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Giáo trình vẽ kĩ thuật Giáo trình vẽ kĩ thuật Biên tập bởi: Biên tập bởi: Đại học sư phạm Hà Nội

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#?[E JHaD> L Ao J>KJ #?[E JHaD> L Ao J>KJB?`D JF 8?: B?`D JF 8?:l}? >9 I| F>}C $Z )?#?[E JHaD> L Ao J>KJ #?[E JHaD> L Ao J>KJB?`D JF 8?: B?`D JF 8?:l}? >9 I| F>}C $Z )?C[9 J[9 =?~: C[9 J[9 =?~:l}? >9 I| F>}C $Z )?+>?`D 8~D JH9 JKOD:>JJF://LE;H.;:K.LD/9/;76:5178(C 'C (C 'C1. /?`K 9>KD A> =?O JHED= 8~D L Ao J>KJ............................................................................... 22. /?`K 9>KD A>KD= 8~D L, A>KD= J`D JHED= 8~D L Ao J>KJ ............................................... 33. /?`K 9>KD L J B JHED= 8~D L Ao J>KJ .................................................................................. 54. /?`K 9>KD L m|D= D_J JHED= 8~D L Ao J>KJ...................................................................... 65. /?`K 9>KD 9> L?J LZ I JHED= 8~D L Ao J>KJ..................................................................... 96. C[9 A>[? D?C L =>? Ab9> J>|9................................................................................................ 127. D= m|D= J>D= IED= IED=..................................................................................................... 188. D= m|D= J>D= LKeD= =d9 .................................................................................................... 199. C>?7 mK CJ m|D= J>D= LZ CJ m|D= JHcD..................................................................... 2010. 1 m :9 LZ m 9eD..................................................................................................................... 2411. 1 D? J?F...................................................................................................................................... 2712. 1 9[9 m|D= 9ED= >aD> >9..................................................................................................... 2913. $aD> 9>?K J>D= =d9 ................................................................................................................. 4114. $aD> 9>?K JH9 mE ...................................................................................................................... 6615. $aD> 9>?K F>? 9~D>................................................................................................................. 9716. . >aD> J>ZD> H;D.....................................................................................................................10517. C[9 A>[? D?C 9>KD= L C? =>_F 8D= H;D......................................................................10618. C[9 OK J 97 H;D.....................................................................................................................10919. B?K :?D 9[9 C? =>_F 8D= H;D..........................................................................................11120. B?K :?D GKO |9 H;D..............................................................................................................12021. (J I BE}? H;D J>|D= =F.....................................................................................................12522. (J I LD m JHED= 9> J}E LZ A?C JH7 H;D.....................................................................13023. C[9 9>? J?J =>_F JHED= C? =>_F H;D...................................................................................13224. B?K :?D mzD =?