itovg xccl 10
rovg %Qovovg t&v 0o^iva)v 6vvyi,G3v r&v re ngbgroc [i6cc xwtfiiccTcc A,cc{ificcvoit,sva)v xccl rcbv [JLETCC rijg
dv&llCcMccg aXQlfiGbV 0[lG)g df, IW 7tQO%l,Q6T()OV fftltV
xal ccvrai ii&odev&vtai,, 7tQOXT&L[iVG)v f| erotpov
r&v T xccra rag TCfQiodixag Gvvodovg xccl jcccv6^vovg 15
XQOVCOV xccl TOTCCOV xccl xojv xccTK tovg [i6ovg %QOVovg
7to%&v Kv&iicdiag r xccl Ttharovg
&vij
T Ttgbg zccg axQifatg 6vvyiccg
xccl ccTtb TOVTCOV fj TtQog rag x^i7trt>xccg^
0dii&cc JtQog rrjv roiccvrrjv 7ii6Ketyiv xccvovicc 7CQL%ovra 20
rbv rgoxov rovrov.
1. a'] om. AD. 2. foj] corr. ex &v D 9. wGutTwa.? A.
3. xcu] TS v,ui D. 4. cvvodcov] c- in ras. D. xat] re
V.GCI D. 5. Iwtcxai/x-ff] -n- corr. ex t D 2. 6. v.ccrd).r}{iipis D,
sedJLI
eras. 7. SKdregov] corr. ex stsgov D 2. 8. dia] D, re Sid
ABC. 9. xaTOKVoutf) D. snoods] ~tr corr. ex >l D 2. 10. #(>o-
vovg ucii rovs ronovs D. 14. [tsd'odevov'ccci CD, corr. in scrib.
C et D 2. 16. XQOVOVS] %gov- in ras. D 8
. 18. ytVstca] suprascr. comp. et mg. D 2
.
462 KAATAIOT HTOAEMAIOT
ar eicc xavovi&v [i6a)v
Tlg&rov plv yap, IW ndhv nal rag rcbv
&<5ttQ Kal rag aMag, ano rov a k'rovg Nafto-
aoov GvcfrrjG&iisd'a) ryv ctTtodEdeiypevriv iv r&
rovra) G)& vBo^via, nar Atyvitriovg ri]g
ajto%ijs poiQcbv ovticcv o Af Tt
TO j]^eQ^iov [isdov xivr
fij Ay ? cog itQQ toGovT&v ysyovsvui
TJJS v ty v0{ir)via rov co-fr ^ifffrj^^^as JtQoye-
10 yovvlav [i6r]v Gvvodov. xalr\ f|ij? aga ysyovsv
iiT& %yxo6ra fidgets picis [id i^ rijs iv ryiv $ rats ny [id t, f][iQcu$ 6 ft
ioigas ity
15 avG)[iaMccs pv [IOIQCCS rlrj i,
ridft me. 7ti%v d xal v TTJ rvjg
ftgia rov cbO1
ft<?cog 6 ply ijfoog 'Iffivcw
jjf, curb $ rov aitoyfiov rov tdCov dice rb
lioioas 6% tf, fj$ 6&rjvr] auo^Atag pv ano rov
20 K7toiov rov
1. p'] om. D. 3. ^trovg] post I- ras. 2 litt. B, corr. exinl TOV$ C 2
,ex h D 2
. NafiovaoccQOv D. 4. Gvotrjcoped'a C.
Trjv] corr. ex rjT D 2. 5. IVft] corr. ex IVrj D 2
.
-tea in ras. D 2. veo(ir]VLa] a in ras. D. 6. o] seq. ras. 1
litt. D. nctQCifidnovTSs 6, corr. D 2. 9. veoinqvia] a D
r
yp. vovfiriVLK supra scr. D 2. cb-O
1
] cofr rf]s D. 10. &QO]comp. C, di D, yg. CCQCC supra scr. D 2
. ysyovev] -v eras. D.11. HyyiGTcc] $y- e corr. C. 12. TOVTSGTIV] comp. BC, -v
eras. D. sr)*o6rd] || B, comp. in ras. D 2. 15. ri ^] B 3D 2
,
Ttrj ABC, TITJ D. 16.
|3 xa] jhia A. f'jrf^f D, -ft- in
ras. D 2. vopj}VLag\ -o- ins. C 3
;a D, corr. D 2
. ^Gt](ji^r D,
corr. D 2. 17. rov ob-fr]
om. D. ju-o^ag] om. D. 19.
o- corr. ex A. 20. nidrovs] corr. ex nldtos D 2.
MA0HMATIKHS STNTASE&S ?'. 463
dnb rov fioofiov Ttsgarog rov ho%ov xvxAov poiQagrvd IS. Xal iv TG) TCQOXSlpdvG) CCQK %QOVG) Xi] flrd
rr\v v0[ir]vi'av fif'tf^g Gvvodov 6 psv ijfaog xal ^ 6s-
Atfvr] [ifa&s aTtsfyov d[i(p6rQOi rov faiaxov ditoyeiov,
rovrfanv r&v sv rots didvpois poiQfbv A, fto^agd\ GsAtfvrj dv&iiccMag [iv aito TOV axo-
6ir] v% is, nAdrovs d' onto rov j$ooiov
ttQaros {lotoag rrj it, MX.
ovv jto&Tov xavoviov
f, 6fadiG)v d f, xai jtaoad"t]6o^v iv rots 10
itl [iv rov jfQ&rov tiekidiov rb a'
frog Napovcc66ccQOv ,iit\ $ rov dvroov rag rov
(&&& vj[iQccg xd [id tf, itidri ra 7tovrcc QrixoGrK ryg
iv rfi xd' 6rl ii6rjn(}oiccg, lid ds rov roirov rag rqg
7to%r\g anb rov anoysiov rov fjMov poiQag tiny 15.
3tl d rov rfrdgrov rag anb rov anoyeiov ryg
avG)yiakiag poiQag (Sit] i/f tf, sTil $ rov
rag aicb rov j3ooiov 7toarog rov n^drovg
rrj tj xd. tTtsidri de xal iv r& fftiiGfi rov [i-
6ov [irjviaiov %QOVOV rj^ioai [ilv 7CgiB%ovrai idji
vs 20
8s ri\g plv fifaaxyg 7to%ijg id Ky ifa
rr\g de 6hr}viaxr}g dv&iiaAiag @9/3 vd A, rov ds nkdrovg
Q<j x ^ 9 dcpshovrsg rovrovg rovg doi&povg ditb TCQV
2. I?] i- in ras. D 2. 3. vov^r\VLav D. 5. rovrtirctv]
comp. BC, -v eras. D. 6. d] comp. supra scr. D 2. 7. itka.-
rovg] corr. ex nhdrog D 2. 10. iv 11. cxi%oiq] om. D. 12.
hog'] corr. ex t,' D 2. NafiovccGaQov D. dsvr^QOv] -ts- e
corr. in scrib. A. 14. &mV D, -v eras.; comp. B. 17. as-
s] corr. ex G^vr\g D 2. Ts] corr. ex st D 2
. 19.
corr. ex insi D 2. TJfu'ffft] -ft- e corr. A 1
. (irjviKtov. 20. 7?/i.cu] -at renouat. C 2
. nQii%ovtcti\ -at
renouat. C 2. 21. poiQai\ -at renouat. C 2
. 22. Si (pr.)]
ins. D 2. 23. fyifyiovg] gs"* D.
fis
]
D.
464 KAATAIOT IITOAEMAIOT
Gvvodov rovg hoiTtovg ngord^onsv xal
avrovg Iv r<p dsvrsoa) xal bpLOicog %ovri, xavovicp,
7tav6A,rjViaxG) ds f'tfoftfVca, xara rov avrbv rots ngors-
ooig rooTtov xarateiTtovrat, ds fjiisQai, [lev & vri x/J,
5 polQat, ds anb plv rov dnoysiov rov fjfoaxov tfod s
Ar], av&iiaMas d' aitb rov anoyeiov rr\$ GsAtfvys x?
/3 /if, TtA.d'covs d' cutb rov fiogsCov Jtegaros Qifi v^ is.
XCci V K
10 uTtctQri^ovraL, ual fTtiAaiiftccvst, nsd*' o^ovg
b plv ijfaos [loigag tvy vfi Ad Zy, ^ $*
yLv {loiQccg vt, KM [id a, TtAarovg ds
3 fid1
vd, ra plv ttQGbra tiMdict rcov dvo uavo-
jtccQccv,ij(jo[iv rolg %s sr6iv^ ra ds dsvrsQa V7to-
15 iLid)6onv rolg o(I [i e, rcbv ds koiit&v ra psv rgira
ytaQav%il<}0[jiv rolg rvy vfi Ad ly, ra ds reragra rolg
v xa /Ltd a, ra ds itipitra. rolg QI, i$ pft vd.
rovroig d' d<peij$ rd^o^ev xav6viov tviavtiiov iitl
Grfyovg xd xal akko vrf avro ^vLalov 7tl Grfyovg
20 t/3, tiefodfav ds sxdrsoov rcbv i'G&v rolg nQ&roug, xal
Irii [ilv rov [irjviaiov Ttagaftevrsg iv rolg Ttoaroig
6rC%ot,g BTtl [isv rov itoarov tiefodfov rov TCQ&rov [ii}va,
7tl d rov dsvrsoov rag rov (irjvbs ^soag x& Aa v y
2. TW] del. A 1,om. D. 3. TCQoartQOig A, ngmtoLs CD. 5.
ds] d' D. rjh'ov D. 7. nldtovs] corr. ex nlidtog A 1,
-I- e
corr. in scrib. C. 8. ds xca] d' D. fasaiv] comp. D, corr. D 2.
leCnovGi D. 9. ffjijxotrrofs] &l B, "| D. dvaiv B, B D.10. 7uafi/3cb't] -i ins. A. xvxZovg] supra scr. D 2
. 14. rots
16. n<XQKvrioo[isv~] bis A, corr. A 1. 14. et6w~] comp. D,
fT86i D 2. v7to[iia>60[Lv B et pr. loco A, corr. A 4
. 15. rots]
-i- ins. D 2. o ^] o|3 A utroque loco. 16. rsTccQta] -rcc supra
scr. C 2. 17. Post vd del. a D. 18. fqpt|^g] -gpe- e corr. in
scrib. D. 20. d\ d' D. 21. sv] ? B. 22. no&rov} corr. extva D 2
. 23. v n\ C 2D 2, ^ ABCD.
MA0HMATIKHS 2TNTABE&S S'. 465
X, 7tl $ TOV TQLTOV Tag V TG) T000VTG)
yo[ivag TOV r^Mov [lotaag x& $ wy a, iiti ds TOV
TTKQTOv Tag Tijg dvca^ia^iag Tijg 6^tjvr^g x yL& o77,
itl d rov its^Litrov rag rov TthaTovg iioioag X jiid Q"
7taoav%ri<30iiv $ %ol rccvrci rots ccvrots aoid-pots xccl 5
7tl T&V rtocbrcov <5ri%ov XXiiivois. 7tl d rov
VlKV6lOV 7tCCQCCd'VTS V TOL$ JtQCOTOig 6ri%0l$ 7Ci {LVTOV rtQMTOV 6fadiOV TO TtQ&TOV TOg, 7tl d TOV $V-TQOV rag 7tiA,cc[if3avo[Lvas iv rots ly (irjtilv ^EQCCS
I/YI ~vy vfi JLt/^,eitl d rov roirov rag iv rd) rotiovrw 10
%QOVG) rr^g ri^iccKrlg ixovtiiag poiaag Irj nfi v& 1^, 7tl
$ rov Tfrdorov rag rijg 6hr]vici%fjg avo^aUag iioiaag
rfa Ag a va, 7cl $ rov Jtfynrov rag rov nhdrovg
poioag A^ ~py y we' 7taQav^0o^iv d xal ravra 7tor
ftev ralg xxiiivaig roL6Kaidxa^voig &rovtfuug, 15
7tor d ratg d&dsxaptfvoiSi ^ GwcfyovGiv f][ioccg [iv
rvd xfi a ji, poioag d rijg plv ykiaxijg &to%rjg T[i&
T$ Ag 7g, rrjg d 6&rjviaxijg avG)[iaMag r& ^ a [ifa
rov d Ttharovg j\ |8 /u/fr ft/3, itgbs TO rqv xg&vriv (p'
oAotg AlyvjtriccKoig T6iv tfvfvyfav fi[ilv &ct&s6&W 20
rag pivxQi rtaoa&6i,g aQX6i, ^XQ L r&v devvfycw. xat i<5tiv v T&V xavoviwv xar-
1. x] corr. ex iis D 2. 3. o
j\\ corr. ex OTJ D. 4.
om. D. I> 18] Ijud corr. in ijt id A. W] del. D 2. 5. ds
supra scr. D 2. TCCVTO] corr. ex ravrag D 2
. a^t^otg] g D,
gffd^
D 2. 8. Tr^cbtrov] ^ D. 7T(>corov] a BD. srog] comp. D,
corr. D 2,ut saepius. 10. v^] va D. 14. fioi^ccs] ftoi^" D,
comp. C, ut saepe. de] supra scr. D 2. 16. at'] supra scr. D,
renouat. D 2. 17. K
|Z] a/I AC et corr. ex &p D 2. 18. 5] mut.
ra scr. D 2.
'
in ^r D 2,S supra scr. D 2
. 20. stzGiv'] -v del. D 2,Urea B.
,corr. D 2
. 21. a^xscft] -e- alt. corr. ex i in scrib. A.
corr. ex r D 2. dsvTsgcov t,r\v,oGra>v~\ -TSQOOV s
in ras. D. 23. TOiavrr]] des. fol. 136V D, fol. 137 r uacat.
Ptolemaeus, ed. Heiberg. 30
466 KAATAIOT nTOAEMAIOT
1JI
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to
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S
-^1
MA0HMATIKHS 2TNTASE&S ?'. 467
** OU3
Qn *a.*
IF
2 * *t.U *-* -a
=4. P" if.
a.-srs- a. x
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>. ^ ^ ?>. ^ ?. Qa.oa.ca. ca.ca.co.XXX XXX
a u> s
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30
468 KAATAIOT HTOAEMAIOT
2" 4
\p 5^! aC*
JO
It"4$ t -
srs
10
I
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a *t
SI-I-P
a a- v>d5>5^ a. * x
t
to *o
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l
a.. . S"*r.Sw
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'vo
3 s ^>
a wg o:ik
.rC> ** O O vS Oc3 ^ O O w X
MA0HMATIKHS <=>'. 469
ds in "035=-
oa. u>
t SI:
.
rs.
**Stt*
S" 2C2-
B- gE- S- iB S5- R- P- c- P
8* 8- 8* **IP a \fl
S ?k333 *u> a
II
jSto-w'iOoe-.^B'S? J3 ^ *i ST1
. W ** ^d
^ a B^^ OX"? S
ias -
470 KAATAIOT IITOAEMAIOT
El?
.*
Va 8 8 IP
Q^ Q/
a. a. s
2 a oi
a ?=- a
^
300.
IQ
IP *J ST
O
^O *CO ^ v^
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u S ^iO
a
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" 2 ? QrHCO-*^ 2^ 8.
MA0HMATIKHS STNTA3E&S
"2 g"^^3
2
"
8
^*0X ?!
3 3
-g-
8
-O 'O
-I ^^ ~o o
co to
^ a
11- -aV V
11
II
I
00.KQ,
8 5J
t
a. -*
B 00.
471
?r ?> oo.
Vp Vp J\
j
oo.
ka -
- ^
472 KAATAIOT HTOAEMAIOT
d'.r
&$ dst rag TS TtSQiodLxag xal rag dxoifatg
"Orav ovv TtQoaiQcoiiE&a xara nva rcbv
[ivoov viavrcbv rag pfaeog ^cogov^vag Gvtvyiag
5 Aa/5tv, Aoyufdfievoi, jrdtftrov 6rl rb vitoxeC^vov rog
dnb rov a' f'rovg NafiovaGGaQov ,xccl 6xeil>K[isvoi,)
noloi rbv agi,&iibv T&V STGIV Gxiyjoi 7teQi%ov<5iv ex re
XG)V iv OTtOTSQG) TG)V 7tQG)TG)V dvO XCCVOVLG)V elxoGOC-
TtewtasTrjQid&v xccl sx rcbv xaxa TO rgfaov xctvoviov
10 eviavGicw, xa itaQaxstpsva rots 6ri%oi$ d^cporeQOLg iv
rots %fis Gehdfois 7tc6vvd'^o^sv olxeC&s snl psv x&v
Gvvodixcbv Gv'Cpyi&v ra x rov Ttoarov xavovog xal
ra ex rov rgfaov, 7tl $ rcbv itav6J.r]viaXG)V ra X
rov dsvrfyov xccl ra x rov rgirov byLOicog' xal X
15 ftfv r&v xara rb dvroov <5kidiov
V rbv djcb ri\g ag^iis XLVOV rov rovg
JCQOVov, oioV) av GwafficbGiv f^idgcd, xd
[id ^rjxo0ra rijg v rr] xd' rov
xal Ttakiv, av Ad ftd, {ira ra i'6a %rjxoGra rijs iv
20 ry d' rov (Da&cpl yiSGrnLpQiag, x d rcbv xara rb rgi-
rov rag cbro rov drtoyuov rov fjMov yioiQag, x ds
rcbv xara rb d' rag ditb rov aitoyBCov rijg dvco^ia^ag
rijg 0^tjvr^g^ x d rcov xara rb n^nrov rag dab rov
1. d'] in ras. A, om. CD. cog] it&s D. 2. cvgvyias]--
in ras. A. 4. ju-scroog] corr. ex psaus D 2. 5. nocov BC.
6. a'] corr. ex S D 2. NapovvaaaQOv D. 8. navovav D.
ftKOGiitEVTaeTrjQL'Soov D. 9. %a viov A, corr. A 4. 12. cvv-
vyi&v C, sed corr. Tt^cbrov] a D 2,8 D. 15. xara] V.K D,
xar' D 2,ut saepius. 17. i&v\ corr. ex av D 2
. 18.
'|| B, et similiter saepius. 19. pera] Jra A.
MA0HMATIKHS STNTAEE&S '. 473
itQarog rov ithdrovg. xal Tag (p%f}S ds dxo-
jlav re Ttdtiag Mv re nvag kayifidveiv itQoai-
did rCbv iv rco [irjviaiG) xal rfrd^ra) xavovim
Kara rb otxetov 7ti6vvd'6G)v e% eroipov Gvvemho-
yiovpe&a {ira(pQOiiVG)v stp xd<5rov rcbv %QOVCOV dia 5
rb v%Qri<5rov r&v rrjs fniQag B&puxft&v ft
pivrvi 17 dw^y^ivYi r&v
cog r&v vv%&r][iQa)v o^cdcov ovrcov ^ ravrrjs ,
afel rrjg xaLQM&s xaraA.a{i{lavo[ivr]s, aMa rrls
avG)[idA,G)v ywouwwv r&v vvft&rjiifycov' di,OQ&G)- 10
b roiovrov ^rd^ovrss^ cog vjtodd-
,TO xaQa rovro didyoyov xat, lav plv ^^mv
fi 'Y] Jtgbs rqv dv&naAov dia6ra<5iv litovGua r&v %QO-
vcw, dcpai,QOvvrs ccvrb dnb x^ 6ftaAGog GvvriyyLBvris,
lav de fhdtiGcov, XQOtiri&wrfs afar}. 15
dij rbv rgoitov rovrov rov itQQ rag
&G)QOV[ivov Gwodwov rj Ttavdekiq-
vianov %QOVOV xal rCbv xar' avrbv dv&iiafocbv <p'
xarQov r&v cpcor&v v^ra%LQL^rog k'Grai xal 6 rife
axQifiovg 6v%vyia$ %QOvog re xal ronos xal nr\ 20
xard Hydros rijg 6^vrjg xdgodog X rijg 6vyxQi6cogr&v dvcopafa&v. xa&' xarpav yap av-
l, ri\V Iv TO) XXl[lVG)
did ri}g VQi6xoiivr]g itQo6d'a(pai(}6
v ii^Cov r xal tffA^i^g xal jtAdrovg, lav {ilv 25
xal ovrcng L06^ioi,goi vj did[irQoi zvQitixcavrai) rbv av-
8. cog] corr. ex 6g C 2. 9. ahi] corr. ex &et D 2
.
mut. in &Mr}s C 2, aUaHrjg D. TT)S cb?] supra scr. D 2
. 10.
SioQfi'wGoiiev D. 11. vnodtdeKTcci. D, sed corr. D et D 2.
15. iKmcrtov D. 16. xovrov rbv TQOUOV D. 21. r?)g cs-
htjvriS V-KTCC nldros D. 22. r&v] om. C. opu'ki&v D, corr. D 2.
24. viav.coi^vr]s A.
474 KAATAIOT HTOAEMAIOT
rbv s%o[iv %QOVOV xal rijg aKQifiovg Gvtvyiag, sdv ds
Aa/36vrg rag rijg diatirdiscos avr&v poiQag xal
avralg to dcodmarov avr&v, dv&' ot> 6
ijfaog fyytfra STtixivsttai, tfjc^d^-frtf, v itotiaig tigaig
5 fariiLSQivalg r\ Gehijvr] tag rotiavras poiQas rore avo-
vri&riGs'tai, xal tag ysvojievccs cogctSi &v psv
fi f] KKQifiris rijg Gehtfvyg itdgodos rrjs rov
Qo6d"tj0o^isv rco %$6vG) t& rtSQiodixG), sav ds
, dg)shov[iev an' avrov. GMICCVT&S de xal ccv-
10 rag tag tr^g dicc&rdasog avr&v poiQag (ISTK rov dco-
dsxdrov Ttdfov avrcbv, lav {isv skaGGczvTJ rj
Kara rbv
TtsQiodwov XQOVOV dxQifttjs rtdgodos ri\g Gehrfvys rijg
fjfaaxris, jfQOtf&faceg avrfj, iav ds TiheC&v, ayekovreg
ait avrr^g xard rs rb [ivjxos xal nkdrog rov rs rf\g
15 dxQifiovs 6v%vyCag %QOVOV s^o^sv xal ryv iitl rov
Ao|oi) xvxkov rijs GsAtfvrjg dxQifiij ndgodov syyitircc.
A.a[if}dvsrai, pevroi sxd<5rors rb xara rag
rijg ds^tjvrjg oaQiaiov dvco[iaA.ov xivyiia rbv
rovrov' sfa(pQovrsg yao rbv xard rbv
20 %Q6vov rcbv rrjg dvcopaMag poiQcbv doi&iibv slg rb rr^g
av&iLakiag rijg 6s^vrig xavoviov A^^dftfO'a sx rrjg r&v
3iaQaxsi,[iVG)v avrtt jtQoG&acpaiQSGscov vTCsgo^fig ri\v
diayogav r& svl rijg dv&iiaMag r^-
1. xat] om. D. 2.jurj]
vno D, vito del. D 4.
6ta>s] post -s- ras. 1 litt. D, -OTKG- in ras. D 4. 3.
i$ D. ctvT&v] corr. ex CCVTOV C. 7. zldrxcov D. fffZtVrjg A.
9. U\IQV C. 10. diccGrdGfcog] -Gtd- in ras. D 4. doi-
Ssudrov] t|3D. 11. sldtrcov D. 12. %QOVQV'] %~&, ut
saepius. 13. nteiov C. 14. TO] om. D. 15. s^ofifv
XQOVOV D. fr\v\ om. B. 18. ccvw[icdkov C. 20. x&v]rov in ras. A, corr. A 4
. KQI&ILOV] &QL D, -ILQV add. D 2.
23. TjHTjjtiaTt xat] -i v.- corr. ex JK A.
MA0HMATIKHS STNTASE&S S'. 475
part, xal TtokvjtkaGiaGavrsg avrqv litl rb coQialov
dvcojiaMccs p6ov xtv^a ra o A/3 fto ra yv6[iva,
lav plv 6 rrjs dvopaMas doid-pos lv rots litdvo
rov Kara prjxos MQIULOV peGov xivr)[iecTos r&v o A/3 5
v$ o, lav d' iv rolg VJCOXCCTG}) 7tQo6d"tJ6o[iv rots KV-
,xul ra fyv6^evK S^O^IEV^ a rots ^ 6hyjvrj
ovv
6vvyicov OVT&S v\\n,lv nf&odm&rjGttai, dua rb 10
xal rag rto%as aita^ag xgbg tbv di''
p,6riiiLfigLVOV ti\v r&v cdQiaicov %QOVG)V 6v6ra6i,v
fpBVKi' Qadiov 6s aito T&V v 'Afo&vdQSiy %Q6vov xccl
rovg v oitoi&dtjitorf nU^ati yvr]6o[ivovs TJJS ccvrijs
Gv^vyias VQi6xiv do&wros rov xar' avrrjv Jthij&ovs 15
r&v far]n,Qi,VG)v cagav rijg dab rov p,6riyifiQivov ebro-
^ij^. ano yciQ rqs r&v otxij6G)v diacpogas
rov dia rr\g 3tt,r]
lioiQccis dicc(p8Oi rov di 'AAl~civdoias<) ccv [iv 6
dta rqs 7t^rjrov^vrjs K&QKS [i6r]n(lQivb$ an' dvccro- 20
AcbvYI
rov di,' 'AA.%ccvd()ias<) roGovroig %QOVOI<S v6r-
QOV Xl do&i rsrviQriG&ai rb (pcci,v6^vov^ lav d djtb
orfoov rots avrotg, r&v dxaitvr %o6v(ov
piav d^Kovon noiovvrcov cooav
2. ft o] \L o corr. ex ^o A, ^ D. 5. eb^tatov] -i- corr.
ex a in scrib. C. 6. o] om. I). S'] mut. in 8e D. TCQOO-
D. 9. ysvofifvos D. 11. ndaag D. 13. %QQVOV C,sed corr. 14. ysvo[ivovs D. 15. n^&ovs] -&- in ras. A.
~
B.19. rov~] corr. ex rov D 4. 22. Terr^tiGftKi B. SO] 8' D.
24. co^av] corr. ex &QCOV D 2.
476 KAATAIOT nTOAEMAIOT
'. JISQi T&V KhL7lTiX&V OQCOV IjAt
TOVTCOV d' ovrog <pG)dsv[i8VG)v <xx6A.ovd"ov civ f
ra <5vvrivovra agog rovg wtentriKov
5 OQOVS TK)V TS TOV JjMoV KCil TG)V TVJS (?/Lt?V?? STCITCQOG
) ivcc, xav pi} 7id6a$ rag TtSQiodixas
ds
10 xcc6rrj r&v
iv [iV ovv r& ago rovrov Gwraypan [Vp. 4217 3]
,ori rijg 6^t]vrjg fj did^r^ogrov Kara TO fi
f>
yi6rov avrr^g
15 yQayoyiBvov 7tQi TO KWTQOV rov tydiaxov iiyi
xvxkov [lias {loigas t,r]xo6Tcdv ha x, dta dvo %,%.-
^(DV yyvrniVG)v 7tQi TO a7t6yiov avri]g rov 7ti-
XVX&OV TO TOLOVTOV iltl'kQyi<5a\LSVQl. Xal VVV d'j
7tl
rovg iLyi<5rovg T&V iKfaiTtriKCbv Gv^wyi&v OQOVS TCQO-
20 aiQOV[jid'a hafatV) OVTOL $' ltilv 01
vr]s itQi TO 7tQiyL6raTov ovtirjs rov
dia dvo Tt&hiv r&v itQi TO
kltyK>V) 7tl,dfl fiia T&V
a6(paA.()TQOv avi'rj
ra roiavra dfixvvfiv, arjfa'
1. f'] om. D. 3. erpoSev^vcov C. 4. TtQoa&fjvcci CD,
corr. D. 5. rfig] ins. D 2. IninQOGQ-rjCEcov A. 8. &7ts-
GELV D. 9. yCvETcu C. 10. bY.a.GT'ri] corr. ex sKccGrccig D 2,
xatfT7]s A. 13. OTt] otl
D, ut saepius. 15. gcoduxxov]
S$f D. 20. d'~\ 8s D. 22. TO] corr. ex x&v D. TISQL-
ysiov] corr. ex itsqiytia D.
MA0HMATIKH2 2TNTASE&2 S'. 477
xal svrav&a 7tQi,(pQiav b^ioicog j] Tr\ ^E^rjvrjg did-
TOIVVV'
ETEL <Z>tAo^ro00., o Itirw (pod' dnb
KKT AiyvTtTiovg ^a^isvcad' xtj sis ity'
ditb Gjoccg 17' aQ%oiisvr]g &$ i Arj'yovGrjs iv'Ate&v- 5
fj Gskijvr] rb Ttteidtov an'
ovv 6 ftsVog %QOVO$ yzyovev
~fi L' &Qas xaiQixas rov peGovvxxCov, ai fa
Qivca /3 y' dux TO rbv ijkiov E7t%iv axoifi&s TKVQOVteal GwdysTcci 6 aito rrjg e'jro^g XQOVOS 10
Alyvntiaxcbv
Xttl fjlLEO&V ^ Kttl COQ&V l^liEQlVCbV aTth&S [IEV id y\
nobs de ra 6{iccA.a vv^d"^^socc id /w/dvov, xa^' ov %QO-
VOV TO KBVTQOV T^g Ge^tjvrjg ftfVog {16V 7ti%SV 2JXOQ-
jtiov H,OIQK f pO") axoificos ds poiQas ^ 7?, xai ditb 15
H,EV TOV KitoyEiov TOV EitiMJK^ov [loigas Q^y |iZ,aitb
ds TOV PQQELOV TtsgccTog TOV Aooi> Kvnkov [IOIQCCS 9^ >c,
yavEQOv, ort, OTCLVriK noigag dcp6Trixr] T&V Gwds'tipcov
TO XEVTQOV T^g 6^nvn$ id> fov Ao|oi) xvxkov Ttegl TO
kd%i,6Tov ovtiyg djcoGTrjiicC) xalri
iitl TOV yQacpopEVOv 20
di CCVTOV ttobg og&ag TGJ Ao|w Kvxkco iiEyitiTov KVX-
TO KEVTQOV Ttjjg 6M,&g ,XttO1
'
J]V TCKQodoV CCL [l-
T&V E7tl,6XOTYJ6G)V KTtOTE^OVVTtti,
TO [_' XCCi 1$'
drj T& K Ti Trig tQfays xccTa Kdkmjtov 25
)o i^nv y dnb NccflovaGO'dQOv, KKT
3. (?TH/] comp. B, son D. cpod'~\ <po8' eros D. 4. Na-aGaQOv D. 5. a^^oftsvi]?] corr. ex KQ%ov6T}$ D. 6.
C, corr. C 2. 7. ytyovs D.
IS^fiovov B. 14. tnsfye D.
21. ccvtfjs D. 23. L'] r|T A, i^BCD. 25.
ABCD. 26. NKovvKGaov D.
478 KAATAIOT HTOAEMAIOT
riovg Tvfll /3' si$ rr^v y' &OKQ s' ao%o[ivr)S ivr
ijo^aro xA,i7ti,v rj GsAijvr] xal 7t0xortjd"rj TO
KTtb vorov daxrvlovs y. sitsl ovv Tt^Kiv xal
rj plv aQ%r} rrls Mfafyscos ysyovsv nob dvo ct
5 QM&V rov iisGovvxTLOv, 0.1 fi^av iGruiSQiVul sv'
re xcti sv 'Aks^civdQsia |3 yf
dia rb rbv ijfaov sjts%iv
axQip&s *TdQo%6ov poiQcis rj,6 ds
w rb TtfotGrov 7C6xortj^"rj^ TIQO K L' yr
forjlieQivfjs rov peGovvKrCov, xai GvvKysrai 6 aitb rfjs
10 rto%ijs p%Qi> tov {i6ov rijs bclsfysog %QOVO$ ertbv
%$ Kal vunsQcbv OKCC xal faocbv
ttgbg ra d[iaha vv%d"ij[iaa I xal gr
,
ov OVOV r
15 rov anoyeCov rov frtixvxAov [loioas oor] jitg, aTtb d
rov ($oaiov 7toaros itl rov Ao|oi) xvxAov (loioccs &ji
AST, tpccvfobv KCil vrv&v, ort, orav i AS: poioac; dcp-
rcov 6vvd0iG)v rb
fo r avr
20 rov xvroov rijs Gxi&s iv\v xoivrjv ro^v 7t%ovrosrov r di,a ii6(DV uccl rov dia rov mvroov xv\ <3A.yj-
v*l<3 nobs oo&ag r& Ao|c3 yQafpo^vov [ifyfarov XVK^OV^
ror rb rtragrov psaos ig rf}v Gmav [ut6lrai, rijg
1. y'] ZQitTiv C. 2. sv.lL(indviv D. 3. xat nakiv BC.
4. ysyovs BD. dvo] |3BD. 6. lv] om. D. y'] A,
i' y' BC, /.' D. to] %s C. 7. rj] /.' D. 8. Post y' suprascr. fu
vC 2
. 13. ensile D. 15. (loiqas 16. xvx^ov] mg. D 2.
16. Inf] om. D. ponces G7t A?] corr. ex pcnte D 2, ft ^r Z?
mg. D 2. 17. OTI] o D, o' D 2
. F] f xat D. 18. r&v\ anbr&v D. 19. CCVTOV C, corr. C 2
. 23. TOTS] bis C, sed corr.;om. D. TfTa^Tov] d'
1 BD. 6%idv\ seq. ras. 2 litt. C.
MA0HMATIKHS STNTAEE&S 5'. 479
l' <xv plv rjxal y' poiyac;
7tl rov Aooi> xvxhov rb xevrQov rrjs
xal x' $r}xo6ra pices {IOLQCCS snl rov dia r&v
avrov yoa(po[ivov [ifyfarov xvxhov
rov dice [isGcoV) otccv df dsxa ^IOLQCCS xal yT&V 6vvde6(iG)v uits'm xata rov Ao|6v KVX^OV^ vd /_'
yr
,rjxo6ra [it,as [lotoag tni rov diet rcov itok&v avrov
yQCKpopsvov psyfarov xvxAov dUtirarai, rov diet iisG&v.
jtsl ovvfj [lev rcbv dvo BKtefye&v V7t^o%ri rb rgixov
, rilg GEArjviaxijs dialerQOV, fjds rcov exxst,- 10
rov xevroov avrrls sitl rov avrov neyfarov
dvo dia6ra6G)v ano rov avrov 6q[jiELOv rov
dt,a [i6a)V) rovr6nv rov xwrgo
^a /LtJ, dijAov, on, xali\ dt,d[irQOs
ffitoretvst, rov xara rb Ad%i6rov avrrjs 15
yoacpo^ivov Ttegl rb Ktvrgov rov ^cpduaxov
xvxhov 3tQHpQiav ^rjxo6r&v {loigas [lias
yyi6ra. STCEI d xal iv rr[ dsvreQa r&v mfai-
xa&' tjv rb d' zxtekoC'itEL rqs 6^vLaxrjg SLK-
[iroov, a<p6rijxi, rb xsvrgov rijg GEAtfvrjs rov [iv 20
xvroov rrls Gxias E^xo^ra vd /_' y ',rov ds
xa&' o rB^ivBi rfjv ryg 6xia$ itsoicpSQEiav ^
vvovGa avr&v ra XEvrga, rb d' r^g diaperoov ri}s
1. aHa A. an^Ei D, corr. D 2. 2. TO 4.
bis D. 2. H&VTQOV D. 3. xca] supra scr. D 3alt. loco. xj
mut. in y B, om. D. 4. [leyfarov XVH^OV] om. D alt. loco.
5. $8~\ supra scr. C 2. ns^nta] 'ss B, s
aD. 8. SUGTCCVTCCL A.
9. TQLXOV] y' BD. 10. TOV syiyiBi^svov C. 11. TOV (pr.)]del. C 2
. 13. Tovrtcn D, comp. B. 14. ju-tag poiQ<x<s~\ om. D.
ict\ corr. ex 18 D 2. (ttr]s D. 16. TO] supra scr. D 2
. co-
SIU-AOV~\ ^~ D. 17. TtEQifyft,1
D. poiQKs piag\ om. D. 19.
D.
480 KAATAIOT UTOAEMAIOT
o fanv QyxoGr&v rj /_' y', (pavobv avro-
on xal % IK rov XSVTQOV rffc Gxiag xara TO e2.cc-
%i6rov rrls ^s^tjvrjg a7t66rri[ia xaraksiTtsrai, QrjxoGrcbv
JLtg*xaC 6Ttv ddt,ay>6QG) {isifav rj
diTtkatiiov xccl tots
5 TQLtil JtS[l7tTOlS {1%O)V tr\ X TOV XSVTQOV T^S Gshtfv'rjS
sfyxoG't&v ovtfys t, rB. akka xcclfy
^x rov XSVTQOVrov fyfov vjcorsivsi TtsaKpsasiuv dpofag tov w* Kv~
rov yQccfpo^isvov nsol rb xtvrgov rov ^cpSiaxov
6rov xvxkov sfyxoGrcbv 7f ji' fadxis yao
10 [V, 14] xarcc^isroovvrsg rovs Idiovg xvxhovg o re
xalfj Gsktjvr] xara rb sv ralg Gvtvyiais {isyitirov CCTCO-
orav CX.QO,rb (paLv6^svov xsvraov rijs Gsktjvrjs
rov xsvroov rov fjMov etp' sxccrsoa rov dia
ioioas o ky x, r6rs rtgcbrov dvvarbv
15 etirai r^v (pcuvopevyv fttGiv rijg GsArjvrjs xara xv\v
STtacprjv yevzG&ai, rov fjJitov,
oiovj sav VOYJG&IISV rov [isv dia {isticav r&v
xvxhov rtSQicpeQsiav rqv AB, rov de Ao|oi) rrjg
VYI rf}v
20 ii%Qt> yz rav xara rov$ sxfaiTtnxovg %$6vovs
xal dia r&v rov Ao|oi) x6A.G)v yodiltcoiiev
xvxkov TtSQKpsQEiav Tqv AEP, votfG&iisv ds xal
rb A Grjjistov rb rov i\Uov fiiiixvKliov, itsol de rb Erb
2. ort] om.C. 6. r*~\ r ABC, FB D. Mg. tf AC. 7.
r -D. 8. Supra ygacpoiisvov add. ft O D 2
. q)8i,aKOv
xvx^ov] D. 12. Ante nsvtQov del. TO C 2. 14.
potgas] om. D. rotf] supra est ras. A, & SGTIV in r&v
KVTQ(OV KflCpOT^QCOV T&V CpWTCQV TOT B. TT^COTOv] COrr. 6X Ci D 2.
15. i-Gtcci] om. D. 16. ylvtoftcu D. 17. eodtW] ^co D.
20. tnleaeift D. 22. itegt] nsgl ^v D. 24. rfjg] * rfc B.
MA0HMATIKHS 2TNTAEE&S g'. 481
TOV flfaaXOV XCCTCC TO Z 6^iOV^ f] AE 7tQl(pQlCC, $V
d(p0TrjXv TO E (pcciv6[ivov XVTOOV Tijs Gfhrjvyg TOV
A qAlCCXOV) dvVCCTCCi ItOTS yV6^CCi TG)V XXL^lVC3V O
ky x. aM? v Tolg ccitb MfQorjg Tovtoig, oitov % [ie-
yiGtiri JIILSQCC WQ&V itinv Utlfr&Ql- 5
v&v ly, p>%Qt> Tobv fxfioA&v Bo-
ojtovfj yisyCGTri
0TIV farjHQ{,VG)V Ig,
aoxTovg TO 3tfal6TOvrj
XCCTCC TO TG)V Gvtvyi&v 10
TOV
TO
15
xcc
TCQOS [i
TO TtfatGTOV O VTJ. 3tO.QKM.d<56l $ KKI XCCTK
TtfaltiTov, OTCCV ^sv TO. orj agog Tag aoxTovs
3tQi TOV ASOVTCC XCil TOV 4ldv{lOVS O A SyyiGTCC, OTCiV
ra o vrj rtabg [ie6rj[i(lQiav ,nsal TOV
'I%&vas o Ts syyitiTcc. sav aocc TO
KSVTQOV vnod'to^d'cc XCCTCC TO z/, xccl STU&V-
\v z/JSJ Tys oAqs 7tccQaMd%SG)S) ^ ^ V ^F r/^S 20
XCCTK ftijxog k'yyiGTU h'tiTai 7tccQccMd%O)$) 17dl FE Trjg
XCCTK rtAdTOg. K)<5T, OTCCV [lV Kit' CCQXTOVfj i] GfAyvrj
TOV fjMov xal 7tccQccMd66r] TO TtfatGTov nobs fi6-
TK>V o T ^ AEF
1. AE] A- e corr. D. 2. aqp&Jriptf D. 4. x] xa C.
om. B. 10. nctQullaGsi D. 6vvyi(bv~\ corr. ex
A 4. 12. nccQaUd^
sD. 13. <'] e corr. D. 14.
TO TtteiGTOv] om. D. nccQ<xUd<)8L D. Ttort] supra scr. D 2.
Post xem del. TO D 2. 15. TtKgoi7.la.GGri] Halma,
ABC, TtccQaUdGrj D. 17. rd] om. D. 19. v&a>iie&cc D.22. oroiv] GTS C. 1^ Gflrjvri rj
D. 23. nuQcil.l.a.GG'ri] Halma,TtaQaMdGGei ABCD.
Ptolemaeus, ed. Heiberg. 31
482 KAATAIOT UTOAEMAIOT
a Act syyiGta. xal snel A,6yog 6tlv trjg djtb roi)
iti to P ytQLcpOiag TCQog trjv TA xata rb
t&v ixkemtix&v oaav did^trj^ia^ bv %i, ta
la // 3t$bg to a' vxatav6r]tov yag r^ilv tovto yivz-
5 rai dia tcbv ytooccitodsdsi'ypev&v enl ty
GsAymaxov xvxAov xal avtjj psv ^ cuto tov
pov sjtl to F h'titai {loia&v tf Jcg, [ita $ tijs
t&v avt&v i% jia. otccv d' aito [i6<S/
q[i(lQfa$ ov6cc tov
ri^Cov to nfalGtov xgbs agxtovs 3tccoaAA,a66r] , rj [iv
10 4T 6tai, tcbv o A, i]$ AEP o'A?? tcbv o
jita, xal
dice ta ccvtafj [iv aitb tov ovvd6[iov Inl to F yioi-
o&v g v/3, ^ $ pttu t^S F4 o'At? tcbv avtcov ij xf$.
otav aacc to Kvtaov trjs tiMjvrjg axQifi&s KTtiyr[ bito-
tQOV tCOV 6wd6[JiG)V 3ll tOV Ao|oi) XVK^OV TtOOg ftV
15 aoxtovg ILOLQCKS I't, fi, nobs ii6r]iipQiav de {loioccg v]
xf$, t6t Tta&TOv v tolg XXL^ivois t6rtot,s trjs xa&
lxov^ivrjs dvvatbv eGtcti tqv cpcavo[jiEvr]v ccvtfjs
xctta tqv 7Cd(prjv yV6&cu tov o^At'ov.
i to [iv ti\ fjkLaxrig av(D[icchias ntelo'tov
20 dicupOQOV a7idsi%ftri ILOLQ&V /3 x/y [111, 4], to df t^g
6A,r]VLCCxrlg to itQi tag GvQwyiag {LOIQQOV a [p. 337],
dvvatbv k'titau not xv\v Gekrivriv a(p6tdvai, tov ^Atov
xata tag ttOLodwag 6vvyiag axQificbg [lotaag J xd.
1. [LOTUS'] seq. littera macula obscurata A; 6/noi'cog D,
mg. fta la D 2
. icrt D, comp. BC. 2. iiti~\ corr. ex
C. TifQtcpeQEias] ~S postea ins. C. 4. /_'] ^ D. 5. ccno-
D. 6. otvxZov] Q C. Kmr\~] avrr] B. 9.
&QKrovs~\ post v. del. G C. TtaQaMaGr) D. 11. ru KVTO]
TOV D. 13. orav] -KV del. D 2. 15. ds [i6r]iipQiccv D. 16.
D. 18. KCCTO.] corr. ex KK D 2. 21. TTf^t] 7r D.
23. axtcos om. D.
MA0HMATIKH2 ZTNTASE&2 S'. 483
iv o6G> di,SQ%ercci TccvTccg y Gfhijvr], 6 per ijfoog
TO iy' CCVT&V syyiGra, TOVTS&TIV o A#,
iv o6G) df ndkivfj GsArivr] TCC o Ad sitixivslTat,,
disksvGSTCU, xal 6 tffaog to iyr
CCVT&V ra o y(bv OVK&I yivsrai, TO iy' d^Moyov. sav &QK rd inl 5
to avTO o Ag, a yivtxai T&V f'| dp%ijg g ttd ft()og t/3'9
Tatg Tijs rjAiccxris dvco^a^iccg ^lOiQcag /3 scy,
[toiQccs y } atg TO nXsltiTov dioiGovtiiv T&V iv
Qiodixais Gv^vytccis [istiov naQod&v ^itjxovg TS
xal it^KTovg syyiGTO, ca dxQipeZg. xal OTCCV aget rj 10
rtdgodog TOV XSVTQOV Tijg Gehtjvrjs dfpsdTijxr] T&V
7tl TOV lo^OV XVX&OV TCpOff [lV KQXTOV$x jia, agog psGriiiflQiccv 8s poiQccg Tec xfi, TOTS
TtQ&TOV iv TOlg XXL^VOLg TOTCOig dvVCCTOV 6T(U TYJV
(pKivoyLSvriv avTrig frstiiv XKTCC TJJV sitayiiv ysviGftai 15
TOV fjMov. xal did TCC avTa^ oTav 6 dytb TOV
3ioaTog TOV Ao|oi> xvxhov Tijg 6Aijvr}g 6
[p. 471] Tcctg TtSQLodixaig tivfryicug T&V
pbg iJTOi, TaZg dab %& i& [i%Qi<g yd xfi r) TKig dab
4ttcc tiwsftxfattyi) TOTS povov iv Totg 20
XXl[lVOig TOTtOig SvVKTQV S6TO.L 6vyifti]V(U TO 7COO-
xsiyisvov.
1. ravra B. 2. ty'l if* C, ut saepius; I r corr. ex ri D.N
3. GfHijvri] <[ D, ut saepius. litMivltai\ corr. ex sni-
MEfrcii A 1. 4. iy'] i y' D. 6. ;|] corr. ex ih. D 2
. t^'Jcorr. ex iy D 2
. 7. ^^lax^g] i\- e corr. in scrib. C. 8. Si-
D. 9. Teas] T?? D. 16. 6] om. C. 17. 6] om. D.
18. rats] *?<? D, ut saepe. T<MV JLIOI^COV] fi D. apfd-lfAog A,
19. pi-iQi, D, corr. D 2.
r/'] seq. ras. 1 litt. D.. D 2
.20. ~svr\\ -J] e corr. D 2
. ^X9 L D- cvvf^ninrfi, C. 21.
TO 7tQOY.ipitVOV 6Vfl^f]VCCL D.
31*
484 KAATAIOT HTOAEMAIOT
xccl T&V rijg Gehtfvrjs sxteiitTwcbv OQ&Vx TOV XEVToov
rb kd%i<5Tov KVTri<s djt66Tr][i
O fc JZ, ^ 6s X TOV XEVTQOV Trjg
ov6K xal ri rots XQitii ktyuctotg
v rv\ IK tov XBVTQOV rijc; GeAtjvrjs tivvcc-
yetai, r&v avrcbv o jie vg, dijAov, on xcci, otav rb
XSVTQOV rils Gshtfvrjs dxoifi&s ccit%fl TOV XEVTQOV Tijs
GXL&S BTtl [ISV TOV dt' CCVTG)V Xttl TG3V 7t6k(QV TOV
10 Ao|oi) yQCKpopevov {isyiGTOv xvxhov l(p sxccTeoa TOV
fiotoccv a y Ag, iitl ds TOV Aooi) xvxAov
d(p' OTCOTBQOV T&V GvvdsGp&v XUTK TOV
TOV vbg nobs TCC Id /.' Adyov poi^as t/3 ifi
TOT JtQ&TOV dvVCCTOV 0TKi TJJ
15 Gxi&g. did Td avTa $ Totg ytgl Ti}v dv&iiKUav dito-
xat, OTCCV TO xccTd TJ\V {lEGrjv Ttdgodov
M-VTQOV Trjg 6^tjvrjg dytEGTijxr] T&V 6vv-
l TOV Ao|oi) xvxkov [lotoag Tf t/3, GXSTE Ttdfav
xccTa Tovg dub TOV fioQsCov TtEQUTog doi&-
20 povg i'g T Tovg dnb od ^ p%Qt' ^ i>Pxcti *t$ Tovg
ditb 6vd ^Trj ^B^QL GTCE i/3, rdrf itQ&Tov dvvciTov <5Tai
Tr]v QEKv\VY\v ttJCTEGd-cu Trjg (Sxicig. Jtaoad'rl(30fiv ovv
Tolg 7tQOXi,^ivoig T&V Gvtvyi&v xavovioig xal Tovg
1. ([smg. C. 5. nsfinrois] f' B. 11. loov] ante |
ras. 1 litt. A. 12. &cp'] corr. ex tap' D 2. onorfQov D,
corr. D 2. TOV] om. CD. 14. ngmtov] K D. ftyrca] om. D.
rr)v] corr. ex rfjs D a. G^vr]v] comp. D. otyafftfm D.
15. TG>V avcoiLcch&v D. 16. ft\v} om. D. 17. aqpfffrrjx^-
p. 485, 12. rip/] fuit etiam in mg. sup. D, sed eras. 19.
xara] corr. ex xa D 2. 20. xori 21.
tJ3] mg. D 2. ft's
rovs] efc D. 22. KipaGftcii D.
MA0HMATTKHS 2TNTASE&S S'. 485
r&v re fjhax&v xal r&v 6s^viaxcov oocov rov
rijs GsAijvrjs apt'ityiovg, iva xal rr\v r&v dvvajiEvcov
[i7C6Eiv didxoiGiv e% eroCpov
g'. IJegl rijs dia6rd0a)s r&v sxkEiitrix&v {lyvcbv.