~D LZ L GK? |9 9[9 9>? J?J JHED= C? =>_F 8D= H;D....................14725. #>_F 8D= 9>J ..........................................................................................................................15026. #>_F 8D= m?D> J[D ..................................................................................................................15127. #>_F 8D= >ZD...........................................................................................................................15528. #>_F 8D= J>;D..........................................................................................................................16129. #>_F 8D= J>;D >E7..................................................................................................................17030. /Z? B?K J>7C A>~E L Ao J>KJ ...............................................................................................173/>7C =?7 mdD= =dF ..........................................................................................................................1761/1801. /?`K 9>KD A> =? 1. /?`K 9>KD A> =?O JHED= 8~D L Ao O JHED= 8~D L AoJ>KJ J>KJ/?`K 9>KD A> =? /?`K 9>KD A> =?O JHED= 8~D L Ao J>KJ O JHED= 8~D L Ao J>KJ- />;E /C1) 2.74, 9[9 A> =?O 9>bD> m|9 I :D= =C 9d:&b >?K A> =?O A0 A1 A2 A3 A4&b >?K A> 8~D L 44 24 22 12 11&b9> J>|9 (CC) 1189 N 841 594 N 841 594 N 420 297N 420 297 N 210- Cz I m F>\D 9>?7 9[9 A> =?O BZ A> A0 (9d :?D Jb9> 1C2 , Ab9> J>|9 1189 N 841CC).C[9> F>\D 9>?7 J> >?D JH`D >?D> L.- )=EZ? D>D= A> =?O 9>bD>, JHED= JH|D= m9 8?J 9>E F>_F :hD= =?O F> BZ D>D=A> =?O m|9 9>?7 J A> =?O 9>bD>.- &b9> J>|9 9}D> 97 A> F> BZ 8? I 97 Ab9> J>|9 9}D> 97 A> A4.2/1802. /?`K 9>KD A>KD= 8~D L, A>KD= J`D 2. /?`K 9>KD A>KD= 8~D L, A>KD= J`DJHED= 8~D L Ao J>KJ JHED= 8~D L Ao J>KJ/?`K 9>KD A>KD= 8~D L, A>KD= J`D JHED= 8~D L Ao J>KJ /?`K 9>KD A>KD= 8~D L, A>KD= J`D JHED= 8~D L Ao J>KJ- )? :KD= LZ Ab9> J>|9 97 A>KD= 8~D L LZ A>KD= J`D m|9 GKO mD> JHED= /C1)3821- 83. Cd 2 BE}? A>KD= 8~D L LZ A>KD= J`D: BE}? :hD= JHED= D>Z C[O, Nb D=>?F LZBE}? :hD= JHED= D>Z JH|D=. |? m\O JHaD> 8ZO BE}? :hD= JHED= D>Z JH|D=.&>KD= 8~D L &>KD= 8~D L- &>KD= 8~D L m|9 L 8D= D_J B?D mC, A 9[9> 9[9 C_F A> =?O 5CC ($aD> 1.2).&>? 9D mdD= J>ZD> JF, 9}D> JH[? 97 A>KD= 8~D L m|9 A 9[9> C_F JH[? 97 A> =?OCJ A>E~D= 8D= 25CC ($aD>1.3).&>KD= J`D &>KD= J`D- &>KD= J`D m|9 mJ=d9 F>b7 :|?, 8`D F>~? 9d J> J>;E 9}D> :Z? >7O 9}D> D=D 978~D L. ($aD> 1.2, 1.3). &b9> J>|9 9 J> 97 A>KD= J`D D>| I7K: ($aD> 1.4)3/180W1: lK m 8Z? JF >E9 J`D 9>? J?J W2: 1J B?K 97 9>? J?JW3: / B W4: &b >?K 8~D LW5: $ LZ J`D D=|? L W6: )=ZO LW7: C> Ab 97 D=|? A?C JH7 W8: )=ZO A?C JH7W9: /`D JH|D=, A>E7, BF4/1803. /?`K 9>KD L J B JHED= 8~D L Ao 3. /?`K 9>KD L J B JHED= 8~D L AoJ>KJ J>KJ/?`K 9>KD L J B JHED= 8~D L Ao J>KJ /?`K 9>KD L J B JHED= 8~D L Ao J>KJ/hO J>;E Ab9> J>|9 LZ m F>9 J}F 97 LJ J> CZ J7 9>D J B 9>E 8~D L. / B 8~D LBZ J I =?7 Ab9> J>|9 mE m|9 JH`D >aD> L L? Ab9> J>|9 J>J J|zD= D= mE m|9 JH`DLJ J>./>;E /C1) 3-74 9d 9[9 BE}? J B I7K:/ B J>K D> 1: 2 ; 1: 2,5 ; 1: 4 ; 1: 5 ; 1:10 ; 1:15 ; 1: 20 ..../ B D=KO`D >aD> 1:1/ B F>dD= JE 2: 1 ; 2,5: 1 ; 4: 1 ; 5: 1 ; 10:1 ; 15:1 ; 20: 1 ....