Kal 8ia noGcov d' fag iniTtav ^vcbv dvvccrbv 5
Herat, rag Gv^vytas Exteinrixas yivEGd-ai,, %Qtf6i[iov av
sty rovrois itgodd-elvcci, TCQOS rb Accp6vras pfav Bito^v
xfat,7tri,xri$ 6vvyiccs ^ jfccGag xdAiv rag s'gpsl-ijs, aAAa
rag dt' o<?v av vds%6[ivov TJ [irjvcbv sx^s^iv ysvi-
rcbv OQ&V EJtfaxEiluv itaQaAappavsiv. 10
rb [iv ovv $L $% [irjv&v dvvarbv slvai, rov re
ov xal rqv 6&rjvr]v fafafaeiv avro&sv av si'rj
xara itAdrog Ttdpodog rijs
ev rots <5 [irjGiv tfwdyfl ^to^ccg QTtd a us, aC ds
r&v sxfaLitrixcbv OQ&V TtSQicpEQeiai, xal tnl rov 15
xal eitl rr\g Gshijvrjs aC {LEV svrbs fiinixvxMov
avr&v HOLQKS jtEQi,E%ov6i,V) aC & VTCEQ rb
TtAsiovas' r&v rs yag fifaax&v oo&v TCQOS
ras agxrovs drtohaiifiavovrov acp' OTtorEgov r&v
rov Ao|oi) xvxXov rils ^E^tjv^s *&S 20
[p. 483, 10] potaas x jita, ngbs d%
potoas Ta xfa xalrj pv ait aoxr&v dvsx-
poiQcbv ohy A^, fjd' ditb
1. re] om. CD. xca] re xat D. x&v (alt.)] om. D. 3.
A. 4. s'] BC, mg. A 4
,om. AD. 5. dvvccrov]
supra scr. D 2,Svvatcov C. 6. yevzoO'cti, BC. 7. TtQOG&fjvai D,
sed corr. 9. sxieii/jftj yiVEGftui D. 10. nccQaJicc^dv \
C.
14. 5] gg BC. pj\Gi D. ^rd] ^t C. 17. t] -I posteains. C. 18. i]iu.Y.vY.).iQv] TJ- corr. ex N A. 22.
'
ft D. xcu] om. D.
486 - KAATAIOT HTOAEMAIOT
OiQ&v Qvt, Zs, r&v rs Gshyviaxcbv aito-
ig sxdrsga ra [isoy rov did [is6G)V snl
rov avrov uvxhov [loigas aito r&v 6vvds6[LG)v is t/3,
xal sxatsQcc r&v dv^sCitrov Ttsoiysosiav Gwdysrai,
5 {loiQcov ^ftO" Ag.
on, ds xal dia tovr&v r&v VTto&sGs&v dvvarbv
dia rijg
rjv 6
10 ldoi[iV av ovrcog'
7ti8ri pay v rfl [itey 7tVTcc[itfvG) xv\v
KKTQOV t&V
litl rov STUKVKkov ^lOioccg QX&,rovtcov
15 df ccC [ilv o{i A/3 rov rikiov ^LOIQCH, Kara rv\v scp %d-
rov ttQiysuov [isyfarrjv Jtdoodov
rqv [teGrjv [loioas d A^, ai $ rov
r?ls 6^tjvris QX& * poiQai Kara, rr\v iy sndrsQa rov
aTtoyLov &a%i6rr]v xdoodov dcpaioovGi,
20 poiQas y P) v r& XQOVGJ aoa rijg fA<?^g
orav 6 [ilv ijUos rfv psyfarriv itoirpai rtdgodov, i\ds
ryv &a%farr]v, sn TtQoriyov^Bvri 6rau rov
rats f' d^igjorsocov r&v dv&tiafa&v
Qais 1/y 1/rj.&v nakiv rb i$' Aafiovrsg
25 did ra JtooaTtodsdsi'yiisva s'^o^sv [lolaav a xal s%rj-
xotird g fyyiGra, r^v 6 TJAtog TtiKivrfov\6rai p%Qi rov
1. tg] corr. ex vg D 3. 6. dvvccrov] dwccrav A. 7. GB-
D. 8. TOVTEGTIV] comp. B, -v eras. D. 15. 8\D. 16. bulappdvowiut D, -v eras. 17. at] corr. ex
Sid D 2. 18. [taigas C, corr. C 2
. 21. TrotTyrort] D, TtoifmaABC. 24. lunpdvovTes D. 25. nQodtdsiy^vcc D. 26.
ante ras. 1 litt. A.
MA0HMATIKHS 2TNTAEES <;'. 487
V7CO T^g tffA^V^g. 1tidr] OVV X 116V
T^g iSiag av&paMag jrtAr?<pt (loiaag d xal
A??, x ds Trig pfyQi tr]g axQifiovg (Svtvyiag
[lOLQccv a xal z^xoGTa ,Etittu xal
fj
naga TJJV (isGyv 7tsi,hr]cpvttt Kara 5
xccl t,r]xo6Ta [id. ToGccvrag ago.
GTCC ncclfj
xara rtkaros Jtl tov Ao|oi) uvxAov
fl<3 0^t]vris 7ti,Ar](pvta 6xai [IOLQCCS rots
\Li6v\v jifvrcc^vov ffvvayo^voig Ttlarwolg
Qvy KK fyyitira' &<5te nal q axQifl&s &G)QOV- 10
xccra nhdros xaQodog iv TTJ psyiGrri Ttfvra^vc)
QV& KKl %r]XO6tK)V . AA' 01
<p' xdrQa tov dia [i<5cov x2.t,nri%ol Kara TO
rijg G'fA^V^g OQOI 7tQi%ov6iv iitl \JL\V
TOV dia T&V nolcov TOV Ao|oi) ygayoyidvov \ityi6TQv 15
[lotaav [iiccv lyyiGTU dia TO T^V ply XCCTK TO
slvai [lotaav a ~y Ag, Tr\v ds KKTK TO piyi-
GTOV &vvd'y6d'ai o v$ xd, iitl d TOV Aojoi) xvxhov
ano T&V 6vvd6(iG)v T^^JLCCTCC la A, rjd [iTcc,v av-
xal dvx^L7tTos 7tSQi<pBQt,a dice TOVTO GvvdysTai, 20
o, af
iTive$ ^KTTOVS i<sl T&V xaTa TJ\V
itiKa^avQ^ivKtv TOV Ao|oi) xvx-
Aov oi,QG)v V& xccl xo&c&v TriaGi, dvdl xal
1. f'x] coir, ex ^ C. 2. fTrfdrjqpft] -I- corr. ex ^/ A,
post qp del. -O1 C 2
. 4. Y,CU f^rjxoffTa ?] e; D. 6. (IOLQKS]om. C. xca f^jtoara] om. D. 7. rj] om. D. KCCTO] -TK
add. D 2. TtvxAov] uvnlov
r\D. 12. xal rjxo(>T<a?>] om. D.
14. nQl%QV6lv] TteQli^OVGi TOV lo^OV D. 711 - 15. TWV]bis D, sed corr. 15. TOV AO|OV] om. D. 16. jtuav] a BD.
17. fld%iGTOv] hinc inc. A 1fol. 175 (quatern. %y). a] jiitav A 1
.
21. ftfft] mut. in tt'atV C, sed -v rursus del.; comp. B. 22.
-o- in ras. A 1. 23. QV& v.ccl I |rjxo(7T<m'] 9? ^f D.
B.
488 KAATAIOT HTOAEMAIOT
. <pavQbv ovv lx rovr&v, <m dvvarbv
<5rai r^v 6eAijvr]v ivrift peyfavfl Ttfvra^irivc} xard rrjv
no&ryv navG&rjvov xfafaov6av xura r^v dcp'
QOV r&V 6Vv86p,G)V KJtO^COQ^iV XCcl V
5 jtavGsAtjvG) rtdfov exfafasw xccroi rfjv iitl tbv svctvriov
tQOtfodov anb t&v ccvr&v pSQ&v rov dia
sv aiicpOTQat,g ral<$ sxtefysGiv rijg eTUGxoTijGs&g
xal ovdejtors aitb rear svavri&v.
on jiv ovvYI iLfyfaTi] ytvra^r]vos dvvatai, dvo
10 TtQivfiui GfArjviaxas fxtefyfis, ovr&s r^ilv
or i, $ dt,' itra [iqvcbv advvarov 6rca rovto
fti]vai) xav r^\v lka%C6rriv fjtrd^vov V7to&co[id'cc, rovr-
qv 6 {lev ijA
d 6&ijvr] ityv iifyfoTrjv , i'doi[iv av
15 CiVTOV TQOTtOV CpodVOVtS
7tidrj ya$ jtdkw iv
y ^t, ^ d' v TO) 3tixvxA.G) ri}g 6-
[toiQag ^r jity, TOVT&V d' at plv ~6y
20 rov i]Uov xara T^V (p xdra rov
1ii6r <
Y\v nccQodov acpaiQOvGi, rijg
d/Lt/3,
CCL df rov 7tixvxhov rijg
xaru rr\v (p' fxarfya rov
jtQoed'yovGiv rri \ii^ poiQag 0- v^5iv raj %QOVCO ago,
25 rijg listing 7trtt[njvov ,orav 6 plv ijfaog rrjv
3. &cp'~] A 1C*D*, V BCD. 5. TOV] T&V C. svavricov C,
sed corr/ 6. TtdgoSov D. 7. ixlffyeti D. 11. a.8vvoirov\coir, ex dvvurov B 2 C 2
. 12. TOVXKGTI D, comp. B. 17.
nard] corr. ex v.a D 2. 18. d'~] de D. 22. QTC jZy
ft gn fty D. 23. fieyiar C. 24. nqocdyovGi D.-fr]
corr.
ex o D 2. 25. pearis] A 1
, i\a^ierrig BCD; cfr. p. 493, 14.
MA0HMATIKHS 2TNTASE&S S'. 489
6rai rov yhiov r\ Gshtjvr] rats f| cip-
riibv av&uaAi&v Gwccyopsvais poCgais idjit.
dia ra avra TO ifi AccflovTSS xal rtQoe&svTSs ratg
&[iaMccs zhkekoiTtviaig [lOiQdig d pp 5
[IOLQCCS vs syyiGra %0[iV) oGais ij
re Kara pfjxos ndgodos ev ir\ ika^iGiri 7tra[irjvq) v6ts-
sv ffi ftfV^, xai % XKTCC rtAdros axSavr&s
et r&v XKTCC rrjv iifayv ^XK^VOV 6vvayo[iva)v
ft/3*v rfj lka%C6Tri CCQCC eTtraiirivcp inti- 10
xccra jrAatog v\ GfAujvY] eitl rov Aooi)
xvxhov riirniarcx. ^rj [i oAys r^g psraZv rcbv
x&v xccra TO pfaov anoGrri^K T&V trig
TOV Aojot) xvxhov peyfarris ytSQKpsgeias rov re XCCTK
rrjv nooGcc'y&'yriv rov sregov r&v GwdeGiicov xal rov 15
uccra r^v a.TtQy&gr\i5iv rov eva
ov6r]s isy o. ovx CCQCC dvvarbv eGrai rqvovd
1
iv fi\ A.ct%farr]
Kara rr^v TtQarrjv TtavGeArjvov oitcotidrjitoTE xal Kara
r^v rztevraCav TtavG&rivov hi, Exfafafiv. 20
dfixrsov drj nakw, on xccl rov ijAiov dvvarbv
6rai, itaga rois avrotg dig MfafaEiv iv rr\
xal xarcc jtdvra ra
fi ya$ iv ry \Ltyi6xri Ttsvra^vG) rrjv xara 25
Jtdoodov rr\$ 6Aijvr}s a7Cd^aiiv [p. 487, 10]
QV& rife dvExfafarov 7tQi,(p()iag iitl rov
xara TO [iGov ano^rrnia T^S GfArfvyg r&v av-
1. noiSiTca C. 7. iv Tj]] coir, ex Jyyiffra D 2. 13. r&v~]
om. D. 18. ovd'~\ ovSs D.' 20. hUni-iv D, corr. D 2;item
lin. 22. 26. tf^aVrg A 1.
490 KAATAIOT HTOAEMAIOT
r&v yivo^isvrjs 015 k% SIM fb xal rovg il
ooovg avrov rov dia psticov aiti^iv 7tl [ilv rov dia
r&v itoh&v avrov xvxAov r^itj^iara oA/3 #, siti ds
rov Ao|oi} tils tiskrivris [lotoag g /3 syyiGxu, d^Aov,
5 on ^dlv ply TtccQCiMattovGrjs r^g GeArfvyg ctdvvatov
TO JtQOxsipevov dia ro [i%ovcc elvai rrjv ccvex-
tys sv rfi psyfa
7tl plv rov Ao|oi)
7cl ds fov itgbs oofrag iti dice ^d^cov o
10 OTCOV ft av dvv^TKi TtaoaMccGGsiv ovrca^, co6re rag iv
OTtorsoa rCbv axocov Gvvodcovrj
xccl rug 6vva^i(porQ03v
7taQcdhd,i,g ra oft vxsofldMsiv ,
sxet dvvarbv
xal rag axoag Gvvodovg a^i(poroag xhf,7tnxag
15 7tidrj ovv idstifrpsv [p. 486, 20] iv red %QOVG)
yLeyiGrvis 7tvra[MJvoV) oravrj [iv tfehfan} rqv
6rr]v itoi,r\ra,i jtdgodov, 6 d ijfoog rqv [ifyfarrjv anb
r&v dvo iiQG>v rijg JlaQ&svov ^%oi rcov dvo
rovf
TdQo%6oV) Jtoorj'yov^evrjv BXI rov r\^iov
20 htfvrjv ralg x r^g a[i<porOG)v r&v
~iy Irj) ravrag $ xal b'u rb i$' avr&v
on rov
25 TCfvra^iTJvov %QOVO farat iftLSQcbv opy xal faoatv1/rj
xal dia rovro rf}g Ttocoryg xal itQl ra dvo
14.
TttVTCi-
5. ftj>] om. C. 10. TtUQcduGGtLv A 1. rag] om. D
\6ftai D. 16. iifyiGrrjs] -ijs in ras. A 1, fi&rrjs D -
/u.rjvo'u]IT- in ras. A 1
. 19. 7tQor}yov[jiVT]v] -j\v comp. add. C 2.
20. r&v] om. D. ccvapccUKS D. fiotQccg C. 21. i(3']
t'^' A 1
(" in ras.), C. 22. fiG\cog mut. in [ts\Gcos A 1. WQUS C;
comp. D, ut saepius.
MA0HMATIKHS ZTNTABESS '. 491
yi,vo[ivr]g Gvvodov % TEtevraia xccl JCEQL
ra dvo pegr] rovr
Tdoo%6ov ywopEvr] noorEoov 6rai,
rats tg oAag r^iEQag fainovGaig agcac; g.
aga, jtov Kal TtoTE dvvcttai, % Gektjv'r
r\XOl V t& StZQCi rCOV JtQOKSlllSVCOV dG)dXCCrr][JiOQlG)V 5
iv r&f
Tdgo%6G) tys iv rrj
TG)V
CCQXTOVS jiV ovv ovdapij rrjg xa.& JHJL&S ol-
)%a&' ov ftgrfxccfiEv tgoxov, ffbyfaxeccu TOG- 10
ovrov 7taQah%d66ov6a rj <3^vrj' o&v ccdvvcctov yi-
rb iv rr) psyiGrri Ttfvrcc^vG) dig mteiTtsw TOV
xara rfjv anb (t4qpfiya$ rov dice pfacov
itdgodov, rovrfatw orav XKTK plv r^
Gvvodov aito%G)Qri rov xaraflipd&vTos (Jvvde^ftov, 15
xata $ rr\v rskevraLciv Ttgo^dyr] r& KVCC^^CC^OVTI'
yipftofav ds 6%dbv onto r&v fira xov fay-
oiKOvvtcov &$ itQOQ rag KQXTOvg dvvctrat, rb
roGovrov iv a[icporQOi,g rolg xxt,(ivoi,g dodwccrrjiio-
Qtoig Kara rr\v itQO 2 GZQ&V ftteiv 7taQaM.K66i,V) 20
orav ra plv r^g Ilag&svov dvo [legy Kara ri\v JCQO)-
rrjv Gvvodov itl rijg xaradvGf&g vnoxfyrai,) ra df
rovr
TdQO%6ov Kara r^v devrtgav tivvodov 7tl rov
Kara pay rag rotavrag &E6i,g vafaxo-
ETtl rov pEGov aTtotirtfiiarog nobg 25
1. Trap D, ut saepius. 2. vdgo D, ut saepius. 4.rj]
in ras. A 1. Tta.ga.lla.GG
A\
C. 6. vdQr]%6o) A 1. 7. ntefav C.
10. TOGOVTOV tvQiGKerai D. 11. 77 Gs7.r\vr]'] om. D. 12.
Jx/lftjrftv] supra -fat- add. i D 2. 15. aTro^cop^] D, ccito%co()i
A^C. Kapifidfrvros D, corr. D 2. 22. VKOKSLTCCI D, corr. D 3
.
25. Post 7t$6$ locus relictus ob naturam pergam. D.
492 KAATAIOT HTOAEMAIOT
rrjg r\^ia-
xi]g TtaQaMd&cog vitb [ilv rbv farjpfQivbv v {lev xr\
rr}g UCCQ&SVOV fteGsi [loiQcts o xf$ fyyiGra, v ds rfi
rov *T$Qo%6ov o id, onov dsi\ psyfaTr] r^neQa
5 Idrlv ifi /.',XCCTCC [isv TYJV Tijg naQ&svov &<3i,v
o x xardi de v rovf
TdQo%6ov loiag o
rag
O
rovg POQLOTQOVS ad rojcovg
10 xaQaMd%G)$ yivo^vrjs yccvfyov, on xal paMov addvvarbr ztixcu, rots v avrotg ofaov6i, dig v
(5rri itVTa[itfvG) (pawfjvai rbv ijfaov xfofaov
pswoi rqv an aQKtcov rov dia [i6a)v rqs 6-
TtaQodov, rovrttSnv orav 7tl pv rijg
15 xtefy(Qg aitoG)r rov avaf$
r] rip
rtdfav, on, xal v rr\ ifajfatft
dvvarbv 6rai, dig rbv ijAtov Tiaoa rotg avrolg
7tiv. 7tidr] yaQ v ry &a%i6rri BTtra^vG) rr\v xara
20 n^drog rrjg Gfhijvrjg xdaodov dnd%a[iv [p. 489, 10]
rcov EKketTtriKcbv OQGOV 7tQi(pQia rov Aooi>
rqg ano rov xara rj]v itgoGaywyfiv rov MQOV 6vvd6-
uov ii%oi rov xara rrjv aitoi&QriGiv rov wavruov
4. 8i] -s in ras. D 2. 5. iott D, comp. B.
om. D. 6. x^] corr. ex v.$D 3
. [IOIQCCS] om. D. 7.
om. D. 8. ^TJ] corr. ex Se D 2. 10. (i&Uov ccd dvvarov -v
ccd S- euan. et eras. A 1
(NA//J). 12. snteinovTcc]-- in
ras. A 1. 15. ano^co^ri] D, ano%a>Qi A^C. 17. i^viA D.
18. rbv rjliiov dig D. TCCCQCC TOI$] post ras. 5 litt. corr. ex' D 2
. 19. Post &a%i<nri del. rjj C 2. 21. S'] Ss D. 23.
6- in ras. A 1.
MA0HMATIKHS STNTAgESS g'. 493
tivvd6[iov Gvvdyerut, xal STtl rov fjMov rj roiccvrri
did0ra6i,g itl rov psdov rife G^ijvy
pq/3 xd, dijAov, on [iqdsv per itdfov
rijg ^s^vrjg ddvvarov 6rai, rb
did TO [t%ova slvat, r^v rfjg A,a%0T'r]s 7Crcc^tjvov rov 5
Ao|oi) Kvxkov 7iQi<pQSia,v rijg vnb r&v
OQGOV rov Y\Mov [isyfaTrjs djto^cc^ftccvo^
7tl [isv rov Ao|oi) xvxhov Tg 3cy, iiti $ rov diet rcbv
rov q)diaxov a Jci, oTtov d' av dvvyrai, jtaQak-
og, &6re rag iv OTtoxsga r&v KKQCSV Gvvo- 10
d&v rjxal rag evvaufporfyov aua itaoaM.d&ig vitQ-
iv a xie [lotoav, Xl dvvccrbv 0rca nal rag
ovv di%a[iv [p. 4887 24] v TCO %QOVG) rr}g [i
7Cra^it]vov ,orav
i\ pey 6^vr^ xv\v {iyfarr]v itoii]ra,i 15
vtdoodov, 6 d ijfoog %v\v &a%farr]v aitb r&v
rovr
Tdgo%6ov p%Qi> r&v ILSG&V rrjg naQfAykvd'vtav ijdrj rr\v 6J.tfvr}v rov ijfaov dxaifl&g \LQI-
gaig idji, rag $ roGavrag [toioag xal sri ro i$' av-
r&vYI GfAijvr] Kivelrou, [i0G)g iv fjlifya [iia xal coQatg 20
7 (pavoov, on, rov %QOVOV r^g iieGrjg 7tra^it]vov 3t-
Qis%ovrog fmsoag ~6$ xal coaag i^ fyyiGra 6 rijg &a-
%farr]g 7tra^vov %aovog h'tirca yiiQ(bv 6 xal
fc/3,xal di,d rovro 6 ri\ reXevraiag xal itol rd
3. fiev'] supra scr. D 2. 9. nccQcdccGEiv D, alt. I supra
add. D 2. 10. rag] m D. 11. xca] om. D. nagulJ-a.&is D.
13. ylyvE6&\cci D, yLyveG^at
\
D 2. 15. iisyiGryv] corr. ex
'arjv D 2. TcoLeucci A a C. 17. nKQEtekv&victv C, sed corr.
18. /LUHpcag] A 1
CD, comp. B. 20. rr\v ctlirjvrjv D, sedcorr. ^GCOS] om. C, a ly fifffco? B. fita] a C. 21. xf)s]
seq. ras. 3 litt. D. 22. tat] comp. postea ins. C. 24. 6]
postea ins. D.
494 KAATAIOT HTOAEMAIOT
Tijg nagfrsvov Gvvodov %Q6vog {tTd i$ cogag
TOV rils rtQ&trjs xal itegl TO, 6%ccTK TOVe
Tdoo%6ov.
r]Tr]Tov #(>, itov xal Ttors dvvaTair\ Gfhtfvr] nkeiov
Tf}g a x poiQag itaQaM.d<56iv r\roi iv t<p Toc) x&v
5 itQoxi,[iVG)v dcodsKKTrftioQicov rjiv d^cpoTS^oig xccra
TJJV dia i$ cdQcbv #tfiv, TOVTS'GTW orav TO per
,to df TQOV ccvctTekkri, dice TO
Tag htefy&g d^(poToa
apKTOvg [iv ovv nakiv ovdccfjii} rtjg XK&
10 OMOV[lVr]S XCCT* Ol)d[lLaV ftiGlV TOGOVTOV VQfaXTCCl,
3taQaAA,d66ov6a i\ 6^vrj jLtT/d' ccvTotg Totg VTCO TQV
fay[iQLVOV iilov %r]xo6T&v ~wy Tijg xaTa TO
KKTK ithaTog jtaQaMd&cog'v Tfi eka,%<5Tri fjrta^Vcj dig
15 7tlV TOV ij&lOV KttTCt T^V OLItQ /X(???fl/3(Mft:g TOV did
(i6G)v Tijg 6^vyg ftdgodov, TOVTBGTIV OTCCV xaTa fti>
TYJV TtQOTBQKV GVVodoV TCQO^d'y^ To5 dvK^iftd^OVTi 0VV-
$ T^V TffavTaittV d?tO%G)Qfl TOV XCCTaf3l,-
'
itgbg ii6r][jipQiav $ Trjv ToGavTrjv TC
20 kc&>w VQi6xoiiv d7COT^ov^ivrjv (3%dov dttb TOV
*P6dov jc()aAA^Aov, OTKV TK (iv 6%KTcc TOV
TK $ [i6a Tfjg IlaQ&tvov dvvy.
ydo v 'P6d(p xccl Totg V7tb TOV avTov
need'' xaTav TOVTCOV T&V &6G)v f 6e-
3. nov~\ supra scr. C 2. 4. nctQulaGGSiv D. 7. CCVKTB^JJ D,
corr. D 2. 8. yLyvscftai D. 9. ovv] om. C. 11. JtccQaiccG-
GOVGCC D. 12. [isigov jLtf'ywirov] supra scr. D 2. 13. Hara]
A XD, wtu TO BC. Ante oftw del. ccdvvccrov D. 14.
ytyvfTort D. inteinBiv] -v.- supra scr. C, post I- del. y D.
17. Gvvodov] corr. ex cvvohov D 2. 18. ccno%co(>i B. 22.
[IGU xfi<s\ corr. ex (iGo\/f]s D. naQ&sv C,v
supra Q add. C 2,
sed euan. Trapa/Uaaft A 1
; naQK^dcGei D, corr. D 2. 23. roig]
-S supra scr. D 2.
MA0HMATIKHS STNTAgE^S S'. 495
Kara rb [i6ov ditoGrrjpa rijg
v(pciLoov^,Evrjg nobg ^lE^r^L^Qiav dvd ojits
fag tag EV d[i(porEQcug ralg Gvvodoig 7tccoaA.Ad,Ei,g EV-
rEv&EV ijdrj pstfrvg ywea&cu, rqg [nag ILOLQCCQ xccl r&v
XE E^iyxoGrcbv. Ttfaiovog d^ yivQ\LivY\s rijg itgbg fts^ft- 5
d&og EV rotg En rovrov rov yta^a^tj^ov
(pUVEQOV ,OTt dvVCCTOV iGXUl tOlg XCCT
ccvrovg oiKovtiu dig EV rfi A,a%i6TT] ETtrafiijvG)
KQXT&V rov did [IEGCOV ryg GEhtfvrjg naQodov, TOVT- 10
E'GTIV orav ETCI [iv rijg itg^r^ ExfafyEcog nQoGayri
rd5 xccrafiifld&vTi 6vvd6^G)^ Eitl ds rfjg dEVTEpccg dxo-
d' av E7tidt%cci xcci, Qti did
Evbg ov dvvcctbv EGtai, dig rbv ijfaov EX^ELTCEIV EV rr\ 15
xad"1
fjpccg otxov[iEVfl ovr1
EV rd5 avr& xMficcti, ovr*
EV dicKpoQOig, xdv itdvra rig apcc vTto&rjrai, rd prj dv-
vdiiEvcc psv 6vvdQK[iEtv, 6vMcc[iflav6[iEva d' ccMcog r<5
dvvccrbv itQi^ai rb TCQOXEL^LEVOV , Asya) df, xav rr\v
xard rb E2.d%i,<5rov d7t60rr][ia VTCO^GJ^E^K^ 20
taQctkkdGGri, rbv d [ir}vcc Ekd%i6roV) iva
O'(?GJ dvvccrbv Ekct%C<5rG) ^IE^COV ^ xccrd TtAdrog [lyviatcc
Ttdgodog yivyrai, rqg vitb r&v ExhEMriK&v OQCDV rov
,xdv ddiacpOQCog ratg r &QKIS xal
2. o] ins. D 2. 3. rag sv\ TULS Iv C, TKIGVV D (t mut.
in <>?). 4. yivsG&cci] corr. ex yevec&ca D 2. 5. ytyvo/LtfVrjg D.
6. Tt] -T- in ras. A 1. 8. ftax^rroo D. 11. nQK>tr\g\ bis D,
sed corr. 14. inidttgai] -n- mut. in t C 2,
%ti ^ft|at D. dia]
post ras. 2 litt. D. 16. O%T' Iv (pr.)] o- corr. ex r in scrib. C,otirs D, otirs sv D 2
. otir' iv (alt.)] ovte D, ofas sv D 8. 17.
v.a.v} s* C. rtg] corr. ex rrj D 2. 18. Gvvlcc^avo^eva A^C.
20. HUTU TO] corr. ex V.KT D. 21. Ttagcddccr] D. 23. vnb
T&V] vnb r- in ras. A 1. tllimiY.&v D, corr.' D 2
.
496 KAATAIOT IITOAEMAIOT
rotg dadexaTr][iOQioi,s xara%or}6G)iid'a, xad1'
&v rag
7Cl rOlVVV V TG)ftf'tftO [l^vl f} flV XttTtt
xars'oov r&v (p&r&v yfdoodog 7tiA,a[jifldvi {isGcos [ioi-
5 Qag x& g? j]ds xara rbv ^Ttixvx^ov rijg 6^tjvrjg
xefi-0
1
,TOVTGJV d' at plv x& g rov qMov
ey sxursQct rov axoyeiov sA.a%L6rriv
rrjs iitGys [IOIQCCV {iiccv r], aC ds rov
xvxhov rrj$ ^s^tjvrjs x P& ^OLQCCI, xara rr\v stp* sxd-
10 rsQa rov rteQiysfov yisyiGrviv ndoodov
9<XV CCXOhovd'COS TOtg
rag % a[i(pora(Z)V r&v
r&v yivoyisv&v y Ag ro if}'ra o
^ oig 6 t/Atog AAAot^t? Jtot,tj0o^i
15 K xg xal roGovroig ^o^iv hd<56ova rqv rov
pyvos vt&Qodov rrjg v TCO ^eVoj [irjvl xard rs
xccl xccra nhdrog' &<5r', isutft'Jp&Q r\
rov pfaov [irjvbg
xccra Tthdrog ndoodog iioia&v 6rw A ji, rqv rov
Grov xdoodov yivBG&ai [loia&v x& id, ainvfg
20 Bid rov Ttobg oo&ag r& Z&diccxc!) [iyi6rov xvxAov
riMJiiKra ft Ay fyyitira. aAAa ^ naGcc r&v fxfainrix&v
OOGJV rov fjhiov xdoodog 6vvayrcci xccra rb &d%i6rov
rijg 6A.tjvr]g ovGyg r[t,r][idrG)v a g, fag
6. ju^1
]corr. ex fts D 2
. 8. KcpaigovGiv] -w e corr. A.1
C,BD (-1 in ras. D). 10. rov] supra scr. D 2
. 11.
isvoLs] it- e corr. in scrib. C. 13. yiyvopsvoov D.
14. TtoiiJGofiev] corr. ex TCOLI/JGCOIISV D, noir\6ay^v A X BC.
-roc supra scr. D. 15. a] [iicc D. s^cofiev D,
sed corr. 16. Ante nqvos del. T D. %ara D, ut saepius.17. >' 18. ndgoSos] mg. D 2
(5ffre), wapodoff etiam in
textu. 18. ffftir] comp. B, -v eras. D. 21. r^(ia D. 22.
D, sed corr. 23. a] ftta D.
MA0HMATIKH2 ZTNTASE&S <5'. 497
fY]v tov A.a%i6tov [irjvbg it&Qodov
a x. $f
ov ovv av sty itavtcog, sfaeg v t& vl
dig 6 tjfoog inteCitQi, rjtoi, Kara [LEV trjv toav t&v
Gvvodav prjdsv 7taoaM.d66i,v tqv tisAtfvriv, xata ds
K H, T}KCttf XCCTQKV flV
rcc avra naQakk(x,(56iv , rrjv
rcbv itaccMdcw ova elvat, T&V a
rj 6vvauq)OTQas rag ituQahkK&KS itfaiova r&v avrQv
oravi\ pkv if\% TQccg Gvvodov
, r\de tils *$& #pog p&S*ipfy{av. 10
'
ovdccprj tijg yijg iv tats Gv^vyCais ovdl xata to
ka%i<5tov aitotitrjiicc ittelovf) 6^vrj xata nhcctog
tijg yfaaxijg
ovx aga 6tca dvvatbv iv
l dig Kkei7ti,v tbv r/Aiov, otccv ijtoi xccta ^ilv trjv 15
t&v 6vv6d(ov {tydE
tec avta
i) Tttetovog yivo^vrjg tijg [nag [lotgag dovxccl t&v a K\. [lov&g av ovv to 7tQOXi^ivov dvvcuto
,i 7tl ta fvavtta yivo^svrjg xatQag t&v 20
1. elajfTov D. 2. oj pice D. ccv ovv D. 3. 8k] 8g
supra scr. D. 6] om. D. Mg. 6 y Sis D 2. 4. n<xQ-
andGtiv D.^
5. Ante a eras, ^f D. Ixar^av] corr. ex
SV.CCTSQCC D 2, srigav A 1
. 6. TtKkiv\ om. A 1
,corr. ex ndgodov D 2
.
nctQccMdaJi \
D. 7. S' vnQO%r^v] corr. ex dvongo%i]v D.
8. nteiova] D et post ras. 5 litt. A 1
, nleipvaaBCD 2
. 10.
&QKTOV D. 11. TKts] TgC D. KKTCc] X/ : D. 12. KKtK,]corr. ex ds Kcitd D, %ara TO C. 14. Svvarov] corr. ex ccdvvu-
rov C 2. 16. Gvvodcov] Gv&yi&v D. i] cslrivi]] TJG D, 17 c D*.
A 1 C. 17. TtUQct'kl.dGri D. 19. a] pia. D. TO]ins. D 2
. Svvairo] corr. ex dvvctirov D; dvvcctui C, sed uide-
tur corr. C 2. 20. aviccLvsiv TO ffvtveiv C.
Ptolemaeus, ed. Heiberg. 32
498 KAATAIOT nTOAEMAIOT
r&v a
tivvdyowo. rovro d' 7tl diuyogov psv otxov[ivr]g v-
d%6[ivov h'Grai 8ia rb dvva6&ai itaoa psv rots POQEIO-
rfyoig rov fayiiegivov rcbv v ry natf V^LKS OLXOvpEvrj
5 JtQOQ [isdrjiiflQiav TtccQcckhccGGsiv r$\v ^s^tjvrjv^ naga de
rolg voTicoTSQOis rov farjpLeoivov r&v avn,%&6vc()v ua-
ccaxrovg 3tccQKA,Ad66t,v fisra ryv rov
v cato o jcf ^%Q^ poioac; a, enl ds
ofaov[isvr}s ovx av itors 6v[ipair] dt,& rb
10 rtteltirov rqv (Ss^vriv xccQcdhaGGsiv fatiavrcos XCCQK
[ifv rolg bit' avrbv rov t6r][iQi,vbv ov ntelov efy-
xo6r&v xs agog ccQxrovg rs xccl [isGrjiipQiav ,TCCCOK ds
rolg poQiordroi,$ i) von&rdroig ccvr&v[irj xfalov enl
ra dvri,KL^va rr\ 2tQOXi[ivr]s [nag [lot'oas, &s xal
15 ovr&s k'ri, hd66ovccs 6vvdy6d'ai, 6vva[i(porQccs rag
rcbv a H riirjiidr&v itoM.ca de
rtov [ircc%v rov r l6rj^iOivov nctl rov
xaraag rcov avrMi[iva)v rtccQccMd&Mv del
3tQOx67troi, av sri n&Mov nag avrolg rb
20 advvarov. itaga, plv rolg avrolg CCQCC ovdafiij ri\
dig v rca vl [irjvl dvvccrbv b'Grai rov j\Kiov
diacpoooig ovdci^Lij rijg avrijg ofaov[i8vr]g' ccit(>
dl%(U.
1. a] (jiitt D. T/irjfia D. 2. owdyoi D, corr. D 2. 6.
corr. ex VOXSLOTSQOIS D, et similiter saepius. l6r\-
I- ins. D 2, -QI- e corr. D. avTi%&6v? D. 8. xf]
dx B. 9. oHovjLtfVrjg D, sed corr. 12. iisasfi^Qiccs D, se
corr. 19. yiyvo^vjig D. 21. yhov] et seqq. multis
compp. C uersus finem fol. 188r .
MA0HMATIKHS STNTASE&S $'. 499
'. UQccy^iareiK xavovi&v exAeiitrixtov.
Iloias psv ovv dicc6rd6is ribv Gv^wyicbv sis rfvrCOV exhefye&V OtyfttopfV 7Caoa^CC[lftdvl,V^
did rovrov ri[iiv yeyove dijAov, OTtcog de r&v re xar'
ctvr&s {i6G)v %QOVG)V diKXQi&Bvrov KCil r&v v avrolg 5
7taQ6d(*)v rfjs GsAtjvrjs eitikoyiG&siGCbv sal [iv rcov
cfvvodix&v 6vvyi,G)v r&v (pccLvo^isvov ,3tl ds t&v
t&v ocx^tft&v^ dia rCbv xccra
rag r ndvras fao(ifoas MfoiTtrwag r&v Gvtvyi&v xal 10
rovrov rd t [isysdy xal rovs %QOVOV$ t&v iti,6xoTij-
XCCVOVLK
TG)V ri^LCCX&
ds x&v 6&rjvi,axG)v Hard re rb peytfrov xccl rb
6rov rijg GeAijvrjs ajtoGrrjiict, fato&tpGVQi r^v xaQW&fyftw 15
r&v eniGxorriGe&v dice d&dexdrov [isgovs rrjs 7116x0-
exaregov rcbv (p&r&v.
rb ftfv ovv rtQ&rov XCCVOVLOV rcbv yfauxcbv ex-
)6 iteQifyei, rovs xaro, rb [leyufrov cbrdtfri^a
MfaiTtrixovs ooovs, rd^o^iev sitl Grfyovs 20
[iev xe., GfMdia de d. rovrov de ra [iev dvo rcc nocbra
rtoi,e%i, rqv xara nAdros rijs 6^t]vrjs eiti rov Ao^ov
xvxhov (pcuvo[ivr}v itdoodov (p' xd6rys i&v 7tt,6xo-
1. ^'] mg. BC, om. A X D. Ttgay^aTSLcc KCCVOVICQV
>twj'] cum superioribus coniuncta D sigiiis rft distincta, etiam
mg. D 2. 3. sylsfysoov D, sed corr. 4. yfyovsv BC. 7.
TtKQoSiK&v D, mg. 7to%(bv D 2. 6vvyi&v\ 6v- supra scr. C.
8. Ante did del. * D. r&v (alt.)] corr. ex -c^g D 2. 9.
tito%rig D, corr. D 2. 10. vyi&v C. 12. TIQOS xr\v] no6t*\ C.
14. rs\ om. D. TO (alt.)] om. D. 15. xr\ GS^VT] D. 16.
xfis 17. fxar^ov] om. D. 18. TO] r- ins. D 2. M&MtyMMr]
mg. D 2. 19. TO] om. C. 21. 8] corr. ex a D. o^vo] B B.
32*
500 KAATAIOT HTOAEMAIOT
TOV
6Tiv Act x, ^ d Tilg Gfhtjvrjg xal avtfi XKTCC TO /Lte-
ytGTOv dTtoGTrjpa IStfyfhj [p. 421, 3] T&V avT&v Aa x,
xal dtd TKVTK, OTCCV TO fpaiv6^vov KBVTQOV Ttfg 6-5 A.YJv'rjs d(p6rrixrj TOV pv fyiKKOv XWTQOV 7tl rov dia
TCDV KSVTQG3V <X{iq)OTQG)
TOV $ 6wd6llOV 7l TOV
XttTa TOV 7tQOXT&l,[JiVOV [p. 482, 1] Ad^OV TOV TC3V
Itt A, JtQOg TO,TOTS 3tQG)TOV KCtTO, TrjV IjtKyrjV 0TttL
10 TOV ^AtOV, XCCTK ILV T&V 7tQG)TG)V <5TC%G3V TG)V 6%l-
TOV [lV 7tQG)TOV TCig ltd flOlQCCg^ TOV $
(?0^, XKTK $ TG)V 6%ttTG)V TOV [lV
Tag 95", TOV d dVTgov Tag (?|d. xccl
15 TOV Xo^ov xvxAov piag noioag %r]xo6TK A,
Tolg ToGovToig av%0[ii,cc)6o[iv TCC 7tQOXt[iVK dvo <?-
dltO TG)V CCXQCOV CCQ%dlLVOl pfyQl T&V ItSQl TOVg
6Ti%ovg' rtl yap T&V ^i6cov Ta^opfv Tdg T 9
nut Tag <?o. TO df TQITOV 6kidiov TCSQIS&L TCC
20 {lyd"r] T&V 7116X0^6 G)V 7fl [lV TG)V aXQ&V
7CaQCiTL^^VCSV TG)V Tljg fJtaqpTJ/gO O, lltl $ TK)V
KVTCOV TOV vbg daxTvAov dvTi TOV i$' Tq
Xal OVT&g 7tl TG)V koiTtCdV TG) Vi dcMTvJiG) Tfjg ItCCQ-
TOV ft<?ot> ^rt'^ov, ig ov 6
2. 6tiv~\ comp. B, -v del. D 2. 4. TKVTK] corr. ex TCC
CCVTCC D 2,
roLvra, B. 7. (IOI'QKS g] om. D. 8. TOV (alt.)
9. a] mg. D 2. 9. a] ? Jf s D. 10. T&V 0/UdtW] corr.
ex GtMdav D 2. 13. 9s] corr. ex tg D 2 euan. 15. I] e
vroig D.corr. D. 16. xoiovroig D. av^o^Kocoftfv] D 2, avo[iia>6o-
(isv A^CD. TtQOKf-wK D. 18. Ante Tag del. TE D. 22.
TOV (alt.)] TO C. t{T] ffi A^D, ip B. 24. yiyvo^vr]? D.
MA0HMATIKHS 2TNTASEZ! S'. 501
T&V dcadfxa daxTvh&v doi^bg xaTavTijtiEi. to ds
GsMdiov TtEQiE&i, rag ywoitEvas TOV XEVTOOV
ytaoodovg xa& ExaGTyv EititixoTridiv, cbg fii?
)v [lEVTOi, [irjdeTCco [HJTE TOV
Gscov rov fjMov [IIJTE T&V iti,7taaaAA.d%(Dv T^S
TO ds dsVTSQOV KttVOVlOV 1CQV T\klWKG)V
o itQis%E(, roi>$ XCCTK TO eAd%t,6Tov dj
AtfvrjS xfal7tTI,XOV$ QQOVS) fd^O^V TK [IEV
CCVTCQS X& 7CQCOTG>^ 7ll 6Ti%OV$ $ K^ XCil
dltt TO Tqv [lV K TOV XEVTQOV T^g 0^VYJS 7(1 TOV 10
A.cc%i6Tov ajtoGTiJiiaTog TOLOVTOV ddZ%&ai [p. 479 ; 14]
it, Xttl %r}X06TG)V ft,O
f
lG)V 0TiV J]X TOV XEVTQOV TOV
i\Mov TE xcti E^rjxoGT&v ji, otav d TCQ&TCOS KKTCC Tr\v
3tcc<priv ytvrjTai, TOV fjMov 17 GEkyjvr], TOTE TO (pcuvo-
pvov XEVTQOV avT^s atpEGTrjXEvcci, TOV psv yfaaxov 15
XEVTQOV xdfav poious [nag E^xotiTa ky xccl SEWEDX x,
dl GwdEGpov 7tl TOV Ao|oi) xvxAov {lOLQKS g xd'
01 (JLEV fitl T&V dxoov Griytav TOV tpcuvo-
{LEVOV IfActTOVS doi&liol TE T&V tty A^ XCil 6 T&V
60% xd xal Ttafav o TE Tcbv 9^ xd xal 6 T&V 6%'y A, 20
6 d' ETtl TOV {lEGOV TG)V dttXTvA,G)V ditt T^V
vitEQO'xriv dcodfXK daxTvAcov xal ETI TOV EVOQ
pooiov d, xcctf ov xal /ioinjg yCvETm itdgodog.
1. ^cbdtxa] i{3B. 2. riruQTov] j B. yiyvopevas D-
4. 6vv\endoyio(j,8vcov mut. in ovvf JTrtioyt^oftfVtov A 1. 6. dtv-
Tf^ov] B B. 8. fy/UtTTTntovg D, corr. D 2. 9. d] supra
scr. D a. ^] corr. ex f D s
. 12. TJ] postea ins. D. 13. f)Mov]corr. ex rj/Uaxov D 2
. ngmrcos] corr. ex TtQ&Tov D 2. 14. fCyvr\-
TCCL D. 16. ju-tag] om. D. 17. TOT;] e corr. D, deinde del.
K-HQCOV Gtfyoi TOV cpaivoptvov n^drovg. 18. yiyvovrui D. yap]supra scr. D 2
. (m%oi D. 20. oo?] corr. ex als D 2. o]
ins. D 2. 9s] supra scr. D 2
, fs D. 22. frt] corr. ex frt xi C 2,
ex Ini D. 23. yiyvztai D.
502 KAATAIOT HTOAEMAIOT
TG)V ds 6A,r]vi,KXG)v xavovLG)v XttToov
6Ti%ovg psv jZf, GsMdux, ds,xal r& pv jrpcora) rovg
TOV xA,KTOvg doi&novg 7tccQCC^6o^iv cog rtl tov {*>-
yitirov (XTtotfTriiiccTog ovff^g Tijg 0^vrjg. eitel y&Q i\
5 per SK rov KSVTQOV Tris ^s^vTjs sdefydrj xara TO
[isyiGrov a7c66rr}iia efyxoGt&v Is ji, ^ d' sx rov xsv-
roov rr\$ Gxias r&v avrcbv p ftd, &6T, orav
amrirai rys Gxiccg % 6htjvr)) ror TO XWTQOV
a(p6rr]xsvcci, rov [iv KSVTQOV rrjg Gxiag jtl rov
v$ nd) rcbv d 6vvd6[iG)v 7tl rov Ao|oi) xvxhov
oag 7 xccl ^TJXOGTK jil^,XKTCC [ilv T&V JtocoTcov
TCC%0[lV TOV T TG)V 0& ifi fylfrftiv Xttl TOV TG)V
XKTtt $ T&V G%aTCW T6v T T&V Q XCll' t
15 xal TG)V 6v$ i$' xal dice TK CCVTK rotg TtQcoToig rv\v
CCV^O^iG)6iV CiVTCbV 7tOL'Yl66^i%'K TOtg 7tL^DC^OV6i TG)
i$' TfjS roT GfArjviaxijs di,ct[iTQOv TQIKXOVTKTG) $ dVTQGJ XCiVOVlG) TOV$ TOV
7fCCQCid'yJ60^V G)g 7tl TOV k(X,%i6TOV
20 Tijg 6^vrjg^ xa& o aito6Tr](ia f\ [iv X TOV
avTflg sdsfyftri ffcyxoGTcbv it, jit, fjtf x TOV XEVTQOV
rrjg 6xiag T&V UVT&V ^ vg, w^r, OTCCV JtQ&r&g aitrriTai
Trig Gxiag i\ <?A^V^, TOT TO xtvtgov KVTijg a<p6Tr]Xvai
2. pe] -s e corr. D 2. n^w-toi] cc B. 4. Ante otfffTjs del.
D. ovarjs tflS Gelrjvrig] -arjg TTJS ( in ras. A 1.
ex parte mg. A 1. 7. r&v 8. cs^ijvr}^ mg. D 8
(17
etiam in textu D). 11. vg] corr. ex v8 C. rov] suprascr. D 2
. 15. y.ui (pr.)] nai rov D. GV&] corr. ex GVS D 2
euan. ra] -a del. D. 16. sn^dKlovciv D. 22. ft] piv C,
fdel. C 2
, mg. fZ^e C 2. 7T(>a>roog] nga* D, o mut. in co D 2
. 23.
ro] om. D.
MA0HMATIKHS STNTASE&S '. 503
rov {lev xvroov ri\g Guides zcdhiv o^otcog {totoav yiiav
xal QrjxoGra y AS, rov de 6vvd6[iov iit\ rov Ao|ou
[toioag t)3 xal $r]xo6ra ifl.dia rovro dy xara
r&v Tto&rav Grfy&v rd%avrg rov re r&v oj ^rov rcbv 67tf$ i$, xara df rcov 6%drG)v 5
rov r r&v Q/$ ^/3 KCCL rov rcbv 6v jit^, itdfov ri\v
av%o[ita)6i,v avr&v xoirps&p&n rolg ju/3Hoix?t rw
i$' rrjg rore faArjVLccxijs Sutpl'CQOV Ad %r]xo6roi$. ra
d r&v duKrvkcdv rgira, GekCdia, rov avrbv rgonov
7CQiE^i rolg fjAiaxotg xal byioi&g ra (p^ijg nal 3tgi- 10
%ovrcc rag TCaoodovg rijg Gf^vrjg natf Kd6rr]v rcbv
titi6Korri<5G)v rag r txarfyag rqg re [MtrG)6G)g nal
rfig ava7thr]QG)<5G)g xccl n rag rov fipfaovg ri^g povrig.
tit^oyiGayi&a d xa&' MccGrqv r&v Tti(3Kor^Ktv
rag XXi,^ivag TtagoSovg r^g 6&ijvr]g y^a^ix&g^ 6wy- 15
1Qr\6a^voi [ivroi, ralg dEi^fGiv <bg <p' vbg
xal csg it v&iCbv dia rb rag H%Qi> rov r
lieytftovg 7tQi<pQCag adiaytootfv Ttobg ai'G&rjGiv rcbv
tin? avrag v&i,G)v xal n fog jiydwl itafav a^io^oycp
ri\g iitl rov Ao|ov xvxAov 7tao6dov rfjg 20
TtaQa r^v xgbg rov dia pfa&v r&v
&scc)Qov[ivrjv. pri yap V7toA.K/fr] rig fjjiag
dion xal xa&ohov ngbg ri\v xara pijxog Ttaoodov rqg
Gfhijv'rjg yCveraC rig diacpooa itaoa rb 6vy%Qa6ft'ai ralg
rov Ao|oi) xvxhov 7tQicpQiaig avrl rwv rov dia [i6av, 25
xal h'n rovg r&v Gv^vyiav %oovovg ovx
1. IILUV] a B. 5. anp] -|3e corr. D. 7. IntfaMova D.
10. 7lBQl%eL BC. TtQl%OVTK\ 7t%OVTU D. 11. XT D.15. Gvv%Q7]GdiJisvoi, D, sed corr. 16. imnsdov'] -i- e corr. C.
21. TIJV] -r\- e corr. D. rov] -6v e corr. D 2. 24. GWIQKG&KI D,
sed corr. 25. r&v'] r&v did D.