- &b >?K J B JHED= 8~D L: 1:1 ; 2:1 ....5/1804. /?`K 9>KD L m| 4. /?`K 9>KD L m|D= D_J JHED= 8~D D= D_J JHED= 8~DL Ao J>KJ L Ao J>KJ/?`K 9>KD L m| /?`K 9>KD L m|D= D_J JHED= 8~D L Ao J>KJ D= D_J JHED= 8~D L Ao J>KJ/%U0 C$0 /%U0 C$0) 1%/ )A( 8 - 1993 ) 1%/ )A( 8 - 1993- C[9 BE}? D_J L J>|D= m|9 :hD= JH`D 8~D L 9z A>b LZ D= :D= 97 9>iD= (B~D=1.1) m|9 GKO mD> J>;E /C1) 8 -1993 C>?K HD= D_J L m|9 Ab >?K BZ 8 (CC) LZ m|99>D J>;E :]O GKO mD> I7K: 0,18; 0,25; 0,35; 0,5; 0,7; 1; 1,4 ....- /H`D 9[9 8~D L A> A4 >E9 A3 D`D 9>D 8 = 0,5CC6/180- C[9 D_J JH`D 9hD= CJ 8~D L I7K A>? Je mCF>~? m}J m|9 I mD= mK L 9>?K HD=,m m;D LZ L 9[9> L (9>?K :Z? D_J =}9>, A>E~D= 9[9> =?7 9[9 =}9> ..)- &>? >7? >7O D>?K D_J L JHhD= D>7K J>a L J>;E J> J |K J?`D I7K:v )_J B?D mC (l|D= 87E J>O, 9}D> J>O)v )_J mJ (l|D= 87E A>KJ, 9}D> A>KJ)v )_J 9>C =}9> C~D> (#?? >}D CJ F>D= 9J 9d >7? D_J mC>7? mK)v )_J 9>C =}9> C~D> (l|D= J\C, JH9 m? ND=)v )_J B?D C~D> (l|D= Ab9> J>|9)- /HED= C? JH|D= >F, J\C m|D= JHcD F>~? m|9 N[9 mD> 8D= =?7E m?C 97 >7?mE}D =}9> 97 D_J 9>C=}9>; 9[9 D_J mJ, D_J 9>C=}9> F>~? =?7E D>7K 8D= 9[9 =}9>.7/180|? m\O BZ Lb : C?D> >7 L D= :D= 97 9[9 D_J L.&b >?K LJ B?Kv (J I Ab >?K LJ B?K JH`D CJ 9J J>|D= :hD=8~D L 9z A>b D>| I7K:8/1805. /?`K 9>KD 9> L?J LZ I JHED= 8~D 5. /?`K 9>KD 9> L?J LZ I JHED= 8~DL Ao J>KJ L Ao J>KJ/?`K 9>KD 9> L?J LZ I JHED= 8~D L Ao J>KJ /?`K 9>KD 9> L?J LZ I JHED= 8~D L Ao J>KJ/%U0 C$0 /%U0 C$0) 1%/ )A( 6 - 85 ) 1%/ )A( 6 - 85- &> 9> BZ =?[ JH m|9 N[9 mD> 8D= 9>?K 97E 9> ?D >E7 JbD> J>;E CC. />|D= I:D= 9[9 BE}? A> 9> I7K: 2,5; 3,5; 5; 7; 10; 14; 20....- C[9 9>, 9> I m|9 L?J J>;E /C1) 6- 85 L? >7? A?K 9>: &?K 9> B mD= LZ A?K9> B D=>?`D=. |? m\O N?D =?? J>?K A?K 9> B D=>?`D=9/180- C[9 J>eD= I 97 9> L?J A?K B D=>?`D= D>| I7K:10/1801.27: #>? m 9eD11/1806. C[9 A>[? D?C L =>? Ab9> J>|9 6. C[9 A>[? D?C L =>? Ab9> J>|9CS CSC &$S% )%( 1 #$% &VC$ /${ C &$S% )%( 1 #$% &VC$ /${C C,KO J9 L =>? Ab9> J>|9 LZ 9[9 I7? B9> =?? >}D m|9 GKO mD> JHED= /C1) 5705 t1993. ,KO J9 =>? Ab9> J>|9 DZO F>h >F L? /?`K 9>KD GK9 J %.* 129 - 1985.,KO mD> 9>KD= ,KO mD> 9>KD=- lzD L =>? Ab9> J>|9 :Z? BZ CC. &>eD= =>? J> D=KO`D DZO I7K 9> I Ab9> J>|9.- . B|D= 9[9 Ab9> J>|9 m|9 =>? L7 m m N[9 mD> >aD> :[D= LZ m BD 97 LJ J>.(? Ab9> J>|9 9> =>? CJ BDL JHb : m9 D>J.- &b9> J>|9 m|9 =>? BZ I mE J>9 97 LJ J>, Dd A>eD= F> J>K9 LZE J B 97 8~D L.- hD= m, F>iJ, =?\O BZC mzD L mE =d9 LZ I7? B9> =?? >}D 97 Dd.- &b9> J>|9 A>eD= JH9 J?F :hD= JHED= GK[ JHaD> 9> J}E CZ 9> JH =?iF 9>E L?9 m98~D L m|9 =? BZ Ab9> J>|9 J>7C A>~E. &b9> J>|9 J>7C A>~E m|9 =>? JHED= D=E9mzD.C[9 OK J 97 Ab9> J>|9 C[9 OK J 97 Ab9> J>|9(? Ab9> J>|9 J>|D= 87E =C 9[9 OK J I7K:$aD> 1.9l| l|D= =?dD= D= =?dD=- l|D= =?dD= m|9 L 8D= D_J B?D C~D>>7? mK CiJ LZ LKeD= =d9 L? mE}D 9D =>?Ab9> J>|9. l|D= =?dD= m|9 L A_E :Z? L|J GK[ m|D= Ab9> J>|9 CJ mE}D 8D= 2mD 3 BD 9>?K HD= 97 D_J 9z 8~D.- /H|D= >F m9 8?J 9>E F>_F L N?`D.12/180$aD> 1.10l| l|D= Ab9> J>|9 D= Ab9> J>|9- l|D= Ab9> J>|9 m|9 L 8D= D_J B?D C~D>, 8`D JHED= >7? m|D= =?dD= LZ IED=IED= L? mE}D 9D =>? Ab9> J>|9. $7? mK CiJ 97 m|D= Ab9> J>|9 m|9 =?? >}D 8?2 Cp? J`D./H|D= >F A>eD= m 9> 9d J> L m|D= Ab9> J>|9 LZ Cp? J`D H7 D=EZ?m|D= =?dD= ($aD> 1.11).