504 KAATAIOT HTOAEMAIOT
rovg ccvrovg ditaQaM.dxr(Dg dvai rolg pfaoig r&v
aav yap djto^d^co^ifv d?tb rov A tivvdfanov dvo
r&v 3taoKi[Lva)v KVKk&v i'6ag 7tQHpQiag rijv rz AB5 Kal r$\v AT Kal liti&v^avr^ r^v BF OQd"f}v aito
rov B itobg tv\v AT ygd-
avro&ev 0rai rijg filv <?-
Atjvrjg litl rov B VTtori&-
10 iiwrjg, on, rr\ AT rov dta r i
iiicbv avrl rrjg Ad diet rb nobg rovg dia
r&v jtoh&v rov fydiccxov xvxfov rag itabg avrbv Ttao-
odovg &G)QZ6d'ai rr\ Td dwitiei, rb itaaa rr\v
15 rov GfAyviaxov uvxhov didcpoaov. rov ds ^Li) rov xwroov rrjg 6ma<s 7tl rov B vor}&vrog 6 ftfv
rijg GvQwyiag %oovog k'Grai Kara rb ddidcpooov r&v
Kvxk&v., orav xai fj GfArfvrj Kara rb F ywrjrai, 6 ds
[i6og rr^g KkEifyG)g^ orav Kara rb z/5dia rb itdkiv
20 rovg [ifaovg %oovovg rcbv jc^xort]6K)v nabg rovg did
rcov Ttok&v rov 6A.rjvi,axov xvxAov &G)Qi6&ai' Kal
6 rfi<$ 6vvyiag %aovog rov pfaov rijg mfafyfcog
7tQl,(pQia.
alnov rov pr} Kal ravrag q^ag 6vvitiko'yi-
1. anccQK^d^Tcos D, corr. D 2; &naUdyn;fos C. 9. VTTOTI-
D, corr. D 2. 11. 6vv%Qr}Gaiivcov D, corr. D 2
. 12.
d~\ A- e corr. D. 14. fyx/Lqcti; B. 15. ^t'ov] D.17. didyoQov D, corr. D 2
. 19. Post orav del. TO ^fV D 2.
23. Ty] r D. itEQicpEQeia D, t add. D 2. 24. v.ccl ravrccs]
-ccl r- corr. ex ar C. TCCVTCCS] TUVG D, a eras.
MA0HMATIKHS STNTAgESS 6'. 505
rag itSQHpEQSiag iv rats Kara pegog
reiaig rb pixQag slvai xal av7tai6d"tjrovs avr&v rag
diayogdg, xal on rb [ilv dyvoijGai n rcov roiovrcov
aroitov, rb <?' SVEXEV rijg iv ralg itag sxatira {is&odoig
xaraexsfaiag exovra xarayoovijGai nvog rcov rrjfaxov- 5
rcov.) fjMxa xal icapa rag vito&stieig xal naga rag
rrjQtjtisig avrag svdfyerat, TCaQa&scoQstd&at,, rov ^evxara rb aTtAovGrsgov %Qrj6iiiov nkefarriv afo&rjGw ep-
noisl, rov de neql ra (pawopsva diapaQravopsvov i)
ovds^'av vjnavranatit, figa%siav. rr\v yovv bpoCav rfi 10
xa&ohov [isv ov {isifrva svyfaxopsv
[nag poiQag' dsixvvrai yaQ rovro diet rov
avrov &G)Qij[iaTog ,di,' ov xal rag diacpogag STCs^oyt-
<5d[isd'a rcov rov farjpsoivov TtSQKpsgsiGbv TCQog rag
rov dta [lEd&v rcbv fydi&v cog snl r&v dia rcbv no- 15
rov fariiLEQivov yQayoyu-v&v xvxA.cov' snl ds r&v
ov pEitpva dvo ^xo0rcav^ eitEidr^yceQ^ otcov
pdv 6nv sxarsga rcov AB xal AT TtEOKpsysicov t/3'
6%edbv yaQ p%Qi ryfaxovrcov (p&dvovGiv at xara rag
exfatyeig rr\g 6e^yrjg itdgodou' roiovrov ztirlvrjB<d 20
evbg k'yyiGra' dia rovro ds xalr\Ad rcov avr&v la vrj
aj xal xarateCnsrai ^ F4 KQITI'YI dvo
ovds sxxaidexarov JtoieE niag &oagd$ rb rotiovrov axQifavsed-at, xsvodo^ov
1. xara] V.K D,a
add. D 2,
ut saepius. 3. ort] ox- in
ras. A 1. j^^v] corr. ex Its D 2
. Totovrcov] supra scr. D 2.
4. sv] corr. ex ? D 8. 5. &V.QV D,
aadd. D 2
. 6. rag (pr.)
18. iGTiv x-] in ras. D. 8. svnoifiv D, sed corr. 11.
evQiGxcoiiev D, sed corr., supra sv- add. TJ.12. ydg] y* C.
13. srtsloyrjcdiis&cc A X
D, corr. D. 15. r&v (sec.)] rov B.
16. 8t~\ d- in ras. A 1. 20. TOIOVTCQV D.
'
23.
-g add. D 2. 24. Post TOGOVTOV ras. 2 litt. C.
506 KAATAIOT nTOAEMAIOT
rj (pihahrjd'ovg av/'??.
dia pv dfj TavTa xal Tag x-
Xi[ivag TCOV 7tt,6xoTrj0G)v TCaoodovg Ti]g Gfhtfvrjg fag
Ttobg al'G&rjGiv TCOV xvx&av jC7Coa /
y^ia-
:, ysyovsv d' fjptv 6 ToiovTog STCikoyiGiLog cog
6TCO yap TO [lV TOV ^AfcOV T}TO
Trig 6xt,ag XBVTQOV TO A, i]d' dvTl
Trig itEQKpSQSiag TOV tifhyviaxov xv-
xhov v&ia r] BTd, xal VTtoxsiG&G)
10 TO yikv B XWTQOV Tr]g (JfA^V^g, oTav
artTrjTai, TOV
.ag, TO df z/, OTav Ba7to%G)()Ov<ja' xal rtt,%v%d'i,6G)v TOJV
AB xalAd ijxd'o ditb TOV A snl Tr\v B4 xd&STOs q AT.
15 OTi [lV OVV) OTCCV XCCTCC TO F 'ySVrjTCCi TO XSVTQOV
Ti\g **tyMft ^ r ptGos XQ VO$ y^vsrai Tr\g sxtefye&g
xalTI pzyfaTri jUGKfaj\<Sl, (pavsgbv sx TB TOV TYIV
ply AB Tri Az/ L^V elvcci, dia TOVTO ds xal Tqv BFTtdoodov T?I Fz/, xal sx TOV Tqv AT 7ta6&v
20 dvai T&V rtl Trjg B4 TK dvo XWTQK
d', OTL xal XdTQa plv T&V AB xal Ad 6vv-
Qi%si Tag x T&V XBVTQ
xal TOV fMov r Tr Gxia r $ ATxaToag
25 /LtfVcO [lQl, Ti\g TOV xA,L7lOVTOg
3. &dia(poQovvra)v~] ante -r- ras. 1 litt. D. 4. ytyovs A 1.
5. ni%a>v D, et similiter saepius. ovt D. 6. j^t'ov]
j}tf D. 7. d'] e corr. D 2. 9.
jj] corr. ex v D 2. 10. B]
seq. ras. 2 litt. D. 13. int^v^tiG&v D, corr. D 2. 16. Tr}$
a^vris] om. C. 19. itaQov A 1. 20. KTti&vyvvovG&v] -o-
in ras. C. 23.77] ins. D 2
.
MA0HMATIKH2 STNTABE&S '. 507
rovrov ovv ovr&s fyovr&v ywd(f&<Q TC
VXv y 7fi6x6r^6is daxrvhcov y, xal vnoxffa&G)
rov rb A rb rov i\^iov xvroov. eitl psv ovv KQCC
rov yisyfarov dno6rij[iaros ovtirjs ri\ GeAtjvrjs i\ {LBV
AB yivsrui ^yxoo'r&v hot. x [p. 5007 4] xccl rb an 5
ccvri\g %7ta ft?, ^ ds AT t&v ccvrCbv
yccg iGtiv rrjg AB tots y i$' rv\$
TOVTSGTW rots S v to & &d avrqs yvp Is' &6rE xal
rb [iv coco rijs BF farm [Eucl. I7 47] rcbv avr&v
avrr} $f\BF iitjxei, x ~\[y eyyiGru, a xal 10
iisv sv Tea TtgcorG) XCCVOVIGJ r&v yfoccx&v rots
rot,6u daxrvhois xara rov d' 6&1tidfov' iitl de rov
kcc%iGrov aitoGrtfiiaros t^S Gshtfvrjs % psv AB rtafav
yivtxui Qrjxoer&v ky x [p. 501, 13] xal rb an' avrijs
J, f)ds AF r&v avr&v xs I xal rb an avrijs 15
,hombv d rb dnb rife BF sfyxoGr&v v| vfi'
xal prjxsi, aoa % BF stirai rcbv avr&v xa xrj^ a xal
avra jtaoa&TtJGotisv ev ro5ft
f
xavovfo r&v r\haxCbv
rots y daxrvAois xara rov d' Gekidiov.
rtoxEfad'G) rb A xsvroov rrjs Gxias xali\
20
rov avrov dr
rijs 6^r]Viaxi]s dia[irQov.
7tl {iv aoa rov yisyiiSrov dTtoOr^^aros t^S Gfhtfvrjs
$1 pv AB yivsrai ^yxotfrcbv ~vg xd [p. 5027 8] xal rb
1. ytyWffoho D. 2.i]\ om. C, del. D 2
. 7116*6*7)61.5] corr.
ex '7rSc<mj<ns D a,et similiter saepius. 3. ovv] om. D. 6.
avTfjg] -g in ras. A 1. ^nci] C 2D 8
, -^nu BC et 7 in ras. A 1,
Jwrn? D. 7. la-civ] comp. BD. i(T] i'J' A^CjD. 8. rovr-
ianv] comp. B, -v eras. D. f v] D, gv A^C. 11. nuqcc-
ftriGOfiai, D, corr. D 2. sv] addidi, om. A 1 BCD. 14. yiyvs-
tcci D. 19. roig] corr. ex rjjg D 2. #'] supra est ras. A 1
.
20. ri] seq. ras. 1 litt. D. 21. $'] supra est ras. A 1. 23.
D. Il-Tjxoffrcov] -|- in ras. A 1.
508 KAATAIOT nTOAEMAIOT
an avrrjg ygit vrjj YIds AF r&v avrCbv py Ad
yap 6nv ryg AB red d' rijg tffA^vfcemjg
rovT6nv roig itl rov [isyforov arto6rri[iccTog
v* rb d' Kit avrijg ^rvrj jily* &6re xccl
5 rb {Lev ajtb rijg BF KKTakeKp&ridettti coup tf, avrrj ds
riBF 6rui IMJXSI rcbv avr&v iwj jitS,
ci xal XKQK-iv t(p XQcoTG) r&v Gshrjviax&v xavovt&v rots
daxrvAois Kara rov d' tishdfov TttQiiypvia rv\v
rrjs fiMtr&Gscog ndgodov ri\v avr^v ovtiav agog ttfo&rj-
10 6'iv T?? rijg Kvaithr]Q(b6G)g. sjcl ds TOV &a%farov aito-
fj psv AB yiverai efyxoGrcbv %y Ag [p. 503; 1]
xai rb ax* avrilg d[id vrj, fjdl AT r&v avr&v vd
ra yag rijg VTtQO%iig rjv rerK^rov 6nv Ttttkiv
rb kKi<3rov art6GrriK 6&rvicixig diarov rb
15 d' ait' avrijg y /3%9'9' wy' &6T xal rb [iv aitb rijg BF, avrrj $ ^ BF ^xt, r&v avr&v
a xal avra TCKQK^^O^V aGavrcog rolg
Kara rov d' Gffadiov rov iv r& /3' r&v
navovi&v.
20 Tt&'klV VXV T&V Xal ^OVij^ %QOVOV %OV6K)V tffA??-
viax&v ni6xor^G)v faro rb plv xtvroov r^g tixiag
rb A 6rj[itoV) fjd' avrl rijg jtai(pQiag rov Ao|oi)
1.tygii\ corr. ex OTTT D 2
. 2. scnv] -v eras. D, comp. B.
5'] supra est ras. A 1. (^VLKY.^ D. 3. TOVTSGTIV] comp. B,
-v eras. D. 4. Post ccvtrjs eras. Siitl . . . D. favq] D,
\rvTf] A 1
(t renouat.) BC. 7. ngmrfo] ~& B. 8. TOV] -o-
corr. ex co C. 8'] supra est ras. A 1.
'
10. T#] xr\v e corr. B.
12. ftg] v? C. ;13. Anterj eras, o D. SGTIV] comp. B,
-v eras. D. 14. anoGriJtiKrog mut. in ccTCOGTr^ia rfig D. rd (alt.)]
ins. D 2. 15. ^S&9#] -%9 -e corr. D, BS&9# A J BC. 16.
D, a e corr. 17. x] D, ^aABC. 18. ^'] ^A a
C, devesQa* BD.20. xat ] comp. supra scr. D 2
. 22. ntQicpSQfiaccptQfius D, sed corr.
MA0HMATIKHS 2TNTASE&S S'. 509
rrjg 6krlvr}s xvxhov v&lafj BF4EZ., xai rb [ilv B
VTtoxactd'a),
xatf ov rb xwrgov h'tircti rf\ G^ujvyg,
orav TtaotidyovGa XQcbrcog l~G)&v aTtryrai rife Gxiag,
TO df jf, xa&' ov 6rai rb XSVTQOV r^g GsAtfvrjg, orav
r ov
E
b'tirui rb xvroov rrjg 68-
,orav <x7to%G)()OvGa Ttaa-
0co^v artrrjrai, rov xvxhov
rijg <jxi&s, rb d Z,rb XVTQOV 0rcci rij
orav Ixfiaivovtia rb 6%arov
^aftw rijg 6xia$ xal
rtdfav anb rov Ari\v jBZ xdfaros rj
Ad.vovrcov df} xal v&d$
10
7tl
[t- 15
r&v
In xal rovro <pavaov, on, xal
rcbv AT xal
jK rov XBVTQOV
Ttdoodov l<5r]v rfj
rb r^Litiv rijg
r EZ
AEK
7tQi%i,XSVrQOV T^
xal rr\v pv F4 20
xal 3tQi,%i,v xaroav
Aot3tiji/ d rr\v BF rijg
ivai.
ddxrvkoi ri\ ^rovrfanv xa&' rjv rb /I xevrgov 25
1. Gtlijvris] -s e corr. seq. ras. 2 litt. D. rj] corr. ex
v D a. BTJEZl Jyd ej BC. 3. ore D. TtQOGayovccci BC.
Post ^co-frfv relicta lac. 6 litt., deinde del. novGu gcoo&sv D.
rfjs 5- &n-rr]rca] om. D. 13. Uga&sv &7trrjraL D. cm&s]6- e corr. A 1
. 15. BZ] corr. ex KZ A 4. A4] cc J' D.
19. vTtSQEfci] corr. ex vnsgo^ri D 2. 21. yt'yveaflm D. 23.
tlvca] ins. A, supra scr. D 2. 25. rovrsGTiv] comp. BC, -v
eras. D. z/] corr. ex A D 2 euan.
510 KAATAIOT HTOAEMAIOT
avrrjg IvdorEao yivsrui rov Kara rovg
OQOvg rtEoarog \Lia GeAyviccxy SiayidrQG) xal STL
Et, avrrjg, rovrfarw oravfjAd sAaGGov
ft xaroagr&v AB xal AZ, rfi ycooxi^ivrj pia GfAqviaxfj
5 dia^iroc) xal b'n rsrcc^rcD avrrjg [legst, Exatsgccs ds
AT Kctl AE rsrcc^rcj (legei, pices dia[it!rQOv GeAr}-
litl [isv CCQCC rov iieyfarov anoGrtj^arccg
{isv AB yivsTat, r&v rtQOXi,[iva)
xccl to an' aviv\ /YQft vy? $1 & AT10 tCbv KvrGbv xe d'
fj yap rrjg 6A.ijvr]g did[iETQog itl
rov peyfarov aTCo^r^arog %r]xo6rK>v zGnv ha JT not
rb ait avrijg pcrj ic, ^ $ Ad o^ioicsg i^ id xal rb
an? avrijg 6g$ v%" &6re xal rb plv ano rijg
xarafaMp&rjfarai, [Eucl. I, 47] ^owry v^^ xal
15 prpiEi, k'tirat, r&v avr&v vy /tt/3,rb $ catb rijg
rka xa^ xal avrri {irjxfi, b'tirai, r&v
avrtbv1/rj 6/3, Aoiitrj $ xal r\
BT r&v avr&v Af A.
yta^ccd'^o^fv ovv r& r&v TE daxrvAav aQi&nG) rov
ito&rov xavoviov r&v GEArjviaxcbv xA,fyfG)v Kara [iv
20 rov rfrocorov 6kidiov ra rrjg {i7trG)6G)g %rjxoc>ra
Aa A i'Ga '6vra rolg rrjg ava7t&r]QG)6EG)g, Kara 81 rov'
ra rov fiiifaovg %aovov rrjg povrjg ~ir\ t/3.ETCL d rov
1. fvdor^ou BC. 2. OQOVS~\ corr. ex %qovovg C 2. Post
nut ras. 2 litt. D. Tfra^rou] ^ B, item lin. 5 et 6. 3. rj]
ins. D 2. 4. AB~] -B eras. B. GB^vrjcc-A^ C, sed corr. 7.
Ante OI;(>TJS del. frjxo()T<5j; IGXIV "ka. ).' D. 8. ytyvftat D._ /,
|r])to(7rcov] om. D. 9. *.$} -8 e corr. C. ^^ji D. 11.
IGTIV] comp. BD. x] I D. 12. x, 17] %r] D. 14.
A!BC, Bony D, jfey D 2. 15. 8s] 8' D. 19. ngw-
TOV] a B. 20. TB-cdgrov] ^ B. 21. rots] ins. D 2. 22. ra] D,
rag A^C. ^ovov? BC.
MAGHMATIKHS ZTNTA3E&S '. 51 1
rrjg Gshijvrjs f] [iV ABTtaklV r&V 7tOOXt,^VC3V fy> A XCtl tO Kit' KV-
rijs ,$11$ vrj) r}$ AT r&v avr&v M] 7g' f} yap rr\g
dltt[lraO$ 7tl rOV &a%farOV KTtOGtrJUCCTOS
[p. 479; 14] QrjxoGT&v ks K' nal rb ait* ccvrrls 5
o, rj$ Ad OHOL&S & W5 xal rb an avrys ro
> xal rb plv aitb rijg B4 xarateup&riGsrat,
tO", xal avrrj f}B4 ^X8i s'Grat, r&v ccvr&v | Ad,
rb d9
ditb rijg Td xccraA.i,(pd"ij<3rai, vxa KK, nol
k'Grai, rcbv avr&v K Aft AoiTtf} $ xal % BF r&v 10
go. xal v r& /3' KKVOVIG) rcov
rc5 r&v IB dcwrvAcov CCQL&ILG) xccra
rov rtrugrov GsfadCov ra rijs [i7trG)6G)s %r]xo6rci
ft /3IftK Ttccfav ovra rolg rijs ccvcc7c2.rjQG)6C3g^ xara $
rov s' GsXidiov ra rov ruaidov^ rf}$ [lovijs K Aft 15
LVCC $ Kal rti r&v iLra%v rov r peyitirov xal
rov &a%L6rov aitoGrrjuaros ri\g 6Atfvrj$ itl rov im-
xvxkov rtccQod&v rag 7tipakkov6a
rov o'Aov diacpogov 8ia rv\ rcov
7tao%tQ(DS kanfiavGHLBv , V7ird%a[iv roig TtQOXEiyiBvoig 20
xavovioig AAo xavoviov fiQa%v 7tQi%ov rovg rs rife
rri xara rov sniKvxkov aoi,&[iovs xccl ra iiti-
1. AB~\ con. ex ABT I). 2. yiyvsrai D. 3.
, ^j~8 C, Ajltf C 2, A^ D. AT] ay D. 6.
e corr. D, f Q@ BC. o] e corr. D 2. Ante t^- eras.
o D. xs] x C. 8.
BJ] corr. ex 4B C. 9. vxa] supra add. J A 1, rx S C.
12. xara] corr. ex g' rd D 2. 13. TfrdgTov] j B. f|?]-
om. D, |gtt
supra scr. D 2. 14. ^ f] JIp A 1 BCD.
18. TCUQodtov] -dd- ins. D 2. vitQO% D, -uTCf^o^D
2. 21.
D, sed corr. TOV$] corr. ex rfyg C 2.
512 KAATAIOT HTOAEMAIOT
pdMovra ^rjxotira sxatirr} r&v (paLVOpwcov v
X rc5v itQ&r&v xal dVTQG)v xavovicov r&v
TtfTtQayiidrmrat, <f rj^itv r\TOVTOV r&v 8&pt(Htf&v no-
6orrjs 7tl rov rtagaMaxrixov rrjs 6eAijvr)$ xavovos x-
5 re&eiiiwr] XKXK to % GtKCSiQv &s rov sxixvxhov xar<x
TO anoysiov rov sxKsvrgov dta rag 6v%vyas VTCOXSL-
7tsl ds oi jtfoZGroi, r&v rrjQovvrcov rag
xa$ 87UGy[ia6Lccs ov rats dia^idr^oig rcbv uvxAov TCCCQCC-
10 [lergovGiv ra [ifysd-r] rcov 7ti6xor^&C3v^ aW cbg InCitccv
rotg o&ois ctvr&v sxiTtsdois tfjs otys&s xara rb aitkovv
ri]s 7tQo6f$ohrjs rb fpKivo^Evov ccvrb nav r& py (pcuvo-'
vyxQt,vov6rjSi nQotisftrpiKiisv rovtois
xavoviov 7tl tirfyovs y>V i$
15 rovT&v d' Iv [iv raj itQcarcp rovs i>fi dccxrvhovs rd%cc-
{iv &s xd&rov daxrvAov JtQi%ovroSi xtt&ccjtQ xccl v
avrots rots xA>i7tri,xots KUVOVLQUS, rb i$' r^g diaperQOV
XCCTQOV r&v tp&r&v^ v $ rots ^rjs ra itt,/3dA.A,ovra
avrots itttkiv dcodfxara r&v ok&v fjifiad&v., v plv ro5
20 dvrQG) ra rov fjfaaxoV) iv df rw rotroj ra rov 6krj-
viaxov. it&o'yi6dn&a df xal ras roiavras
7tl pov&v r&v yivopivov nsyeQ'&v xara rb
rrjs tfAt?Vr? ov^s' b yaQ avrbs
y rijs rrjAixavrrjs rcbv dia^irQG)v a
25 GEMS Gvvfararai, xal as tov hoyov r&v
1. xa0roi D, corr. D 2. vnsQO%cov] -%(av e corr. D 2
. 9.
STtLGYlflCCGLGOV D, S6d COIT. nCCQCC[lTQOVGlv] -V QYSiS. D, TtCCQK-
iexOvGi B. 10. aUd D. 13. GWAIVOVCJS D corr. D 2.D, corr. D 2.
14. y] tQicc BD. 15. rw] supra scr. D 2. TtQwraji] d B.
17. tp'] B, ip A 1 CD. 'l9. Post uvroLsiel. -x- D 2. >-^
o1.a>v C. 20. dfVT^QO)] B B. TQitca] r B. 22. ytyvo-izvoov D.
MA0HMATIKHS STNTASE&S
rag diaperaovg ovrog ,ov %i ra
"ovrog
513
a rOV
, olg 6
ro ev ovroz vao o AOVOQ ueratv seriv vvi6ra rov
re roiJtAaGiov 3
Ttobg rolg dexa
xara rb aitAov6rQOv 6vv%ori6aro. 5
6ro drj itQ&rov evexev r&v ri^iax&v fxfofyfcov 6
\iev rov YI^LOV xvxhog 6 ABT4 Tteol xevroov rb E^
6 de xara rb peGov aitoGryiia rqg (Se^vrig 6 AZTH
TtSQi xevrgov rb @ rfyv&v rbv rov ^Atov xvxAov xara
rcc A xal F 6rjiitcc' xai Ixifcvz&fforjs rye BESH 10
rb d' sxheAoMsvcci rys diaperQOV rijs fjha-
&6r rqv plv Z4 roiovrcov tivcti, y, oicov dtirlv
fjBJ did[irQos tft rqv d ZH rr\s teAtjvrjs diK^r^ov
rcov avr&v if$ x fyyuSra xara rbv rcov T~fl agog r<x
Ig ]n Adyoi/, di& rovro ds xal r^v E Gwdyftid'cii, 15
3. 4. CD et cuin
ras. post -0TO- B, g^oju^xoffToo/Lidvoig A 1
(-co- e corr.), sfido-
ju-r]jco(>rots [IOVOLS A 4?B 3. 5. %ara] -cc e corr. A 1
. ^"f-Gccro C. 8. AZTH] corr. ex .IZTtf D 2
,
9. rdv] in ras. D 2. Y.VV.IQV\ supra scr. D.
BE(9H] EE&N D, corr. D 2 euan. 11.03 add. D*. -coSwteliointvcu C. 12. y]
14. x] supra scr. A 1.
Ptolemaeus, ed. Heiberg.
10. TK] to C.
s D,e corr. D s
.