(p? J`D (p? J`D- (p? J`D m|9 L>7? mK CiJ 97 m|D= Ab9> J>|9 L? >aD> :[D= LZ Ab9> J>|9D>| JH`D (>aD> 1.12). /H|D= >F m9 8?J 9>E F>_F J>7O >7? Cp? J`D m? D>7K 8D= CJ9>C mC ($aD> 1.13).13/180$aD> 1.12 LZ >aD> 1.13C> I Ab9> J>|9 C> I Ab9> J>|9- hD= A> 9> 2,5 >E9 3,5 JKs J>;E A> =?O m =>? 9> I Ab9> J>|9. C> I Ab9>J>|9 m|9 mJ D>| I7K:+=?7 LZ JH`D m|D= Ab9> J>|9 I7E 9>E 9>iD= A>eD= 8 9J >E9 8 D=kD 9[9> 8? 8JAa CJ m|D= DZE.+ l JH[D> 9[9 9> I IF NF J>;E >ZD= :9, D`D mJ 9[9 9> I IE B; D>7K L >7? F>b797 m|D= Ab9> J>|9, A>? md m|D= Ab9> J>|9 m|9 L HiJ D=D.+ $|D= 9> I Ab9> J>|9 :Z? J>;E >|D= D=>?`D= 97 m|D= Ab9> J>|9 J>;E GKO mD>N;C>aD> 1.14.+ $|D= 9> I Ab9> J>|9 =d9 m|9 =>? D>| JH`D >aD> 2.15.+ &>? =>? Ab9> J>|9 9KD= JHcD (y180 m) F>~? J>`C Ab >?K - JH|9 9> I Ab9> J>|9.+ &>? =>? Ab9> J>|9 m|D= JHcD F>~? =>? Ab >?K (JH|9 9> I Ab9> J>|9).14/180$aD> 1.14 LZ >?D> 1.15(J I 9[9> =>? Ab9> J>|9 J>| (J I 9[9> =>? Ab9> J>|9 J>|D= =F JH`D 8~D L 9z A>b D= =F JH`D 8~D L 9z A>b#>? Ab9> J>|9 J>D= #>? Ab9> J>|9 J>D=$aD> 1.16#>? Ab9> J>|9 m| #>? Ab9> J>|9 m|D= JHcD D= JHcD$aD> 1.1715/180#>? Ab9> J>|9 8[D AbD> 9KD= JHcD LZ Ab9> J>|9 9K #>? Ab9> J>|9 8[D AbD> 9KD= JHcD LZ Ab9> J>|9 9K$?D> 1.18 LZ >?D> 1.19#>? Ab9> J>|9 >aD> LKeD= LZ C_F L[J #>? Ab9> J>|9 >aD> LKeD= LZ C_F L[J$?D> 1.20 LZ 1.21)>?K F>D J =?D= D>7K LZ F>\D 8 mK m|9 F>_F =>? D=D =D D>| )>?K F>D J =?D= D>7K LZ F>\D 8 mK m|9 F>_F =>? D=D =D D>|JH`D JH`D$aD> 1.2216/180#>? Ab9> J>|9 :\ #>? Ab9> J>|9 :\O 9KD= LZ 9KD= O 9KD= LZ 9KD=$aD> 1.23 LZ >aD> 1.24#>? Ab9> J>|9 =d9 , m :9 #>? Ab9> J>|9 =d9 , m :9 LZ m 9eD LZ m 9eD$aD> 1.25: #>? Ab9> J>|9 =d9 LZ 1.26: #>? m =d9$aD>17/1807. D= m| 7. D= m|D= J>D= IED= IED= D= J>D= IED= IED=D= m| D= m|D= J>D= IED= IED= D= J>D= IED= IED=C>E CJ m|D= J>D= 7 LZ CJ m?CC D=EZ? m|D= J>D= 7. $]O L}9> GK7 C CJ m|D=J>D= 8 IED= IED= L? m|D= J>D= 7D= 8D= 9EC F7 D= 8D= 9EC F7v /H`D m|D= J >D= 7 BO CJ m?C B 8J Aa BZC J\C, L 9KD= JHcD 8[D AbD> BC,9KD= JHcD DZO 9J m|D= J>D= 7 J}? m?C A.v 1 9KD= JHcD J\C C, 8[D AbD> CB LZ 9KD= JHcD J\C B 8[D AbD> CA. $7? 9KD= JHcDDZO 9J D>7K J}? .v )? C L? , J7 m|9 m|D= J>D= 8 LKeD= =d9 L? m|D= J>D= 7.$]O GK7D I[J mE}D L?:;E 9B?F L 9[9> L 8D= 9ECF7D= 8D= J>|9 LZ ` A D= 8D= J>|9 LZ ` A;;v lJ CJ 9}D> 97 ` A; JHhD= L? m|D= J>D= m] 9>E LZ [F I[J CJ 9}D> 97J>|9 LZE 9}D> A>[9 97 ` A;.v /H|J ` A; :9 J>;E C_F J>|9 J? m?C C, A m|D= J>D= J>;E 9}D> 97 ` A;m? GK7 C J7 m|9 m|D= J>D= 8 9D :D=.,K7D I[J 9[9> :D= GK7 mE}D L?:;E 9B?F I7K18/1808. D= m| 8. D= m|D= J>D= LKeD= =d9 D= J>D= LKeD= =d9D= m| D= m|D= J>D= LKeD= =d9 D= J>D= LKeD= =d9C>E m|D= J>D= 7 LZ CJ m?CC D=EZ? 7. $]O L GK7 C CJ m|D= J>D= LKeD= =d9 L?m|D= J>D= 7.D= 8D= 9EC F7 D= 8D= 9EC F7v 'O m?C C BZC J\C, L 9KD= JHcD 9d 8[D AbD> BD >zD A>E~D= 9[9> J m?C CJ? m|D= J>D= 7, 9KD= JHcD DZO 9J 7 J}? A LZ B.v 'D B|J BO A LZ B BZC J\C, L 9KD= JHcD 9d 8[D AbD> BD >zD AB/2. $7? 9KD=DZO 9J D>7K J}? .v )? C L?J7 m|9 m|D= J>D= LKeD= =d9 L? m|D= J>D= 8,K7D I[J mE}D L?:;E:D= 8D= J>|9 LZ ` A D= 8D= J>|9 LZ ` A;;v lJ CJ 9}D> =d9 LKeD= 97 ` A; JHhD= L? m|D= J>D= 7 m] 9>E LZ [F I[J C_FJ>|9 L? 9}D> >KOD 97 ` A;.v /H|J ` A; mD L JHb I7E 9>E 9}D> =d9 LKeD= A?7 97 ` A; m? GK7 m?C C.v 1 GK7 C m|D= J>D= LKeD= =d9 L? m|D= J>D= 7l >?K Hf J>`C L 9[9> :D= 8D= J>|9 LZ `A; >]O GK7D I[J mE}D L?:;E 9B?F I7K19/1809. C>?7 mK CJ m| 9. C>?7 mK CJ m|D= J>D= LZ CJ D= J>D= LZ CJm| m|D= JHcD D= JHcDC>?7 mK CJ m| C>?7 mK CJ m|D= J>D= LZ CJ m| D= J>D= LZ CJ m|D= JHcD D= JHcDC>?7 mK CJ mE}D J>D= C>?7 mK CJ mE}D J>D=$]O m9 Bj J>KOJ LZ J>;E :f? mE}D L?:;E m >9 9[9> 9>?7 mK CJ mE}D J>D=: #?~ IJ7 F>~? 9>?7 mE}D J>D= AB H7 BZC 5 F>D 8D= D>7K, J7 BZC D>| I7Kv ,K7 m?C A ($E9 B) A m|D= AN 8J As (=d9 BAN BZ =d9 D>D).v & J A mJ B`D AN DkC mE}D J>D= 8D= D>7K 8? 9[9 m?C 9>?7 1, 2, 3, 4,5.v hD= J>|9 LZ ` A; D? 5 L? B, I7K md JH|J ` A; JH`D J>|9 A 9[9 m|D= 44',33', 2 2', 1 1'.C[9 m?C 1', 2', 3',4',5' BZ 9[9 m?C 9>?7 9D JaCC>?7 mK CJ m| C>?7 mK CJ m|D= JHcD D= JHcD.7K m\O BZ CJ I 9[9> 9>?7 LcD= JHcD H7 BZC D>?K F>D >]O GK7D I[J mE}D L?:;E LZm9 9[9 9[9> 9D D> I7K:A. C>?7 CJ LcD= JHcD H7 BZC 4 F>D, 3 F>D, 6 F>D, 12 F>D 8D= D>7K$]O GK7D I[J mE}D L?:;E I7K m 8?J L? 9[9 9>?7 m|D= JHcD BZC 4 F>D 8D= D>7K LZ9[9 >aD> L L 9[9 9>?7 m|D= JHcD BZC 3, 6, 12 F>D 8D= D>7K I7K:9>?7 m|D= JHcD J>ZD> 4 F>D,K7D I[J >aD> L :|? m\O LZ J HiJ H7 9[9> 9>?7 LcD= JHcD H7 BZC3 F>D, 6 F>D LZ 12F>D.20/18021/180B. C>?7 LcD= JHcD H7 BZC 5 F>D 8D= D>7Kv ,K7 * L AB LZ C LKeD= =d9 L? D>7K.v /aC JHKD= m?C ( 97 *A.v /\C (, 8[D AbD> (C, L 9KD= JHcD 9J *B J}? &.v /\C C, 8[D AbD> C& GK7O 9KD= JHcD 9J LcD= JHcD J}? 1 LZ 2.v $7? m?C 3,4 JaC m|9 8D= 9[9> =? D=KO`D 8[D AbD> C& LZ BO J\C BZ 9[9m?C 1 LZ2$]O GK7D I[J mE}D L?:;E I7K m 8?J J>`C L 9[9> 9>?7C>?7 m|D= JHcD J>ZD> 5 F>DC. C>?7 LcD= JHcD H7 BZC 7, 9, 11, 13 F>D 8D= D>7K22/180#?~ I F>~? 9>?7 LcD= JHcD H7 BZC 7 F>D 8D= D>7K J7 BZC D>| I7K:(GK7D I[J mE}DL?:;E I7K)v 1 AB LKeD= =d9 L? Cv C>?7 m|D= AbD> C H7 BZC 7 F>D 8D= D>7K 8D= 9[9 m?C 1', 2', 3', 4' ...v /\C , 8[D AbD> C L 9KD= JHcD 9J AB A_E :Z? J}? ! LZ ".v / ! LZ " A 9[9 J?7 J? 9[9 m?C 2', 4', 6'($E9 9[9 m?C B 1', 3', 5' J7 I D>Dm|9 9[9 m?C 9>?7).C>?7 m|D= JHcD J>ZD> 7 F>D23/18010. 1 10. 1 m :9 LZ m 9eD m :9 LZ m 9eD11 m :9 LZ m 9eD m :9 LZ m 9eDl :9 l :9l :9 97 m|D= J>D= AB m? L? m|D= 8D= AC BZ J7D= 97 =d9 BAC.? = BC/AC = J=rl :9 m|9 Aj >?K 8D= 9> "?" >E9 :K " (". &>? L :K ( CJ 9}D> IED= IED= L?F>|zD= DCD=7D= CJ 9}D> IED= IED= L? 9}D> :9, mD> >|D= J>;E 9>?K :9 ($aD>3.9). C[9> L m :9 D>| >aD> 3.10.Cd J> =>? m :9 :|? :}D= F>D JHkC, Lb :: ( 5%>E9 12%...$aD> 2-9 LZ 2-10l 9eD l 9eDl 9eD BZ J I =?7 >?K I m|D= AbD> >7? CJ 9J LKeD= =d9 L? JH9 97 CJ >aD>DdD 9J JHcD NE7O L? A>E~D= 9[9> =?7 >7? CJ 9J md.l 9eD Aj >?K 8D= 9> A >E9 :K ( (J7C=?[9 9\D), A>? L mD> 97 J7C=?[9 9\D >|D=L mD> 97 CJ 9eD. $aD> 2.11 =?? J>?K 9[9> L LZ =>? m 9eD./7 9d J> HiJ H7 C? B?`D> =?7 A LZ ? D>| I7K:1a LO CKD L m 9eD A, D=|? J7 L 2 m|D= D=>?`D= m? ND= D>7K GK7 JH9 J\C, C?m|D= D=>?`D= 9d m :9 ? = A/2.24/18025/18026/18011. 1 11. 1 D? J?F D? J?F11 D? J?F D? J?F/H`D 8~D L A J>KJ J>|D= F>~? D? J?F m|D= J>D= L? m|D= 9ED= >E9 m|D=9ED= L? m|D= 9ED=, O`K 9K 9[9 m|D= D? J?F md F>~? JHzD (A>eD= 9d m?C =O). lm}J m|9 O`K 9K md A>? L D? J?F F>~? JK\D J>;E D>D= GK? J9 >aD> >9 D>J mD>.$7? m|D= JHcD, >E9 m|D= JHcD LZ m|D= J>D= D? J?F D>7K J}? CJ m?C A>? J}?m?C md 9>iD= J?F Ni9 D>7K ($aD> 3.12). |? m\O JHaD> 8ZO 9[9> L CJ I JH|D=>F D? J?F J>|D= =F.)