33
514 KAATAIOT DTOAEMAIOT
rcbv avrcbv & 1. xal rCbv 7tQi[ieracQv aoa xara rov
rov vbg nobs ra y j\A Adyov r\ psv rov
xvxAov yCvsrai, r^rj^drcov At, ft/3, fjde rov G
r&v ccvr&v A?? ftg. oftot'cog ds xai r&v oAtov
5 7CidtJ7to fiin tov uevtQOv litl rrjv TtSQiiisTQ
ithaeiKG&ElGa dvo sp/Sada rov xvxhov Ttoist, rb [lev
rov fifoaxov xvxAov Gvvcc'xftriGSTKi, ^lOi^Cbv ^Zy g, rb
ds rov rrjs 6^r\VY\^ r&v ccvr&v ai& A/3.
rovrcw dq ovrog sftovrov rtQOKsfa&G) svoslv, itod&v
10 6rlv rb 7tQi,%6iivov vitb r&v AdTZ sufiadov^ oi&v
6rlv rb oAov rov rjAiccxov xvxhov {i($adbv i/3.
jt&v%&G)6ccv dri CCL AE HOI A xal TE xal Fxal h'n
'Y]AKF udftfros.
fad ovv, olcov 6rlvjjE vd-la & t, roiovr&v
15 xarsaa plv r&v AE xal EF vitoxurat, g, Mccrfycc $
rfbv A xal F r&v avrcbv g 7, xal oo&tf 6nvrj
itabs ftp K ycovict) ia.v rfjv v7tQO%ijV) r\ v7tSQB%i, rb
aitb A rov ajtb rijs AE, rovrsGrw raft
xccl e^-xotfra /5, 7tccQaj3ccA,G)[iv TCCCQCC rr\v E, '|o/iv r^v
20 r&v EK xcd K vxsao%riv r&v avrCbv Qrixotir&v Ty y*
&6r xal xtyv p\v EK GvvKysG&cti d MJ, ryv $ Krcov ccvr&v d ft/3,
dice rovro $ xal xccroav r&v AKxal KF) STtsl facet, sltiiV) rcbv avrcbv d f'yyiGra. rov-
3. yiyvETUi D. 4. spfiodwv C. 5. TtQi^ttQOv D, -QL- e
corr. D 2. 6. noisi 7. MY.IOV] bis A 1
,corr. A. 7. ILOIQ&V]
corr. ex fiot^toov D 2. 10. ictiv\ comp. B, -v eras. D. 11. SOTI'V]
comp. BC, -v eras. D. 12. 8r\\ -ij e corr. A 1. AE] corr.
ex 4E D 2. 13. AKP] -KT e corr. A 1
. 14. oocav D. 18.
A] Tfjs A CD. AE] ci Ti D._ Tovricnv'] A 1
, comp. BC,lac. 4 5 litt. D. ra p 19.
J3] supra scr. D 2 euan. 20.
uvr&v] supra scr. D 2. iy y] supra scr. D 2
;deinde add.
avr&v j /it^Sice TOVTO 8s wi MKTSQCCV T&v AK Iff D, del.
D 2praeter If r. 23. tfatv] comp. B, -v del. D.
MA0HMATIKHS STNTAEESS S'. 515
roig d* axokovQ'&s xal TO per rov AEP rgiycovov
bv %oyLv it> vfi, rb ds rov A&P r&v ccvr&v
TtdhiV 7tl, OLCOV <5TIVf) [lV B4 did^BXQOg
ds ZH 6ftoiO ifl x, roiovrcov xccl fjAT 6vv-
xal oicov psv sGrw r\B4 diduTQO$ QX, 5
TOIOVT&V fj AP 6rai Jr, olcov $fjZH dt,d^irQog OK,
TOIOVT&V O% Vj KKl TCOV ilt VTlJg CtQCC TtfQICpSQfl&V fj
toiovrcov iQxiv my AJ 9oicov 6 ABPzl
T|, r\d AZP TOIOVTCW it vfa otW 6 AZPH
6 avtbs Adyog 0rlv rcbv Kvuhov 10
xccl r&v s^adcbv avr&v 7tob$
ra rCbv vnb rag 7tQi<pQiccs troftf'eoi/, xccl rb ^ev rov
ropfas [t>P<xdbv ^o^iv roiovr&v x tg, oicov
rb rov ABP4 xvxAov oiy g, rb $ rov A&PZrcbv ccvr&v x% VK sitel xccl rb rov AZPH 15
rav avr&v yv QI& A/5. ddt,xro dl xccl rb
plv rov AEP rQiy&vov l^ccdbv roov ccvr&v iC, vfa
rb $ rov AP o^otog Irj ^' xccl koiitov aocc rb plvrov A4PK T[IIJHCCTOS [ifiadbv ^o^iv 77 xd, rb $ rov
AZPK rCbv ccvrcovr\ y. xccl ohov aocc rb VTtb r&v 20
AZPA 7tai,%6iivov fyflccdbv roiovrwv 0rlv 7s x^o'iKtv rb rov ABP4 xvxhov vitoxfircci ocy g.
xai, oi&v 6rlv rb rov fjfaccxov xvxAov fppccdbv
roiovrcov rb jtoi,^6^vov vnb rov fxfafaovrog
7. avriis'] mut. in ccvrccg (comp.) C 2euan., avrdg D. 8.
Post i^add. d supra scr. C 3. 9. xvxAos T|, TJ ds AZT] supra
scr. C 2. 10. iariv] comp. B, -v eras. D. 12. to/iaW] corr.
ex TO ft a>v D. 13. Z?] corr. ex x D. 14. A&TZ] A et Fe corr. D. 15. ro] rd D. AZTH] AHFZ D. 16. ^]supra scr. D a
. ^|3] corr. ex ^ D. 17. AET] corr. exJET D 2 euan. 18. Ante Irj ras. 1 litt. D. 21. gW*]comp. B, -v eras. D. 23. lartV] comp. B, -v eras. D. 24.
TOt-ovtov D, sed corr.
33*
516 KAATAIOT HTOAEMAIOT
a [_' d' EyyitiTcC) cc teal Jtcc^cc&tj^o^LEv EV TGJ
xccvoviG) TO* GtC%G) TG)V y dccxTvh&v EV T& /?' tear
xal T&V
5 EVEXEV &Jtl Tijg avTijg xaTayQacpqg 6 fiev T*fjg
xvxhog 6 ABT4, 6 ds Ti]g xccra rb peGov a
6 AZPH) xal sxfaiTtErco TO df
coGavr&g Tys
diaperQOV , w^Tf, oi&v sGtlvri
J5z/ diu-
t/3,TOIOVX&V rty pev Zz/ rij$ sxtefyE&s ELVKI y,
10 rr\v d ZH rij$ cfxiag didderQOV xccra tbv tov svbs
itgbs raJ3 Ag Adyov r&v avrcbv ha t/3, dIK rovro ds
xccl tv\v EK Gvvd'ysGd'cci, w] ACT. xccl t&v {JLEV
CCQK TtaklVfj [lV TOV GsAyVLCCXOV XVX&OV y
Ag ftjS, % ds TOV rij$ GXL&S TG>V avr&v 977 a,
15 r&v d' E^ctd&v rb fifv TOV ^E^viccxov xvxAov ^iy g,
TO SE TOV Trjs Gxiag T&V CCVT&V ^|d A/3. ETtsl TQIVVV
xccl EVTccv&cC) oicov E0TLVi\E Ev&Eicc Irj Ag, TOIOVT&V
8XCCTEQK [IEV TG)V AE Xal EF VTtOXElTttl, g, EXttTEQK ds
T&V A XKL F T&V CCVT&V is Ag, ECCV coGavTcog TY\V
20 V7tEQO%tjV, i] V7tEQE%l, TO COCO TJJS SA TOV CMO T^g
AE, JlCCQK^K^CO^EV 7CCCQK T^V E, E^O^IEV T^V TG)V
EK xal K V7t()o%riv TCQV CCVT&V la ^, &6TE xccl
1. syytGra a] corr. ex yyt0ra D 2. nuQcc&riGop, sv corr.
ex nuQKfi")]0oiiev D 2. 2. r&
(3corr. ex x& i$ D
2. 4. xca]
comp. supra scr. D 2. 5. /u-sV] seq. ras. 1 litt. D. 7.
seq. ras. 3 litt. D. 8. BJ] B- in ras. A 1,
e corr. D. 9.
y] corr. ex at y C 2. 11. la] corr. ex 1$ D, IK supra scr. D 2
.
13. ylyvtxKi D. 14. fi^] postea ab extrema linea adinitium sequentis translatum D (i- corr. ex cc D 2
). 15. rov~\om. C. 17. oicov] seq. ras. 2 litt. D. Ante t?] ras. 1
litt. D. 18. g] corr. ex Is CD. ds] postea add. D. 20j] ^ B, M C, ^ D, ^ A 1
.
MA0HMATIKHS STNTAEE&S s'. 517
EK 6vvd/
y6d'ai, y ftd, r^v ds K r&v avr&v
id v/3, did rovro de xal exarsgav r&v AK xal KFr&v avr&v d
yifi. dxoAov&as de rovroig xal rb [isv
rov AEF rgiycbvov fypadbv Joftv it, Ay, rb ds rov
AF T&V avr&v %& v($. itaKiv iitd, oi&v l6tlv ^ 5
jifv Rd didnsrQos t/3, f)ds ZH 6ftotojg Aa i/3, rot-
OVTCDV xalYIAT GvvdyEtai, ft xd, xccl dicov \iiv i<5riv
i] B4 didpsTQos px, toiovr&v rjAT tGrai 9^, oicov
dsfjZH didusTQog px, toiovrcov A
'9',xal t&v STC
CCQK itSQHpSQSi&v i\ per AAT xoiovt&v farlv 10
17, oiov 6 AETA xvxAo$ r%, f)tie AZP toiom&v
d?
oicov 6 AZTH KVKko T%. co6re dice ra ngo-xal rb (iv rov AET4 To/iteog [i(}ccdbv roi-
ovrcov f^ojifv Aj3 scd, oimv sdei'xftri rb rov ARTz/
xvxAov oiy s, rb $ rov AT&Z rojif&s r&v avrcov 15
od MJ, ?tl xal rb rov AZFH xvxAov r&v ccvr&v
%v ifj%d AjS.ddixro d xal rb plv rov AEP rgi-
ywvov fpfiadbv r&v avr&v it, Ay, rb de rov AF%& vfi' xal Aowrov aga rb [ilv rov A4FK
epfiadbv ^o^iv td va, TO df rov AZFK 20
r&v avr&v d Ag. xal 6'Aov ciga rb vnb r&v AZ, TA7tQiXO[ivov fypadbv roiovr&v i&rlv i& xg, oi&v rb
2. did 3. tf p$] mg. D 2. 2. xai (alt.)] seq. ras. 12
litt.C._ _ 3. (fcxoAov^r D
,
g add. D 2. 5. if] v- in ras. A 1
.
9. l<s -91
] As B, deinde add. ly supra scriptum C 3. 10.
uvtfis] avr D. 11. ^y] D,_cprr.ex pay A 1
C,_*y B. 12. d]corr. ex ^" D 2 euan. 14. If] supra scr. D 2
, xJ3 D. ABT4]-B- corr. ex J1
in scrib. D. 16. CCVT&V'] om. C. 17. de]comp. postea ins. D. AET] A- corr. ex d D. 18. A0T] A-
corr. ex A D. 19. AJFK] -K postea ins. D, -A- corr. ex
D a. 20. vu] corr. ex o^ D. 21. Is] corr. ex 19 D.
corr. ex TA C 2. 22. fffrtV] comp. B, -v eras. D.
518 KAATAIOT HTOAEMAIOT
rov AET/1 xvxhov vitoxeircu jny . coGts xai, otov
6rlv to rov 6&r)viaxov xvxAov tyfiadov i$, roiovrcov
rb ytQis%6[ivov 'bito rov sxtefaovros avrijs
etitai /3 Keel sn is' [isgovs eyyiGrcc, a xccl
5 7tl rov ccvrov KKVOVLOV t& Grfycp r&v y
iv r& yr
xcci GfhrjviccxG) GskidCci. KKL 0nv17
rcov
xavovi&v
2. Imtv] comp. B, -v del. D 2. 3. TO] e corr. D. 4.
e corr. D seq. ras. 1 litt. tf']t'' A 1
CD, Ts B. a] ins. D 2.
7. KQIVOV D, xavovt D 8.
MA0HMATIKHS STNTABE&S '.
ij'. Kavoviov fjMov sxhefysoov. ftuou $xie
519
5 Ttlcctovg \
yd;
rtlatov;
dax-IV-loi
it$ oltd ATTf O
10 ~7Tf A
Ttg" o
it, o
nt, I15 itr\
o
Jtn I
7t&1t$ I
20
9 o
9 a
a o
9
25 5y o
9d o
aos o<ro Aaoe o
~ood~A~aod o
aoy A
Tty7T(f
118
x
xy its
it?
aoy o
crop A
aop o
<TOOf
aoa oao i
A xA r<?
a ty
7*17
la x
la ty
I vd
xrj
* nXS It]
xy xj 9y
aog y.S
ooe vdaos xd
aod vdaod xd
goy vd
aoy xd
ao/? vd
ao/* xd
xa xw 10xd /d
xg xf
xw tc
aoa vdaoa xdao vd
a ra*Y
ly a
ao xd
Ay x(i o 20
Ay is
ly a
I? Ayla va
oft
at?
A vc 25
x us
*r\ is
9d
30 9
a|s o
9yxd td
xa xrj 30
9? 9* xd
9 rJ
9? xe? oy
1. y'~\ om.A1BCD. xav6viov filiov]
Tjliax&v D. ^xAf^fcov] -Isiipttov inras. D. Inter lin. 1, quae utrius-
que tabulae communis est, et lin. 2
ins. tov lo^ov xvxlov tfjs (J xtvtgovTtaoodo? D. 3. a' <T] om. D. 6.
H<jQla C. 7. o (quart.)] e corr. B 3
.
12. xt] x* D. 16. TTf/] TT^ BC.17. A] a D. vd] corr. ex ra D. 18.
Aa] corr. ex Ac? D. 21. Qa] -a in
ras. A1. 22. A(pr.)] corr. ex a D. 24.
a] -f e corr. C. 28. a^] a- e corr. C.
31. <r(f] aa D.
1.
om. D, u. supra). 3. a' <J'] om. D.4. Alatovq] B C, aQi&/uoi A1
,om. D.
uQi&iu.oi'] rtlarovgD. daxtuloi] aQi&-SfJ.7tt(0\ ----
D. 10.vd]vaC. 13.A?] A-ecorr.D. ig]corr. ex xg
1 D. 14. /<] ps BC. 16. va]-a e corr. D. 17. Ay] vy B. 19. xd] -d e
corr.D. 20. t^df] tft'un in ras. B 3
, ipe
C, ip D. xp o] xp o A1B C, xp corr. exxg
1 D. 26. a^C] o|n D. 28. aV] agg; D.
29.xd(pr.)] xtC. 31. 9*] corr. exvd] mut. in va D.
520 KAATAIOT HTOAEMAIOr
r-1 W Q<**>> fn (H
.s IS 71"'* ga
r
|* ^1 ? . o ^-^,
< 5J R-
2 ji R M *5 2 OT 8 z* S M
Q"SS eNjoto^toS^^^Vo
1
1-S-
Io
ISi
I-
<*> f
r "0 v ^ sto to to to ^
R- R-3.
"
R- R-
t
I" 5.1:
<J>X
8 S
IS- i-'S
U, JJ-
MA0HMATIKH2 STNTASE&2 S'.
|Slafl ||rf 1 | |l|5^i2
521
d P
*.. -r 1 a * I a$r v PQ e1 n &
S S
j> u. 5
S"0X
*, a- R- *
W> JUyito to
X \J> ^,
44
8 <*!.
_
*8
xdja-^o.w'Bb <JO, 8
? S" ? S-%^.
55. S-
^8
8-Wa- a- a- a- a-
<V In>
0-,
P,
s so P
""
p Z s 3tit-x;7c5r>{ 2 * L!"^
-! "-S pq P g i P ^-.S S ^
o< x s
522 KAATAIOT HTOAEMAIOT
dt,OQ&G)6G)$ xavoviov
MA0HMATIKHS STNTAgESS <S'. 523
Tovrov drj TCQoexts&siiiev&v ri]v ftv r&v
x&v sxAsfyeav &efaxfyiv TtoL^o^fd'cc rbv rooitov rov-
rov sx&fyevoi, yccg rfjs ^Ei^ToufteVty
rbv Gwccyonsvov dQi&pbv xard rqv v'
rov peGov %QOVOV rijg 6vvyfas &QCCV r&v re cbrb rov
aitoyeiov rov sitixvxhov rr/S xccAovpevrjg
xal rGbv ccTtb rov (logst'ov Jtsgccros rov 7t
rr\v SK rijg TtQoG&ccycuQsGs&g diaxQitiiv rbv rov
ito&rov efaoitioiiev sis i& i&v ^^VLKK&V 10
sxtefyscov xavovicc, xav tftovepxticfy rolg r&v xo&rcov
dvo GsktdC&v ccQL&yioig ,ra 3tccocc%i[ivcc r& rov xkK-
rovQ ccQi&yiG) KK& exccrsQOV r&v xavovi&v v r rots
r&v Jtaoodcdv tffAtdtotg KOI v rots t&v daKrvk&v CCTCO-
l<s xcc6rct' 7ti,ra xal rbv rijs KVCO^LCC- 15
doi&iibv i(SVyx6vrs ?s tb r
xccvoviov, o6cc txvfi
ra JtaQKXi[iva ccvrG)
roGavra A.af$6vrs ri\$ v7tQO%ils r&v tcatf xccroov
xavoviov a7to'y'yQtt[i[iva)v daxrvh&v rs XKI %r]xo6rG)v
rots ex rov jtgcbrov XKVOVLOV xccrfi^^- 20
bdvroi 6v^aivr] rbv rov itAdrovs KQL%--
ts vb devreoov povov xavoviov itiitrnv^ r&v v
1.-9-']
om. A J D. 4. iKspsvoi] -ot e corr. D. 5. Iv]ins. D 2
. 6. r&v] mut. in xov C 2,corr. ex TOV D. 10. slc-
otoco^ev A 1. 11. fylsfyEmv D, sed corr. 12. fffybjtftW A 1
.
14. catoyQatyccusd'a post ras. 1 litt. D, -o- pr. et -tydfis&K in
ras. 15. ^oo^tg] in ras. D. 17. idv] s- postea ins. A 1,
- del. D. ctvrois D- 18. roGav-ta] ra rooccvra D. rr)t
r. ex SKUGZOV D 2. 19. V.OB. fxart^ov] corr.
corr. ex lv rto KKVOVLO) D 2. ccnoysyga^iLsvov C, sed corr.
21. Gvctiv'ti C.
524 KAATAIOT HTOAEMAIOT
aVTG) [IOVG) TtaQaXEi^lEVCOV 8aXTvA.COV Xal [lOQl&V Ta
voL6x6^iva sfyxoGTa EX&rjGoiiE&a, xal oGovs [LEV av
EX Tijs TOiavTrjs dioo&G>6Ecos
,ToGavTa dcodsxaTa TCEQIE&IV
5 ETtiGxoT'rjGiv rils GEAyviaxijs dia^iEToov xaTa rbv
%QOVOV rils sxfafys&g. rots S* sfyxoGTOts tots ywo-
[izvois XCCTK rrjv avtrjv di6Q&G)6iv TtQoG&svrEs xdvrors
TO i$' avT&v, av& av 6 ijfaos sitiKivsiTcu,
xccl
6CCVTES SIS t6T TVJ
10 XLvrj^icc^ oGccxis &v funsGr] 6
[lQLVCCS KtQCCS %0[lV XCC0TOV T&V
TJJS xfofyG)S') t&S f*v EX TOV d' Gs
X&gls fov TE Tijs tpyiTcfafsmf xal TOV Tijs K
60)S %QOVOV, T&S d9
EX TOV TCE^lTtTOV T^S ^fAitfStaS TOV
15 Trjs [lovfis %$6vov, <pcivQGbv CCVTO&EV yivoplvcov T&V
TE xaTa Tag aoftas xal TCC TE^y TCOV ii($cc6EG)v xal
avaxafrdoGEMV aoiaLcov 7to%&v EX TY\S agog TOV pf-
Ta%v Tijs povijS) TOVTBGTIV TOV Ti}s axoiflovs EyyitiTa
JtavGEhtfvOV %QOVOV, EXCC6TOV T&V XaTa {lEQOS EVQ16XO-
20 pEv&v TtaoG&ayaiQEGE&s' avTO&EV ds xal T&V Tijs <^t-
pETQOv dcodEXccT&v EfaEVEx&EVT&v fis TO ETtl JtaGi P$a%vxavoviov xal Ta i$' TCOV oA&v E^iftadcov Evotj^o^Ev EX T&V
3taQax(,[iVK)v EV T(p y' GEhidiG)) o^ioicos $E xal Ta TCOV
EX TCOV EV TOO dEVTSQG)
1. nuQuy.siv(ov D. 2. sdv~\ o &v D, p (ovv) del. D 2. 8.
t^'] t'|S' A 1(" in ras.) C, ScoSs^ccrov BD. &v&' cov] corr.
ex KV& D 2. lmv.ivthai] -t- sec. in ras. 2 litt. D. 9.
om. D. 10. OG<X.Y.L<S\ OGK D. 14. XQOVOV'] 'v D. 15.
XQOVOV] inter duas ras. D. 17. avaKaQ&dosav D. 18. TOVT-
f'drtv] comp. B, -v eras. D. 22. svQioofifv C. 24./i
B et supra scr. D.
MA0HMATIKHS STNTAgESS '. 525
6 [iv ovv Aoyog aiQEt ^r\ ndvrors rov dnb rrjg
s Mteifa&g XQOVOV [i%()i> rov psGov faov
ro5 onto rov pteov p%Qi rov rijg
dice rqv Jiot rs rov r/Atov xcci fr\v 6^tjvrjv a
t&v fa&v TCKQodcov diet rb TOLOVTOV ev avfaoig %QO- 5
VOlg K7tOTA.OV[lVG)V) t^ $ afad"lJ6G)S VXV Ol)dV
KV K^io^oyov a7tQyd(jcci,ro nobs ra (pcd,v6[iva
rb ^ dvfaovs rovg x$6vovs rovrovg
xccv XQI rovg pfaovg dgopovs &6iv, OTCOV
r&v jtaQav^tj&csv v7tQO%cti, rr^v ye
rotfovr&v ctiQ&v Ttcc^odov^ oG&v stirlv 6 nag rris r-
rqv r^g VTtQO%ri
on $ xal EMor&s dirjiiaQrypwyv evQfaxopw rr\v
VTCO rovr
l7t7tccQ%ov dfdfiyiiwrjv rov TtAarovg rqs 6A.tj- 15
rijg iirav rcov
tteCovog 81 rfjs xccra rovg rjiittfyovg iiti-
XKri&r)[in,vr]s, aitb r&v ccvr&v av itdfav
arccvoi]0cci^v. 20
haficov yaQ ig rr^v roiavryv catodei^iv wfofyfig
dvo Gfkrjvicixas dia prjv&v y j(>| yyvrnLva, V cclg
rb rdragrov rijg
XQOVOV D. LGOV] corr.
ex OGOV D. 3. yiVfffihu] A 1, ysvsG&cci BC, yfyvfG&KL D. 5.
roiovrov] corr. ex toiovr D. sv\ -v ins. C 2. dvtaotff] -IG-
e corr. D. 7. a.v\ supra scr. D. 8. nsQirL&sG&'cii D, sedcorr. 9. V.OLV] KKV ft BD, corr. D 2
. 10. v7tQo%dv A 1. 12.
alGd-rttr)v] sG> D, supra I- add. at D 2
. 13.fr>] supra est
ras. A 1;
fort, delendum. 19. tiari^r]^vrig] -it]- alt. e corr. D.
av ndUv] corr. ex ccvdnaUv D. 22.
Q D. 23. trf'ra^Tov] ^/ B.
526 KAATAIOT IITOAEMAIOT
xccra rrjv avtyv onto rov
srvy%KVv^ cav xoarrjv [iv
ds rqv v rc5 A' s'rsi trig roirrjs xccra Kd^ntitov
5 rtfoiodov5 6vy%oijrai, filv rc5 TTJV ctvrrjv xccru
itgg tr\v r
rov %v\v [isv 3tQOTQttv eKteifyw yfyovwcu xara rb ccjto-
yziotarov rov BTUKvxkov rijs faAtjvrjs ovGrjs,
10 devregav xccra rb xsQiysiorarov, xcd dia rovro
$ xal KKX avrb rovro
xal I
Ttaaa rb
15 wofaxfG&cu rijs oMQipovs nar' K[Kporoas t&
AA' litl ply rijs nooreoas pia [loioa fyyuGra,) iitl ds
rijs dfvnloas oydoa) [lias fiotpag, &s Kara, ye rovro
^L7tLV ir\v rov nAcirovs 3tQiodov sis
xara6ra6i,s v\\ii6i> xcil d' nolrj
f
[lias [lOi
20 6rlv 6 Ao6g rijs teMpnft xvxhos r%. 7Cira ovds
rrjv did ra rijs 6A,rfvr]s cc
7tol ra
yC6a.ro rr^v itfafarrjv pakuSra yyvrnivriv inl rovrcov
r&v fxfafyfov diet rb rr\v \L\V noorfyav notrcc rb [18-
25 yiGrov djt60rrj^K rijs <S^vrjs ovtiys ysyovsvai, rrjv
1. avxriv] corr. ex roiavrriv C 2. 2. xr\v\ om. A 1
. 3.
L D, e* D 2. 4. feet] L D, f D 2
. Kctimnov] BC et -in-
in ras. A 1,Kdllimtov D. 5. 6vv%QfiTcn D, sed corr.
x&v] ins. D 2. f|] -| in ras. 2 litt. D 2
. 11. cog ye] -g yeins. D 2
. were] &- e corr. D. xr\<i\ supra scr. D. 13.
iyiyvsro D. 15. Ante Y.KT' del. sv D. 20. ovds] suprascr. C 2
. 23. TOVTCOV] -TCOV supra scr. D 2.
MA0HMATIKH2 STNTAgESS '. 527
de devreguv xard rb &d%i,6rov' avdyxq yag r^v rov
avrov d' [iQOvg e7ti6xorr]6i,v 7taQr)xohovd"r]Xvai, xard
[iev rrjv rtooregav exAeityiv dxb ehd66ovog dtadrddeog
rov dvapifid&vrog 6vvde6[iov, xard de rr^v dsvrfyavdjcb ^t^oi/og, G)v trp dicctpogav (XTtedsi&iiev [p. 520 5
tab. 1 lin. 10 et tab. 2 lin. 10] fii&s poiQas xai ns^jfTrj-
0vvccyo^ivrjv , fog xctl svrev&tv re!) roGovrco
iv riiv rov Jthdrovg itsgiodov ftfO1'
o^ccg cato-
rb plv ovv o6ov iit avrr] rfj rtkdvrj
rats Q ati<porQG)v r&v dpaQricbv Gwayoiizvcus dvtilv 10
[IOIQCUS fafptxAy civi\ jtsQiodixq rov itAdrovg
el srv%ov diitporsQcci, TCQOS rb skarrov
rb itfatov y>QOv6ai, rr\v Siayogdv, eitsi ^'17
iitoiu rfv ditoxardtirccGiv, f]ds itfaovd-
nva 6vvrv%iav, rp> fa&$ xai 6 "Ixxaoxog 15
ttvravajtA.'r]$ov[ievr]v ytcog ^ccravevo^ei^ fidvco rw rrig
rcbv d^iaQn&v rQirco pe^ei pices [lOLaag
ov6ar] eitttrjilug rqg
i.fHkiaK&v exkettye&v
rH [iev ovv rcov GeArjviax&v Mfafye&v eitfax^ig 20
pov&g av did ravra yivoiro vyi&g, xa&' ovg exre&eC-
lie&a rgonovg, rcbv eTuA.o'yiGii&v dxQt,j5ovnvcov %fj
de rqv r&v fjfaax&v eKkefye&v didxQitiiv xaratixefad-
1. ikd%iGTOv] corr. ex &ct%gr D. 10. avvKyopEvac A 1
. 11.
lioli>' D. 13. Post ntefov ras. 1 litt. D. 14. laolct] om. D.&itoY.a.6TaGiv C. 15. i'cos C. 18. fTrt'A^^ig D, sed corr.
D, ccnoxurcracs cos D 2,
ut saepius. 19. t']
om. A 1
CD, mg. A 4 B. 20. Post tttetysuv del. tniGut-yie C.
21. ysvoiro BC. 23. ^KrGKfUsGrigav D, corr. D 2.
528 KAATAIOT nTOAEMAIOT
rsgav ovdccv 8iK tag TtccQccMd&ig tys 6htfvrjg
ps&a rbv rpdjrov rovrov
6xil>d[ivoi, yap rbv v 'Atet.avdQeiu rijg dxaifiovg
<5vv68ov %QOVOV, JCQO Ttocfcov r) [ir& noting caoccg '|-
5 E7t(3v iGripeQivag rijg ii<5r][if$QiaS) sjtsitcc, sav
ftrb vitoxs[jivov K^lpcc rijs liti&
sccvfti)
VTCO rbv avrbvr\ yL6rm,fiQivbv res
rr^g 'Ate^avdQeia^ TtQoG&acpshovtss rb xccra
sv rots dvtilv [isGrjuflQwoZs rcov
10 COQCOV xctl na&ovrss, ngb TtoG&vr} psra
Qwa$ &Qas xccl nay' sxswois %rt6v 6
<5vv6dov XQOVOS, diaKQivovuev TtQ&rov xal rbv
Gvvodov %QOVOV iv r
rbv avrbv fyyiGra tio^ivov ro5
15 fa&s djtb rijs TtEQi rag TcaQaM.v&.si
v roig 'n,7tQo6&v Hcpodov. A.a(i6vrs yaQ x rs rov
rfbv y&vi&v xccvovog xal rov r&v naaaMd&covrti r Kkiyiari, xccl rri r&v cao&v KTtotirdtiei rov
runfiQivov xal hi r& Gwodixfi {iQi rov Z&diaxov xal
20 agog rovroig r<p rijg Gfhijvrjg Kitotir^an TV\V yivo[i-
vrjv Tto&rov avrrig TCaodMcc&v &g iitl rov dia roi
xctra xoQvcpriv Grftifiov xal rov xwroov rijg
yQKy>o[ivov peyfarov nvxhov xal ditb ravrr^g
itdvror rr\v xara rov avrov 6ri%ov
25 Yifaaxriv Ttccod^cc^Lv d%b ri\g Aot^ijg diaxQivovfisv^
2. Ante rov del. D 2. 9. dvci B, Svtt D. 12. rov]
r&v C. 13. v.U^ari\ corr. ex HUpu-ca. D. 15. Tt^Ud^Lg D.16. dicdapovTsg BD 2
, $LccUc<p6vTE$ D. 18. co^wv] eb- e
corr. A 1. 19. %-u] corr. ex ti D 2
. 22.
ccno] ins. D 2. rav D,
? add. D 2. 25. nccQdJiK^v D, corr. D 2
.
ws] corr. ex GO D 2.
MA0HMATIKHS 2TNTASE&2 g'. 529
did rrjg VQL(3xo^vrjg Ttegl rr\v
rov ^cpdiaxov xccl rov dice rov Kara xoovcpyv
y()cc(pO[ivov {LEyfarov xvxAov ycoviccg rr^v
cog rtQog [lovyv rrjv xard ^xog itdgodov 7t
xccl ravrri TCQQG&SVVBS Ttdvrore rb 7tifidM.ov rotg TCSQI- 5
%0[ivoi,g 'bit avrils ^^>dvotg faqfttQitrblg rtj?
r&v jcaoaxL^vcov dvo
r TtQ&rr] rov xard xoovcprjv 6r){iiov
xal rrj [ird rijg 7tQo6&rixr]g rcbv I^^BQLV&V 10
d rr\ xard [liJKog povrj itdkiv Jtt,fldA,A
L [ird rov rotiovrov pfyovg avrobv^
ft,o6ov xal avra pfyog 6rlv rijg
?,xal rotg ovroo 6vva%&st6i, rijg oAqg xard
pijxog itaQaMd%G)g [looioig TIQO^^O^V itdhv rb do- 15
dexarov avroov, av& ov 6 r\kiog 7Cixivirut,, xal roc
tg &Qag i6rm,Qivag x rov
rcbv 7tol rqv Gvvodov rijg GfAtfvrjg dv&pd-k&v G)Qiata)v ^dftov, xav [iv tg rd 7t6^iva r&v
^cpdi&v 17 xard pijxog TtaodMal-ig $ yivo^vrj' dfdffya- 20
( jiv YCCQ v rotg fpTtooGd-fv, nag r^lv ^ roiavrr] did-
^ xoiGig A.a[if$dvr}rai,' rd yiv ig rdg &Qag rag l6riyiQi-
vdg dva^f^,v(jt,va poQia dcpk6vrg dnb rcbv xard rbv
5. ravrrj] corr. ex ruvt D 2. nt.pdUov~] corr. ex TtfidHov D 2
.
6. atmfc] corr. ex ccvtois in scrib. C; CCVTU!> D,
g add. D 2. iiii-
jtaQcclLa.CQs D, corr. D 2. 7. rovrear D, comp. B, TOVCSGT
I D 2.
13. #] corr. ex v D 2. IOTIV] comp. B, -v eras. D. 14.
xat] supra scr. D 2. ovroog CD. Gvvax&fiGL] GVV (a supra
add. D 2) fji8g lotl r itQcor ffitiGi D. 18. Gvvodov] corr. ex
cvvofc D 2. KvaiiccMav D, sed corr. 20. gcodicav] corr. ex
ZQJ^IKK&V A 1 et A 4. yiyvoptvr] D. 22. rd] corr. ex
rd<s A 1.
Ptolemaeus, ed. Heiberg. 34
530 KAATAIOT HTOAEMAIOT
rfjg Gvvodov %g6vov
[loioobv %K)Qig exdtirov rov re [itfxovg xal rov
ithdrovg xal ri]g dvco^a^Lag ^o^,v rag v
rijg (pawoiiwyg Gvvodov axgifatg nagodovg rqg
5 v^g, avrag $ rag &$&, eGope&cc svQrjxorsg, o6ai,g
rsgov -Y] (pccivoiitvr] Gvvodos ysvritisrat, ri^g catQi
eav de elg ra 7tQorj'yov[ivcc rcov tydC&v f)xara
g r] VQ^^vr]^ rcc(i
rcclg xccra rov (xxQifir} rys Gvvodov %QOVOV10 7tQodiaxXQi,iivai,g nagodoLg xd<5rov rov r
xccl rov ithurovg xal rfjg avG)[iaMag, rag $
, oticcig vtirQov i] (pcuvojiwr] Gvvodog k'tirai rijg
ndfav ovv xara r^v rrjg q>aivo[ivrjg 6vv-
odov rcbv l6r]^Qivcov WQ&V axb rov
15 GrccGiv rti,6xil>d[ivoi, dia rcbv avr&v (p6dov^
xocorovr] 6A,7Jvr] 7tccocchA,a66i, itgbg rov dt' avrijg xal
rov xara xoQV(pr\v ^r^iBiov/
y^a<p6^vov [ifyitirov xv-
xhoV) xal aq)^6vrg aitb r&v VQi0xo^idvK)v ryv r&
avrGj aQi&[i(p 7taQaxi^ivrjv rov ^LOV jtaQdhha&v enro
20 rcov Aoiitcbv G)6avrcog x rf}g ror jtQl rqv r&v xvxh&v
ro[ifjv voi,6xo[ivr)g y&viag diaxQivovyizv rqv xara
Tthdrog ag itl rov yf^bg oo&ag roj ^G)dtaxc3 xvxhov
aQakha&v xal ra 6vva%&vrafig ra xara rov Ao|6v xvxhov
25 riitfpara, rovrfarw d&dfxdxig avra ttoiiJGavrsg, rag
,sav psv rj
xara xhdrog
1. Ante alt. tfi<s del. r D 2. 5. evQiOKOvreg BC. oaaig]
(xlg D. 11. >tca (alt.)] oin. D. 13. TIJV] supra scr. D 2.
TTfe] T D. 15. TfOG D. 16. 7l(XQC(ndai A 1
; IlKQaMd&l D,corr. D 2
. 24. XK] TO D. 25. rovrtcriv] comp. B, -v eras. D.
D, corr. D 2. 26. yiyvo^vccg D.
MA0HMATIKH2 STNTASE&S S'. 531
Ttgbg tecs ccQXTOvg i]TOV did [is
TOV %QOVOV Tijg
TOV xaTccfti^d^ovTcc acpe^ov^isv O^IOLCOS' sav $i]
XCCTCC 5
nAaTOS TtccQccA.A.cc&S &S XQOS ^^r^i^Qiav ajtoTe^YiTca
TOV %G)dlCCXOV) XUTK TO SVCCVTIOV 1tQi {lV TOV ttVCC-
Tag K Trig itaQaM.d%G)s ^tOiQCcg ccnb T&V
llVG)V V TG) XQOVO) Ti]S (fKiVO^VYlQ Gwodov TOV Tt'ka- 10
TOVS IIOIQ&V, 1t$l d TOV XaTCi
OVT&S %OllV TOV V
Gvvodov TOV fpaivo^Bvov nAccTovg a^t-0-ftoV, ov
zfe V ^LCCXCOV XfafyG)V KKVOVitt,
<xv tivv^itCTtTri Totg T&V TIQWTOV dvo 6kidCcdv apt^- 15
V <56&tt.l TOV r\MoV (p^O^V ^ ^g [l60VCC %QQVOV TOV TTJV q)CaVO^LVr]V GVVodoV JtSQi-
%OVTCC. X&llVOl, OVV T7]V 7t060Tr]TCl T&V JtCCQCCXt,^l-
VG3V TG> TOV (paiVO[lVOV TtAccTOVg KQL^^tp dct-XTV^OV T
xai [lOQL&v Tfbv T Ti}g ^7tT(b6Ktg xal T&V Trjg ava- 20
xa&aQ6cog x^^S f'l XCCTQOV T&V xavovi'cov ftc>ofaoiiv
KCil TOV KTtb TOV UTtOyflOV XCCT<X Tr]V <pCUVO[JiV7]V tiVV-
odov Ti]g dvG}[iccMag dgiftubv Ttfg 6&ijvr]g tg TO Tqg
dt,OQ&c6<}(Qg xavoviov, xal TCC nccQaxi^vcc CCVTO) Qy-X06Ttt 06CC CCV ?}, TK TOGCiVTCC kafl6vTg T^g XCC0TOV 25
T&V CC7tO''aVG)V V7lOY$ 7t00^r00V CCLi
2. tov] TOV avrov B. 6. jrpog] supra scr. D 2. &TIO-
reJLrjTai] D 2,
ccTCOTsteirai A 1 BCD. 7. rov~\ -cbv uvrov ED.9. 7tQodia-AXQt,[jiEV(ov] TIQO- in ras. A 1
. 10. sv] s A 1. 15.
di;o] -o supra scr. D 2. 16. fo] supra scr. D 2
. 23. r" dio^-D. 26. v7iQo%fig] -o- in ras. A 1
.
34*
532 KAATAIOT IITOAEMAIOT
TOV ztQCOTOv xavoviov xaTt,krj[iiivoig xal Tovg
x
&p' O<JK
r\ rti,6x6Tr]6ig serai Kara TOV [i6ov
5 %$6vov rijs exhsfystog. rolg d' sxarsQag rijs
TtttklV TO 1$' KVT&V,
O.V& G)V 6
)xccl Ta yv6^,va Jtgbg TO
OVTOV f^OpSV TOV %QOVOV XttTQaS TijS T
10 xal Tijs ttvaTtArjQcbGfcos, &g iar}d[uac; pivtQi
%QOVOVS TOVTOVS 7titfvitflai,vov6ri$ dice Tag Tt
xecl ovyl
15 Tijg av&iiccMag T&V (pc&T&v, natf v xal fjt,%ovg aito-
T&OVVTai, X^QiS MKTfOOl T&V 7tQOXT&l,[lVG)V TtCCV-
TOT xal cog 7tl TO Ttokv avitioi cU/l^'/lotg, ov$
v, si xal fig
ovv TOVTO TO 6v{i7tTG)[ia dia TO
20 yuv6&aC Tivag iv rg <paivo[ivr) Trjg
7cdvTOT T&V 7taQaKkdt>G)v VXv
Tivag cpavTa6ia) i [tydlv Idtog ig Ta 7t6^iva dia-
ka{ifldvoiTO xivov[ivrj. lav TS yao TIQQ TOV ^i6ri^Qi-vov 7taQodvov6a yaCvriTai, xaT bMyov dva<pQO[ivr]
25 xal 'ka<56ov alel TOV Ttao^rjkv&oTog
1. KKVLOV A 1
,corr. A 4
. ^ccTEilri^^vr]? C, sed corr. 4.
D, sed corr. TOV] TO D, TOV D 2
. 6. t^'] t'^'
A^BC, Sood^arov D.f
KV&' G>V~\ corr. ex &v&" D 2.
^
13.
ylyvitui D. 20. ysWtfOm BC, yLyvtcftai D. 21. $)GTtQ\
-EQ e corr. D. 25. tlaGGov alet] HO.GGOVK D.
9-drcog C, sed corr. TtccQcddccovGa D.
MA0HMATIKHS STNTAgE&S '. 533
bg fag dvccToAag fioddiov (pKivsrcci, TTJV sis *& eito-
a(5i,v Ttoioviievr]) dv r [isra rov fi<?t?^/5@fc-
vbv TtecQodsvrj, xarci(pQO[iV'r] Ttukw xat' okCyov xal
jthsov aid rov jtaQshrjhv&oros 7tccQccMd66ov6a agog rag
dv6{iag bpoicog fiQadvrsQav ity tg ra sxopsva [isrd- 5
ficcGW (pCiWlJGSTGCt, TtOiOV^VY]. TOVTOV {ISV OVV VXSV06 TtQOBLQrilLWOl, %$6VOL TtKVXOTS [1%OVS fGOVXCU T&V
aTih&s ovrwg A,ctiif}avo[iVG)V) inei^ovog d' ccfel
iv rccts V7tQO%ats rcbv TtaQccMd&coi&v fyyvtfym rov ^TJ^QLVOV nagodov avdyKri Kal 10
rovs ngbs rd3 yL6runfiQiv& iLcckkov r&v wfafyf&v
vovs j$QCidvTQOv aTCOTffaiG&at,) xal dice rccvr^v
altiav, OTCCV plv fig ccvryv tyr ^i67i^QCav 6
%Qovog rilg x^a4>cog imtitttri) tors povov faov
rbv r^g fjjuttaGfwg %$6vov rc3 rijg avcatAr]- 15
xal Trig x r&v JtccQaMd&cov rtgorj'yrjTMrjg cpavraGiccg,
orav d ago rijg fj^^tft^ag^ tore rbv rijg avciTtAqgG)-
6wg fyyvtegov OVTCC rov ^6r^iftQivov pEC&va ytvz-
<?<0m, orav d [iT<x ri]v fiftf^/Spt'ca', tore rbv ryg 20
{jL7ir(b(5G)g eyyvr^ov OVTCC rov
ovv xal rr\v roiccvrriv rCbv %QOVCOV
ov
1. figddsiov D, corr. D 2. qpaiVrjrat D, sed corr. 4.
&i D. nccQuhdccovcct D. 1. [j,%ov D. 8. aft D,corr. D 2
. 9. yty^OjCt^rj? D. 10. syyvtZQcoi BCD. TCCXQ-
6dcov~] corr. ex naaodovav D. 13. TIJV~] om. A 1
,add. A 4
.
15. yCyvBcQ-ai D. rov'] TOV re D. TOJ] corr. ex TO C 2.
17. iv. r&v] supra scr. D 2. 7tKQaM.dCQS D, corr. D 2
;deinde
del. SK T&V TtocQccUd&cov D. 20. otav] o D, o D 2. 24.
in ras. 1 2 litt. D 2.
534 KAATAIOT nTOAEMAIOT
re
vov xaroag r&v xxi[iVG)v naoodov Kal rfjv Kara,
tor pfaov %QOVOV ri]g Ixfofyscog anb TOV Kara XOQV-
svsxev 6 pv %oovog xdroog
, f]ds TOV Kara xogvcpyv
'a drj iv ro3 TCagakkaKriXG) ua-
vovi ra itaQaKsi^ieva r& r&v o ^t^c5 r^g itag-
aHa&Ktg sfyxoGra ajg Kara TO ^yi^rov a7t6(STrj^a
10 Ad/ov SVSKSV ovtirjs r^g (JfA^v^g, nobg o ano^rri^a ra
ev T<p y' GskidiG) 7taaaxiiiva kaiifidvsTat,' svofaxoiisv
ds STtLfiakkovra Taig os ^oCQaug S^KO^TK vfi. Kal sitsl
%oovog rr\g rs fyTtrcoo'scog Kal ryg avaTtkriQG)-
og [ii,ag plv cooag
15 t^^eQivi]^ IQOV&V de is, rovrovg acpshovrsg plv anb
rcbv bs rilg aitoGTaGeog UOIQ&V svofaxoiizv ralg Aot-
TCaig | iioiQaig ra naQaKSi^sva ytaoaMd&cog %r]xo6Ta
ev T& avrti GeUdiG* ^ &g rqv Kara rr}v ^6r]v itabg
r& iLetirnifiQiVK* Ttdoodov sx ri\g TtaoaMd&og ytootj'y^iv
20 QriKoGT&v f Gwriyftai,. TtQoG&dvTsg d' avrovg ralg of
Kal ralg ^vvayo^lvaig 9 poigaig svofaxopsv svmrc3
avrti (JfAtdtco TtaQaxsipeva ra rr^g okrjg xaoaMd&cog
^Kotsra ~vy /.', cog Kal sv&dds rrjv ttQOYiyiqGiv ri\g
Ttobg T& OQ%OVTI Ttaoodov 6vvij%&ai, rcbv avr&v %r)-
25 xodTcbv a L'. rcbv VQ&VTG)V ovv diayoQcov ra rc3
Kal xdroov
3. TOV] corr. ex TO D 2. 7. navovia) D, corr. D 2
. 8. rrjs]
om. D. 11. la^avBTKi' BVQIGY.O^V\ -i s- in ras. D. 13.
xaTf(pog 6 XQOVOS Halma. 14. &coQov^Bvoi D. fi&>] seq.
ras. 2 litt. D. 21. 9] in ras. D. (IOLQOIS A 1. 22. ofoje]
a-Or/jff D. 23. vy /_'] ~r [_'A 1
. TcqoijyrjGw] -r\- in ras. A 1.
24. TtKQodov] corr. ex nccQctdovg D 2.
MA0HMATIKHS STNTAEE&S g'. 535
X rov rij
aoag fatffteQivifai) cog vnodsdewtcci) rb 6vv-
ayopevov dcp' xaroov jrpotftb^oftfv oixsi&g xarQG)r&v iifa&g xal dith&g s^rj^svcov %Q6vcov rr\g re
Xal '
rtfe dvK7t^r)QG)CfCDS^ tb {lV [ISi&V TG) 5
a rr^v iyyvrtqav rov [isGrjiifiQwov itaQodov, rb d
rci Kara rrp> iyyvriqav rov ogftovrog. dr\lov
\ on nal r\rcbv XQOXSIUBV&V %a6vcov V7tQO%rj
ysyovs y L'->&' $ zyyiGra (nag agag
iv otic* ra rooccvrcc %t]xo<5ra iLtd&g r\ 6krjvrj xti^tb?- 10
e x 7tQO%toov xal rb rag
^sav -O'fA
ig rag Kara [iQog KaiQixag Kara rov iv
rotg 7tQO&vvrra/
y^ivoi,g VTtodedBiy^vov fytXv rgonov.
ia'. Ilol rCbv iv ralg Kksity<5i TCQo6vv6G3v. 15
'Etp%iig d' ovrog rov xal rag yivo^ivag r&v iiti-
<5Korri<5e&v 7tao<5vv6ig iitiGxvit&v Gvvfararat, plv f]
roiavrrj xard^i^ig x rs rijg avr&v rtbv
nQog rov dia [ifa&v rCbv tydiav xvxkov
KOI x rtfg avrov rov did {ifacov Ttobg rov doi&vra. 20
rovrcov d' xdroov iv xd<5rc) rCbv ilxfoiJtrix&v %oovcov
av xal aTteQi^Ttrov itaod0%ot, 7tol rdg
4. EiJirnnisvoav] -co- in ras. A 1. 6. TOV (ieor](iQivov^ ro-
et ptai}- in ras. A 1. Ss\ om. D, d' supra scr. D 2
. 9. y^-
yovsv D. &QCCS] {IOIQCCS D. 10. 17] postea ins. D. 11.
Supra TO del. a D. 13. rag] rd C. 14. TtQoaGWTsray^E-votg D, sed corr. ccnodedeLyiisvov D. 15. ta'] at B, om.A 1 CD. 16. rov] supra scr. D 2
. 17. &ri**eTefr C, sed
corr. 18. xataZ?]|u/i/>ts D, p eras. KVT&V r&v] D, T&V dv-
rcbv A 1
,T&V ctvrav BC. 19. TCQOS rov] supra scr. D 2
. KvnUov]v.vJC D. 21. Iv] supra scr. D 2
. 22. nagdoxoi] corr. ex
D 2,et similiter saepius.
536 KAATAIOT HTOAEMAIOT
evaAAayrfv ,si' rig rag dt' 6Aoi> rov %oovov
yevr]6o[iBvag itQoGvsvGsig nsoisoyd&o'd'ai, -fo'Aot, ^itdvv XL trig STtl roGovrov rtooQorjGscag dvayxaiag rj
XQrjGi'iJLrjs VTtaoxovGrjg. rijg plv ydo rov tydiaxov agog5 rbv oQ^ovra 6%&fea)g Q-scoQov^Bvrjg ex rijg r&v dva-
rsMovrcovrj
dvvovrav ccvrov Grjiisi&v xccra rov OOL-
ovros STfo^s ava'yxrj xara rbv rijs fafafyf&g %QOVOV
dicKfoocov 6vv%cbg yivopivwv r&v dvctrsMovr&v xal
dvvovrov [isQ&v rov fydiaxov xal rag i)7t avr&tv
10 aTtorsAovfisvag rov doi^ovrog ropag <5vv%(bg
GXfavr&g d xccl rijg xobg avrbv rbv
7tl rov di d^(por0(ov r&v xwtocov rov rs rij
vyg xal rov rqg Gxiag T) rov rjMov yQayoiiwov [i-
15 yfarov xvxkov ndhv dvdyxrj did rrjv iv rc5 %oovq) rijg
fxtefyEKtg rov xzvrgov rijg (Sekrivrig ndoodov xal rbv
di' d[icporQG)v rcbv Xvroc3v yoatpo^ifvov xvxhov rfjv
&<5iv ah&qv al JtQog rbv tydiaxbv ^a^dvsiv xal rag
Vitb rijg ro[iijg avrcbv 7tQi,%onvag ycoviag Gvvsi&g20 dvfaovg Ttoisiv. avrdoxovg ovv 6o[i8vr]g rijg roiavrrjg
rcbv ennsri^aGiav nvdxal xard rb
Q6roov r&v Ttobg rbv ooi^ovra ^BCOQOV^BV
cpsosicbV) dvvarbv {lev etirat, xal avro&Bv roig ye rb
25 ywopsvov Ttd&og vit oiluv Aa[if}dvov6i,
1. s^ccJiJiaijv D. 2. fvrtfofVag corr. ex sviGoisvas D 2.