? J?F >7? m| )? J?F >7? m|D= JHcD 8D= mE}D J>D= D= JHcD 8D= mE}D J>D=/>9 9>J 97 8Z? JE[D D? J?F >7? m|D= JHcD 8D= mE}D J>D= BZ :D= m|D= J?FJKOD 9>KD= 97 >7? m|D= JHcD.t /HaD> 8ZO 8Z? JE[D J m?C C m] 9>E :D= 9[9 J?FJKOD C/1, C/2L? m|D= JHcD J\C* m] 9>E.t #?? J>?K 9[9> :D= J?F JKOD D=EZ? 97m|D= JHcD J\C *, 8[D AbD> -1LZ m|D= JHcD J\C *18[D AbD> -29>E JH|9:+ 1 m|D= JHcD J\C *, 8[D AbD> -1t -2+ 1 m|D= JHcD m|D= AbD> **1 9J m|D=JHcD J\C * 8[D AbD> -1- -2J}? A .+ 1 J?F JKOD *2A+ )? *1A m|9 /1, LZ L *2/2//*1A. /1/2BZ m|D= J?F JKOD 9>KD= 9D :D=.t $|D= :D 9[9> L J?F JKOD JHED= 97 >7? m|D= JHcD J\C *1LZ *2m] 9>E.$]O GK7D I[J 9[9> L GK7 mE}D L?:;E I7K)? J?F >7? mE}D J>D= 9J D>7K 8D= 9KD= JHcD )? J?F >7? mE}D J>D= 9J D>7K 8D= 9KD= JHcDBZ? JE[D: C>E >7? m|D= J>D= 7 LZ 8. $]O D? J?F >7? m|D= J>D= m] 9>E 8D= 9KD=JHcD 8[D AaD> - 9>E JH|9.C[9> :D= D>| I7K: GK7D I[J mE}D L?:;E+ & 7' //7 9[9> 7 CJ A>E~D= 8D= -; 8'//8 LZ 9[9> 8 CJ A>E~D= 8D= -.+ =?7E 97 7' LZ8' BZ J\C* 97 9KD= D? J?F.+ & */1LKeD= =d9 L? 7 LZ */2LKeD= =d9 L? 8; /1LZ /2BZ 9[9 J?F m?C.+ 1 9KD= /1/2J\C *, 8[D AbD> -.27/180)? J?F mE}D J>D= L? 9KD= JHcD 8D= CJ 9KD= JHcD A>[9 )? J?F mE}D J>D= L? 9KD= JHcD 8D= CJ 9KD= JHcD A>[9BZ? JE[D: C>E m|D= JHcD J\C *18[D AbD> -1LZ m|D= J>D= 7. $]O D? J?F m|D=J>D= 7 L? 9KD= JHcD J\C *18D= 9KD= JHcD 9d 8[D AbD> - 9>E JH|9.A. CKD= D? J?FJ?F Ni9 D=EZ? L? 9KD= m] 9>E (,K7D I[J L?:;E I7K).+ 1 m|D= J>D= ://7 LZ 9[9> 7 CJ mE}D - 9J m|D= JHcD J\C *18[D AbD> - + -1J}?*. * BZ J\C97 9KD= D? J?F.+ 1 mE}D J>D= **19J m|D= JHcD J\C*1J}? (LZ *) (7; ( LZ ) BZ 9[9 J?F m?C. + 1 9KD= () J\C *, 8[D AbD> -.B. CKD= D? J?F J?F Ni9 JHED= L? 9KD= m] 9>E+ 1 m|D= J>D= :1//: LZ 9[9> : CJ mE}D 8D= - 9J m|D= JHcD J\C*18[D AbD> - t-1J}? *. * BZ J\C97 9KD= D? J?F.+ 1 **19J m|D= JHcD 8[D AbD> -1J}? /1, */2( :),/1LZ /2BZ >7? J?F m?C 9D JaC.+ 1 9KD= /1/2J\C *, 8[D AbD> -.)? J?F >7? 9KD= JHcD 8D= CJ 9KD= JHcD A>[9 )? J?F >7? 9KD= JHcD 8D= CJ 9KD= JHcD A>[9BZ? JE[D: C>E 9KD= JHcD J\C*1, 8[D AbD> -1 LZ 9KD= JHcD J\C*2 8[D AbD> -2. $]O D?J?F >7? 9KD= m] 9>E 8D= 9KD= JHcD 9d 8[D AbD> -.A. CKD= D? J?F J?F Ni9 D=EZ? L?>7? 9KD= m] 9>E (,K7D I[J mE}D L?:;E I7K).+ 1 9KD= JHcD J\C *1 8[D AbD> - + -1 9J 9KD= JHcD J\C *2 8[D AbD> - + - 2 J}? *. *BZ J\C97 9KD= D? J?F.+ )? **1 m|9 /1, **2 m|9 /2, /1 LZ /2 BZ 9[9 J?F m?C.+ 19KD= JHcD J\C *, 8[D AbD> -.B. CKD= D? J?F J?F Ni9 JHED= L? 9[9 9KD= m] 9>E+ 1 9KD= JHcD J\C *1 8[D AbD> - t -1 9J 9KD= JHcD J\C *2 8[D AbD> - t -2 J}?*. * BZJ\C 9KD= D? J?F.+ )? **1 m|9 /1, **2 m|9 /2. /1 LZ /2 BZ 9[9 J?F m?C 9D JaC.+1 9KD= JHcD 8[D AbD> -, J\C *.C. CKD= D? J?F J?F Ni9 JHED= L? CJ m|D= JHcD LZ J?F Ni9 D=EZ? L? CJ m|D= JHcDm] 9>E+ 1 9KD= JHcD J\C *1 8[D AbD> -+ -1 9J 9KD= JHcD J\C *2 8[D AbD> - + -2 J}? *.* BZJ\C9KD= D? J?F.+ )? **1 m|9 /1, **2 m|9 /2; /1 LZ /2 BZ 9[9 J?F m?C.+ 1 9KD=/1/2 J\C * 8[D AbD> -.28/18012. 1 12. 1 9[9 m| 9[9 m|D= 9ED= >aD> >9 D= 9ED= >aD> >911 9[9 m| 9[9 m|D= 9ED= >aD> >9 D= 9ED= >aD> >9/HED= A J>KJ J>|D= =F 9[9 m|D= 9ED= A>[9 D>7K. .7K m\O BZ 9[9> L CJ I m|D=9ED= F>D=.C[9 m| C[9 m|D= 9ED= L 8D= 9ECF7 D= 9ED= L 8D= 9ECF7A. 1 e L7DW L7D BZ m|D= 9ED= A>_F AbD m|9 J}E 8? 8D 9KD= JHcD JD= me? CJ m? ND=. WL7D 9d >7? JH9 m? ND= LKeD= =d9 L? D>7K =? BZ JH9 :Z? LZ JH9 D=D 97 e L7D. &>?L D=|? J7 9>E 8?J m :Z? 97 >7? JH9 md.(,K7D I[J mE}D L?:;E >aD> 2.22)1b :: 1 eL7D 8?J JH9 :Z? AB LZ JH9 D=D C.C[9> L D>| I7K:t 1 9KD= JHcD J\C *, 8[D AbD> *A 9Jt *C A_E :Z? J}? !; 9KD= JHcD J\C C, 8[D AbD> C!9J AC J}? ".t 1 JHKD= JH9 97 A" 9J *A J}? *1, 9J * J}? *3.t 'O *4 m? ND= L? *3,*2 m? ND= L? *1 GK7 *. )? *3 L? *1 LZ *2 , D? *4 L? *1 LZ *2. BD J?7 DZO I BZ=?? >}D 9[9 9KD= JHcD J\C *1, *2, *3, *4; J}E J>ZD> e L7D.t 1 9[9 9KD= JHcD J\C *1,8[D AbD> *1A; J\C *2, 8[D AbD> *2B; J\C *3 8[D AbD> *3C; J\C *4 8[D AbD> *4 J7m|9 >aD> e L7D 9D :D=71613(;:6+HE=B. l|D= NE[O 9 D>?K J\Cl|D= NEO 9 D>?K J\C BZ m|D= 9ED= F>D= J}E 8? 9[9 9KD= JHcD 9d 8[D AbD>A>[9 D>7K D? J?F D>7K.&>? L D=|? J7 9>E 8?J A>E~D= 9[9> =?7 9[9 J\C.+ 1 m|D=NE[O 9 2 J\C: (,K7D I[J mE}D L?:;E I7K)t 'O *1 BZCJ\C, 8[D AbD> *1 t *2 L 9KD= *2t 1t 'O *2 BZCJ\C, 8[D AbD> *2 t 1 L9KD= 1t2t 'O *1 BZC J\C, 8[D AbD> *1 t 2 L 9KD= 2t3...+ 1 m|D= NE[O 9 3 J\C: (,K7D I[J mE}D L?:;E I7K)t 'O *1 BZCJ\C, 8[D AbD> *1 t *3 L 9KD= *3. 1t 'O *2 BZCJ\C, 8[D AbD> *2 t 1 L9KD= 1t2t 'O *3 BZCJ\C, 8[D AbD> *3.2 L 9KD= 2t3t 'O *1 BZCJ\C, 8[D AbD> *1 t 3L 9KD= 3 t 4+ 1 m|D= NE[O 9 4 J\C: (,K7D I[J mE}D L?:;E I7K).t 'O *1 BZCJ\C, 8[D AbD> *1 t *2 L 9KD= *2t1t 'O *4 BZCJ\C, 8[D AbD> *4 t 1 L9KD= 1t2t 'O *3 BZCJ\C8[D AbD> *3.2 L 9KD= 2t3t 'O *2 B\CJ\C8[D AbD> *2 t 3L 9KD= 3 t 4...NE7?E92J7C(;:6+HE=29/18011 9[9 m| 9[9 m|D= 9ED= 8D= J>|9 9ED= D= 9ED= 8D= J>|9 9ED=A. !B?F!B?F BZ GK Jb9> 97 m?C 9d JD= I A>E~D= 9[9> mD >7? m?C 9 mD> "1 LZ "2 BZ CJ>D= I.(" (" 11 + (" + (" 22 = 27 = 27"1 LZ "2 =? BZ J?`K m?C97 ;B?F (A>E~D= 9[9> "1"2 < 27), AB BZ JH9 :Z? 97 ;B?F, C BZJH9 D=D 97 ;B?F (>aD> 2.26).C[9> L ;B?F* 1 ;B?F 8?J >7? JH9 AB LZ C (>aD> 2.27).v 1 >7? m|D= JHcD J\C *, m|D= AbD> BZ AB LZ C.v C>?7 2 m|D= JHcD md H7 BZC 12 F>D mK D>7Kv / 9[9 m?C 9>?7 1, 2, 3...LZ 1', 2', 3'... A 9[9 m|D= J>D= IED= IED= L? JH9 ABLZ C.#?7E m?C 97 9[9 m|D= 1 t1', 2 t 2' BZ 9[9 m?C D? J>ZD> !B?F.* 1 !B?F A>? 8?J 2 m|D= AbD> B?`D >F !" LZ #$* +>|zD= F>[F >7? 9>hC J?7: (>aD>2.28).v ,K7 ! LZ " A (+ LZ ), // #$v ,K7 # LZ $ A +, LZ () // !"v C>?7 9[9 mE}D *$, +$, ,$ H7 BZC 3 F>D 8D= D>7K 8? 9[9 m?C 1, 2, 3 LZ 1',2',3' ($ BZ m?C 9>KD= 3 LZ 3' 97 9~ 3 mE}D DZO)v )? ! L? 9[9 m?C 1', 2' J>K9 +$ LZ L? 1, 2 J>K9 *$ ; D? " L? 9[9 m?C 1', 2'J>K9 $, LZ 1, 2 J>K9 *$.v #?7E m?C 97 2 J?7 J|zD= D= J>K9 2 9>hC J?7 ! LZ " N[9 mD> 9[9 m?C J>K9!B?F.* +>|zD= F>[F J[C m?C (>aD> 2. 29).v ,K7 A LZ B A m|D= J>D= IED= IED= L? C, GK7 C LZA >7? m|D= J>D=IED= IED= L? AB J7 m|9 >aD> 8aD> >ZD> !"#$.v D= J7C =?[9 LKeD= 9\D !%C (LKeD= J}? %).v 1 9KD= JHcD J\C C, 8[D AbD> C% 9J m|D= J>D= !" J}? & LZ '.v ,K7 & LZ ' L 9[9 m|D= J>D= IED= IED= L? C, 9[9 m|D= J>D= DZO 9J 9[9m|D= 9>_E !# LZ $" J}? 4 m?C 1,2, 3, 4 BZ D>D= m?C J>K9 ;B?F 9D N[9 mD>.30/18031/180B. +7H78eD+7H78eD BZ GK Jb9> D>D= m?C 9[9> mK CJ m?C 9 mD> LZ CJ m|D= J>D= 9mD> (>aD> 2.30).1b :: m?C ( J>K9 F7H78eD J7 9d(" = ($32/180l?C9 mD> " =? BZ J?`K m?C97 F7H78eD, m|D= J>D= : 9 mD> =? BZ m|D= 9>KD97 F7H78eD, m|D= J>D= *N A GK7 " LKeD= =d9 L? JH9 : BZ JH9 97 F7H78eD.C[9>L F7H78eD+ 1 F7H78eD A>? 8?J J?`K m?C " LZ m|D= 9>KD.C[9> L >aD> 2.31/H`D JH9 m? ND= *N BO CJ m?C8J Aa, Lb : m?C1.,K7O 9KD= JHcD J\C", 8[D AbD>H2(8D= A>E~D= 9[9> J m?C * mD m?C1)9J m|D= J>D= IED= IED= L? : LZ m? GK71 J}? >7? m?C. $7? m?C md 9>bD> BZ >7? m?C J>K9 F7H78eD. C[9 m?C A>[9 9pD= N[9mD> J|zD= J.+ 1 F7H78eD D? J?F JHED= CJ =d9 9>E JH|9 (>aD> 2.32).v C>E =d9n. 1 F7H78eD 9>7 >7? m?C A LZ B mD= J>? D? 