6. rot;] r corr. ex r D 2. 8. dicccpoQcov] corr. ex dicccpoQcao D 2
.
D. 11. ytVfff-frca] A 1
, y^vtcO'cti BC, yiyve-14. rf| ins. D 2
. 16. TOV~] corr. ex r&v C 2. 18.
as. D 2.at] a- in ras. D 2. 19. VTIO] corr. ex ccno D. 20.
$ T^S D. 21. novaov x&v\ in ras. D. 25. yivonsvov] -i-
in ras. D. ^uidvov6 D. rfttu.cafff'ftm -act- in ras. D 2.
MA0HMATIKHS STNTAJ3E&S S'. 537
dice t^s wi d[ji(porQag Tag xhfafig dva&G)QiJ6G)g rag
r&v 7tQo6vv6G)v Lxavrjg iv rolg roLOvroig
rr\g xa&' 6/lo^()tav, <bg s(pa[iv, dia-
o[iG)g de,f
iva pri TtaQsArjhvfi'otss Gzpev rov
rOJtOV, JtlQa66ll&a Xal JtQOg XV\V TOLCCVTrjV k'tyoSoV X-
rivag rgoitovg cbg Ivi iidhiGrcc 7tQO%iQOVs.
T&V [iv ovv 7ti6xoTtf6a)v ytaQ^tj^a^v xal
3tL6r]na6La$ U&KS tr^v xs rov XQ&TOV
rfj &Q%ri rov <Uoi> %$6vovxal riiv rov 6%drov f^Aftjroi/rog, ijng & rri <XQ%?J 10
rov rijs /Ltovijg %QOVOV ytVfrat, xccl rr\v rov
iv ra [i6a) %QOVG) rijg
ytVfrt, xal rfjv rov ito&rov
iv r<p ritei rov oAov rr\g fioi/^g %oovovxal rr^v rov <5%Krov avci7t^rjoov^ivov^ r]rig iv 15
rc5 Tf'Aft rov olov rr^g xfafycog %g6vov yivtxui. xal
r&v 7tQo6vv6G)v $ Jt&Uv o> vA.o /
yG)rQag re xal
[i(pari,xG)rQag 7taQiA,ij(panv rag acpooi^o^iBvag vjto re
rov [i6r}npQivov nal r&v rov dia [i6G)v dvarohcov r
xal dv6G)v L6r}[iQivG)v re xal &QLV&V xal %i[ioivG)v 20
rijg rCbv avi\i&v ^fjg diacpooag ^nlv av itokkolg no'k-
kaxig vjtaxov<3&q<5oiivr]g, dvva[it'vr}g d' ovv^ l' rig
j3ovAotro, xal dnb r&v xxi^vcov rov ooi&vrog ?&-vitiv fycpavi&o'd'ai,. r&v plv ovv yivo^dvcov vitb rov
3. dicdrjinpews D, (i eras. 8. cog] om. D. 9. yiyverat D.11. yiyvsxai D. 12. rifr l*Ae/^fl9ff] om. BD. 13. avev]
om. D. 14. rov 16. o/lot;] mg. D 4. 14. oJiov] A 1
,
6'Aov rov BCD 4. 16. rov oAoi;] etiam in textu D. TS 8x-
?)g IH- in ras. A 1. yiy^frat D. 18.
-A- in ras. D 2. 19. r&v] -&v in ras. A 1
. 21.
a A 1. 23. Post oQL^ovrog del. royf ndvrors D. 24.
corr. ex cov C 2. yiyvopivtov D.
538 KAATAIOT HTOAEMAIOT
v ropCbv rov bat&vrog rip plv fioosiov
axovG)[isv aaKrovg, iv\v de vonov ineGyuflQiav^ rCbv d'
dvarofan&tv xal dvnK&v rag {ilv VTCO r^g dgp^g rov
Koiov Kal r&v Xrjk&v yivop&a$ rov OQi^ovrog ropdg
5 Ttdvrore rb faov rsra^r^ptiQLOV aite%ov<jccs r&v V7tb
rov nsGynflQivov yivo[i8VG)V faqtiSQivrjv avccrokrjv xctl
rag d' vnb rrjg KQ^S rov Kaguivovxccl dv6iv, rag d' vitb rrjg ciQ%i]g rov
XSQCO %LHQt,vfiv avatQ^v xccl dvGiv, r&v {iv Kara
10 ravrag diaGraGscov xara xhl{ta dia<p6$G)v artorsAov-
ds ri\g rav TtaoGvsvGscov aitotpa-
,orav J\XQI Kara rwog rj nsrat,v nvcov r&v TCQO-
OQCDV dfixvvrjrai,.
roivvv ri\g xa6ror rov ^cpdianov nobg
15 rbv bgC^ovra 6%e6G)g itko'yi,(5diL&a Kara rov v roig
Tta&roig rijg Gvvrd&og v i
jtoddei'yiivov rgoitov rag
ywopdvag itl rov doi&vrog iv raig dvaroAatg xai
dv6<5iv VTtb rrjg do^g fvbg xd0rov r&v
ILOQI&V djto6rd6i,g (p*xdroa rcbv ditb rov
20 vov yivQ\iiv&v ropCbv xa&' sxatfrov r&v ditb
Boov<5&vovg xfoiidrcov, <p* cbv xal rag
'a, Kal diyadil>aiiv Kara rb fv&fcoorjrov avrl
xavoviov KVK^ovg r\7tol rb avrb Kvroov iv rc5 rov
voovpsvovg Kal 7tQiB%ovrag rd r&v
1. tr\v\ corr. ex x D 2. 2. a^xTov?] -%- in ras. D 2
.
corr. ex r D 2. r&v] post ras. 1 2 litt. D. 3. Post
A&V del. tag ^ vnb r oQifrvtos D. tag] corr. ex rd D 2. 4.
yiyvoptvKS D. ro^ias rov OQI&VTOS B. 6. lGJ]pEQt,vri D,corr. D 2
. 7. rag d' vnb rfjs &QVls T v KctQulvov ftsQivriv
avccro^v nut dvGw~\ D, om. A^C. 9. ccvarokriv] ccv- in
ras. D. 16. anodsdet-y^vov D. 17. ln'i\ A X
D, vno BCD 2.
20. yiyvopivcov D. 22. xca] x- in ras. A 1.
MA0HMATIKHZ STNTASESS g'. 539
dt,a6rtj[iara xal rag 6vo[ia6t'ag' eiteitK TCKQCC-
sv&eiag dvo dia itdvr&v r&v xvxh&v
ycovtag aAA^'Aatg, rr\v [ilv sregccv xal
<bg xoivrjv roprjv rcbv iTtntiS&v rov re OQi&vrog xal
rov farftLSQwov, rr\v d' srsgav nccl OQ&JIV &$ KQivriy 5
jv T&V srtiJtedcsv rov rs OQL&vros xccl rov[lECirjii-
rtaQ6r]neiG)6(xn&cc Kara r&v ngbg rov sxrbg
rtsodrov r^g {isv Tthayiccg y^K^ilg farjusQwiqv
rs avarohriv xccl farjiiSQwfjv dvGiv, ri\g $ OQ&iig CCQK-
rovg re xal iisGrnifiQiav. caGavrcog $ Tta^cc'yQKi^avrsg 10
dia ndvr&v ndfav r&v
xal xara rovrcov v [iv rotg {ira%v iitra
rag VQr^LVKg ua& f'xatirov Klipa r&v
liiG)v ano rov <5rjiiQt,vov dia<5rd&ig 7tl rov OQL^OV- 15
rog G)g rov rfragrrjiiogiov [toiocov ovrog 9, iv $ rotg
rb Ivrbg r&v xvxAcov iteQaGi rotg
WYIV avarohfiv xal
rolg dl TtQog ratg agxroig frsgivriv avaroMjv xal
VKv dl r&v [ira%v d&dxarrjnoQia)v 20
ra%v xd<5rov r&v r06dQK>v diatirri-
ahkag dvo 'yQa^dg 7taQ&ijxa{iv xal xard rov-
rov rag r&v olxsicdv dcodxarr][iOQiG)v sttl rov bat^ovrog
a7to6rd0ig rov i6r^iQivov rijs ovonaGi'ag fxdtirov xara
rov |co xvxAov iti,'yQa(poiivr]g. 7taQ6r][ii,K>6d[id-a dl 25
xal rt$l ri]v p&fiifliviiv yccftfi^v rdg r
5. 8'] 8e B. 10. Post xai del. G in scrib. D. Ss]om. BC. 11. iGJi^givfi^ -Gf]- supra scr. D 2
. xar'] -x in
ras. D. 13. dtccGT^^KGL B, diaGTi]^K6i\ D. 14. Ante T&Vdel. Gr^si D. 17. TOI$] comp. D, ut saepe. 18. ^Gr\^-PQLCCV D, sed -v eras. 19. TKLS] roig C. 22. xara] V.K C.
23. otuEiwv] om. D. 24. xara] TOV nurd C, corr. C 2.
540 KAATAIOT DTOAEMAIOT
rcbv TtaQaMtflcdv xal rd fooiaicc iieyeftr] xui roc r&v
nokcov %dQ[iarcc rrp r&v poofiordrcov bftyfayfo dnb
rov psftovos xal 7tQi,'xovro$ xvxAov rtoirjGcciievot,.
OTCCOS # xai tag avrcbv rwv 7ti6xortJ6G)v TCQOS
5 rbv did [lEGov tpawoiievccs TtQodvsvtisis xxsi[iva$
ycoviccg <p xd&rrjg
rijg TOfttj^ rov re
xai rov di' a[i(porQa)v rcbv ddrj^co^ivcov
QKtpo^vov ^i^i(Srov xvxhov, Kdl ravra$ iit-
10 ekoyrfttiL&K xa&' xd<5rr]v r&v vl daxrvhc) x^ 7tt-
rr}s 6hvjvys, iiti
a rb ccvraQXs r&v xara rb [itiov
yivQ\Ltv<av xal cbg xaQccMtjAcov nobs ai'G&rjGw
ovticbv r&v v rats 7ti6Korri66i, 7toi(pQicbv rov rs
15 diet ii6cov rCbv %G)diG)v xvxhov xal rov Ao|oi> ri\$
j plv avrl
rov did ii6cov r&v ^cpdC&v v&Zcc i]
) l(p' tf$ rb rov ^At'ov xvroov rjrb rijs Gxias vno-
20 Xfa&n rb A, r\dl dvrl rov Ao|oi) xvxAov rrjs 6Atjvr}$
ri P4E, xal rb ply F (?^tov, xcc& ov rb xwroov
xccrd rbv {i6ov %QQVOV yCvwui rf\$ x-
jrb dl z/
9KK& ov ndhw h'tirat, rb
orav jtgoir&s o/l^ btfafaty j no&rcos
1. Y.KI to.(alt.)] corr. ex KCC D 2
. 5. fisaov C. 6. rovr-
comp. B, -v eras. D. ytyvofisWg D. 7. e/^ft&w?] D,wv A^C. 10. r&v\ D
2,rto A X
C, x&i B, t8T D. 8a.v.-
l~ D, SciwvU31 D 2,ut saepius. 11. naQodcav] nago- e corr. D 2
.
13. yiyvo^ivav D. 14. S7ti6ytOTi](>G D. 18. fv&si&v C.
22. TOV] TO D. 23. xatf' ov] -AaQ^ D. 24. KQO)T(DS (pr.)]
T mut. in TIQWT D, corr. D 2.
MAGHMATIKHS 2TNTAEE&S '. 541
)TOVTBGTW orav h'tio&sv (pcc7tTr]Tcci, TOV
Gxiag xvxkov, TO $ E, xct&' ov yivtxui to xw-
TQOV CiVTijS^ OTCiV 7tQG)TG)g
aQ%7]Tai, sxhsiiteiv rjTO
6%ttTOV KVaJthrjQOVG&CCl,
TJrot 6 ijfaos % xalf)6-
)TOVTSGTW OTCCV f|-
Xttl
KalAE. 10
OTI lilv ovv CCL ILZV vnb BAP xal ATETOV (JLB60V XQQVOV ItSQlfyovGai, TCOV xkefyG)V
TCQOS cd'6d"rj6iv, rjd' VTTO BAE 3tQi%si
iiti TS TOV TCQ&TOV fxAewrovrog xocl TOV
dvcc7tA,r]Qov[ivov , fjd' vnb BAd rr\v iiti TS 15
TOV 6%KTOV exfofaoVTOS XCtl TOV 7COG)TOV ava,ltkl]QOV-
(paveQov. dfjlov d' avTO&ev, OTI, xal i\ pkv AET&S X T&V XVTQO)V K[l(pOTQG)V TG)V XVX&G)V
, fj$ A4 tr\V V7tQO%rjV aVT&V.
VTfodfi'y^CiTOS VXV X^l^l<S^ XCC&' 20
7J1/ V TO) fteVfi) XQOVG) TO ^L^V Tf}S dlK^LBTQOV Tijg
xal tdTO TO A XWTQOV TOV
&6T ity ply AE TCKVTOTE dia TO [i6ov vno-
TO rijg Gfkrjvrjg a7t60Tr][ia 6vvccy6d'ai, {LOQI&V
$ AT foCnovtiav avTijs TCO ^fifost, Tij$ 25
dia[iTQOv T&V KVTCQV Tg ji.titd ovv, O'LK>V
6. r/]om. CD. 8. &nr(ov\tcovrca A 1
,corr. A 4
;anrrcci D,
corr. D 2. 11. Post on eras. TO D. 13. slciv] comp. B,
elti mut. in stci D. 14. yiyvopevriv D. 15. rj6' 16. ava-
nlj]QOv^vov\ om. D. 15. RAA\ BA- e corr. A 1. 19. rrjVj
om. A 1. 24. TO] supra scr. D 9
. (LOQIOJV] (JLOIQ D. 25. TW]corr. ex vvv TO D 2
.
542 KAATAIOT nTOAEMAIOT
v\EA vttOTivov6a 2,ft x, TOIOVTCOV
xal f) AT Kara TO xxi[ivov rijg
&og 7g ji? xal oicov i<5rlv aga fjAE
TOLOVTCOV xali\ fisv AT h'tiTai, %a v~a, v\
d' iit amijg5 TtSQKpeQEia TOIOVTCOV |/3 ft otcov fatlv 6 Ttsgl rb ATE
ogd'O'ycaviov xvxAos r|. &6rs xali\
vitb AET^ rovr-
0ri,v<fi_vjtb
BAE [EucLJI^ 29], oi&v piv tfaiv cc
ogfi-al T|, rotovrov stirlv |/3 ft GLOW d' CCL d ogfrcd
10 itakiv xccl r&v GsArjviax&v sxfafyscov tvexev
TO A TO Trjg Gmag XWTQOV, &6T^ 7td TO [i6ov d
Tr}g as^vrig ajcd^r^^a, T&V avT&v ccd 6vv-
TYJV fjiv AE sv&elav 1, TJJV dl A4X^ |Lt,
Xal xA,MtTG) fj 62,1JVY} XCCTK TYJV T&V Irj
15 Acov Ttdgodov^ &6TS TK> YULIGEI Tr^g dia^Tgov jtdA.iv
EkaTTQva fivcu rv\v AT T^g AzJ, xal xaTafafasG&ai
T&V avT&v 1, o.
7tL OVV, OiCOV <5TIVYjAE V7tOTWOV<5a, ^5C, TOi-
OVTOV xal ^ pv AT yivtrui x o, y d' in avTijg
20 JtQl,<p(>ia TOLOVTCOV 1$ tft OiCOV fttlv 6 7tQi TO ATETOiycovov ogd-oycbviov xvxfog r|, fl'rj
av xal fjvnb
AET ycovia, TOVT&TIV ^ ^^6 BAE, OLCOV pvai
ft OQ&al T$) TOLOVTOV L& t/3, oicov d' aC d ogftal
1. 1^] x, %- in ras. B 3. 3. Igl corr. ex g D.
EA D. 6. y^ET] corr. ex ,4E ET D^; deinde add. ycoi/ta D.
7. B^E] corr. ex_^BE D 4
,BE^ B.
^J3] A 1
,Wo BCD.
8. ToiovTtoV 9. a] mg. D 2. 8. #'] 5f I)
2. 9. TOLOVTOOV
Jia a] etiam in textu D (ooa). 11. V.KVXQQV ,
in ras. B 3. ware -f add. D 2
.] -f add. D 2
. 12. anoGTri^K, ra>v~\ corr. ex_
D 2. a-urwv] supra scr. C 2
. 13. Ante del. at A 4.
14. ^xAftTrf'rco] supra -ft- add. t D 2. 15. Ttuqodm D, corr. D 2
.
ro5] TO C. 16. xca 17. TWV] in ras. D. 18! AE} EA D.
19. ivfTcci D.
MA0HMATIKHS STNTAEE&S S'. 543
TOLOVTOV ft AS. aGavTcog fo', sxeidr} xat, oiav etirlv
% Ad VTtoTivov6a QX, TOLOVTov xal % [ilv AT yi-
vsrai,jits, ^ ^' >jr> avrijs JtSQitpsysia TOLOVTOV pd ft,
oicov 6rlv 6 Jtol to AT4 OQ&oycoviov xvxkog T|, /'^
cfv xa^ ^ vTtb A/iT yewfa, tovr&nvfj
i)itb BA4, 5
oicsv isV i6w at
avrov di\ tQoitov xal titl t&v aMcov
rag jr^Atxdr^rag r&v ttccGtiovcov
jtl rijg piug r^^idrcov ov0r]s 9, fiff&v xccl 10
TO rov b^i^ovrog reragrrmo.Qiov vn6xsi,tai,, drd^cc^isv
xavoviov Jtl Gxfyovg [isv x/3, Gskidia ds d, (bv TO [iev
TOVS ebqitfxoii&tovs avrr^g rijs Kara
sxksfys&g, TO ds dsvTsgov Tag iv Tatg 15
sxhsfystii, yLvo^evag y&viag k'v TS TGJ TOV
jtQG)Tov exfafaovTog XQOV& xal iv TGJ TOV 6%aTov
,TO $ TQLTOV Tag iv Tatg
&viag xaTa T TOV TOV
XQOVOV xal TOV TOV 6%aTov dvayt^^ov- 20
,TO ds TTaQTOv Tag yivopwag y&vtag iv Talg
6hr]viaxatg itaKiv extefyedw xaTa T TOV TOV
xA.i7tovTog XQOVOV xal TOV TOV TCQWTOV
[ivov. xai i<5iv at diayoacpai TOV TS xavoviov xal
T&V xvxhcov TOiavTau' 25
1. Ss] S' D. 8. xai snL] add. D 2. 9. Za/*j3avovTg] A 1
,
Hccfiovtss BCD. 10. yaviccs] corr. ex ycovt D 2. $n~\ el D,
mg. 10 cog inl rfjs fti^s D 2. offcav] corr. ex oV D 2
. 11. TOV]TO- in ras. A 1
. 12. ds<?]
corr. ex j A 1. wv] corr. ex co D 2
.
13. 7iQa>Tov~\ a B. 15. dtvrsQOv] & B. 16. yiyvopsvccs D.18. TQITOV] f B. TO.?'] supra scr. D 2
. 20. rov] om. B.
21. TETKQTOV]^ B. ytyvoufWg D. 24. at] at' Tf BC.
544
if} '.
KAATAIOT HTOAEMAIOT
TG)V TtQog rag
cc'
MA0HMATIKH2 2TNTAEE&S '. 545
iy '. 4iaXQl6ig JtQ06VV6COV.
"E%ovre<s ovv 7toodt,axXQi,[ivovg, bv vnedefeapev
rooitov, rovg %o6vovg xd0rrjg r&v ^XXL^LVCOV iiti-
Grjiiao'icdv xal anb r&v %Q6v&v dyAovdrt, ra xar* avrovg
avar&Aovra xal dvvovra ^,orj rov dia {leGov cato re 5
Tijs xarayQcc<pii$ rag XCCTK rbv b^ovra &<3t,s avrwv,
oTctv pv xar avrbv rbv di& [ifa&v y rb xwryov rijg
^roi rb cpawopwov &$ itl r&v rjhaxav tx-
irb axQt,p$ &s till rav 6A,rjvi,ccxG)v, rr\v pfv
xccra rb nycbrov fxfatxov rov qMov 7tQ66vv6w xal 10
h'n r^v xara rb k'6%arov Ixtefaov rs xal avcutArjQov-
[ivov rrjs 6^v^g f^o^ifv anb rijs avrov rov rors
dvvovros xara rbv bgitflvra O-g^tog, r^v $ xara rb
6%arov avan^rigov^vov rov ^Mov xal In r^v xara
rb itQ&rov Zxhetitov re xal avaji^oov^vov rijs GeArf- 15
vrjs an' avrov rov dvarMovro$* orav $ ^ xara rbv
dia ii6G)v y rb xvroov rijs 6^tjv^g^ A,af$6vrg x rov
xavoviov rovg olxetovg rrj 7to66r^n r&v daxrvAcov
Ttaoaxfipwovg r&v ycovi&v aoi&iiovg 7tQo6xj3aAoviLv
xal avrovg anb r&v xoiv&v rop&v rov re bg^ovrog 20
xal rov dia jig'tfaw, av [iv f$OQi,6rQov % avrov rb
xevroov rijg 6e^vrig^ enl plv rov xo&rov IxheiTtovrog
rov iiUov xal rov e6%drov exheiitovros rijg fcAtjvrjg
&g 3tgbg agxrovg rijg dvnxijg roiiijg^ enl de rov 6%d-
1. ty'] ri B, om. A 1 CD. 3. TO %QOVG D, rs %QOVG D 8.
5. jtifff D. 6. frte D, <s
ss D 2. 7. y] D, om. A a BC. 9.
qiu, D. 11. inhtiitov ri\ corr. ex enteiitov D 2. 15. rfjs
Aijvr)s~] -TIS osl- et -v- in ras. A 1. 16. avarttovros D, corr. D 2
.
17. f] corr. ex j\v D. 19. ngoG^KUov^v D, corr. D 2.
Ptolemaeus, ed. Heiberg. 35
546 KAATA. IITOAEM. MA0HMATIKH2 TNTAgES> g'.
rov dvan^r]Qov(ivov rov ^Atov xal rov ngcorov dva-
7tA.r]QOV[ivov rijg 6eA.tjvr]s &S rtQog aoxrovg rijg dva-
roAlXijg) Xal TtuklV 7ll [lV rOV TtQ&rOV xA.LJtOVrog
rijg ^s^tjvrjs cag ngbs5 sal ds rov 6%arov
xgbg ii6qiiflQiccv rijg dvrwijg' KV d vori&rsQov r
rov dia iifacov rb xwrgov rijg 0^t]vrjg^ itl plv rov
fafaovrog rov i\Uov xal rov 6%arov %-
rijg Gfhrivrjg &g n$bg ps^\$$tav rijg dvri-
10 xijg ro^iijg^ 7tl d rov 0%drov dvartAr]Qov[ivov rov
j]Mov xal rov Ttgcorov avait^Qov^vov rijg
&g itobg [i6rjii(lQiav rijg avaro^Lxijg^ xccl
\i\v rov Tto&rov zxheiitovrog rijg 6A.tjvrjg cog Jtobg
aoxrovg rijg avarofaxijg ro^iijg^ rtl d rov 0%drov15 avccjtA.r]QoviJivov rijg 6hrivr]g &g xobg agxrovg rijg
dvrwijg. xal rb GwiGrKpsvov x rijg roiavrrjg dioo&G)-
6(og pfyog rov QQi&vrog s^o^fv^ cp 7toiij6rca rfjv
itQoGvfvtiw, ag k'yapm, bho<5%Q6rQ< ov ra $%6[iVKr&v cpcorcov iiQrj rag xocbrag xctl rag 6%drag r&v
20 exteofv xal rcbv d
1. rov r}Uov &vccn1H]Qov[i8vov~] supra scr. C 2. 2. rfys (alt.)]
supra scr. D 2. 4. Ante rfjs (alt.) del. rf)$ dvTiKfjg D 2
. 6.
vorimreQOv] BD 2, vonoregov A 1
C, vorsidrsQov D. 7. dta (is-
c&v] -ice ft- in ras. D. 8. xca 9. G^r\vj]g] mg. D 2. 16.
Jx] corr. ex t-' D 2. 17. w] om. D, 6 D 2
. 18. bkoGxsQSGtsQOv]ult. o in ras. A 1
. In fine: Klccvdiov Ilro^B^aiOv jwa'ibj^cmxTfc
cvvrd^ecos ? B, KKcrvdiov Uro^f^Kiov fta^Tjaartxcov ? C, rAogrov gxrov D.
PA
4404A2
1898v.l
pars 1
^tolemaeus, ClaudiusClaudii Ptolemaei Opera
quae exstant omnia
flfe
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