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ND= 97 9[9 >aD> 9>?K >E9 9[9 CJ 8`D 97 LJ J> mBZC 9>KD mE Ab9> J>|9 JH`D 9[9 >aD> 9>?K. t &>? L >aD> 9>?K J> 3 J7 :D= m|D=59/180D=>?`D= 45EBZCm|D= F> JH m L. $aD> 3.45 BZ 87 >aD> 9>?K 97 LJ J> 9>E>aD>3.43.60/180#>? Ab9> J>|9 #>? Ab9> J>|9/HED= 9> m 1 m] JHaD> 8ZO D>D= A?D J>9 9>KD= L =>? Ab9> J>|9. )>|D= JHED=J>9 J 9[9 LJ J> 9d 9K JHi9 F>9 J}F LZ A>eD= =?D= D>7K, :E md JKs J>K9 LZE C?LJ J> m|9 8?K :?D, J7 9d 9[9> =>? Ab9> J>|9 9>E F>h >F m F>~D [D> mO m, 9>bD>N[9 m BD 97 LJ J>. C[9 Ab9> J>|9 F>~? m|9 =>? Hf HZD=, : >?K m JH[D> D>CBDJHED= A>? m9 8~D L >E9 F>~? JbD> JE[D B}? JHED= =?7 9eD=.7) +>\D BE}? Ab9> J>|9 )=|? J7 9>?7 Ab9> J>|9 J>ZD> 87 BE}?. t &b9> J>|9 mD> >aD>BZ Ab9> J>|9 N[9 mD> m BD 97 JD= A>? >aD> >9 9K J}E D`D LJ J>. 1b :: $aD>3.45: 9[9 Ab9> J>|9 (22, (38 LZ 44 N[9 mD> m BD 97 JH9, Ab9> J>|9 110, 55, 16 N[9mD> m BD 97 m. t &b9> J>|9 mD> L: 'Z Ab9> J>|9 N[9 mD> L JHb J|zD= m? =?7 9[961/180F>D J 9K J}E D`D LJ J>. 1b :: &b9> J>|9 82 LZ (16 N[9 mD> L JHb J|zD= m? =?72 B JH LZ CJ :|? m 1; Ab9> J>|9 58 N[9 mD> J|zD= m? =?7 3 LZ =? m 2. &b9>J>|9 mD> L BO J>;E 87 9>?K A>eD= =?7D, C? 9>?K A>eD= =?7D F>~? 9>D CJ CJDZE md m BZC9>KD Ab9> J>|9.1b : ($aD> 3.46): l N[9 mD> 9>?K HD= 97 LJ J>9d J> 9>D CJ F>D= m? ND= 97 LJ J> BZCCJ 9>KD (9>KD %).l N[9 mD> 9>?K:ZO 97 LJ J> 9>D CJ I7K 97 m LZ =?[ m BZC CJ 9>KD (9>KD %%). l N[9 mD>9>?K 97E 9>D CJ :|? 97 m BZC CJ 9>KD (9>KD %%%).t &b9> J>|9 mD> A>?: 'ZAb9> J>|9 BD D>J J>;E 87 9>?K A>eD= =?7D 97 LJ J>. &b9> J>|9 mD> A>? 9cD =?BZ Ab9> J>|9 9>E[D 9>.1b :: C[9 Ab9> J>|9 110, 58 LZ (38, 55 LZ 10 Ab9> J>|9 mD>A>? 97 LJ J> m|9 8?K :?D JH`D >aD> 3.45.8) +>\D 8 Ab9> J>|9 l Ab9> J>|9=>? JH`D 8~D L m|9 Hf HZD=, : m9, JH[D> D>CBD 9D 9>i j CJ I LD m I7K:t (?Ab9> J>|9 9> =>? CJ BD, A>eD= =>? BF, =>? J>7.t C[9 Ab9> J>|9 mD> >aD> 97 F>DJ DZE =>?>aD> 9>?K J> >?D Hf D>J m9 JH|D= >aD> :[D= 97 F>D J md.t )>D=Ab9> J>|9 9d B?`D GK7D mD L?9 8?K :?D CJ 8 F>D 97 LJ J> D`D m =D D>7K.(? Ab9> J>|9 m|9 =>?CJ L JHb Hf HZD= 97 8~D L, D`D =>?D=EZ? >aD> 8?K :?DLZ =>? 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JH 9d m[O BZ >aD> LKeD=.)7 m?ND= 9cD B}? 9[9> L 9pD= J|zD= J.$aD> 3.54 BZ 3 >aD> 9>?K LKeD= =d9 I7K A>? m] L>EZD 9>D> LZ >aD> 9>?K JH9 mE m] m|9 9J 8 CJ F>D J| m D>aD Hf 9K JHi9 8`DJHED= 97 LJ J>.65/18014. $aD> 9>?K JH9 mE 14. $aD> 9>?K JH9 mE$aD> 9>?K JH9 mE $aD> 9>?K JH9 mE+>|z +>|zD= F>[F 8?K :?D >aD> 9>?K JH9 mE D= F>[F 8?K :?D >aD> 9>?K JH9 mEA. &>[? D?C A. &>[? D?C$aD> 9>?K J>D= =d9 BZ BE}? >aD> 8?K :?D mzD =?~D, 9>E F>_F J> >?D 9>bD> N[9>aD> :}D= LZ Ab9> J>|9 97 LJ J>. E md JHED= A J>KJ :hD= F>|zD= F>[F >aD> 9>?KJ>D= =d9 BZC F>|zD= F>[F 8?K :?D 9>bD>. .ED= C? >aD> 9>?K J>D= =d9 9> J>>?D Ab9> J>|9 >7? 9>?K D`D D=|? m9 A>d >aD> :KD= H7 >aD> :}D= 97 LJ J>. lA>9 F>9 D>|9 m?Cmd D=|? J7 :hD= F>|zD= F>[F >aD> 9>?K JH9 mE m 8 IKD=.66/180$aD> 9>?K JH9 mE BZ >aD> 8?K :?D D? 97 LJ J> JH`D CJ CJ F>D= >aD> 9>?K8D= F>_F 9>?K IED= IED=. $aD> 9>?K JH9 mE J> >?D mD= J>? 9~ 87 9>?K 97 LJJ> JH`D CJ >aD> 8?K :?D D`D : J>O m|9 >aD> :}D= 97 Dd. C>bD> La LO, 8`D 9}D>9[9 >aD> 9>?K J>D= =d9 D=|? J7 J>|D= L J>`C >aD> 9>?K JH9 mE 97 LJ J> md($aD> 5.1)B. +>|z B. +>|zD= F>[F N\ D= F>[F N\O :D= >aD> 9>?K JH9 mE O :D= >aD> 9>?K JH9 mEl N\O :D= >aD> 9>?K JH9 mE D=|? J7 BZC D>| I7K:t #D > JH9 JE} m l 9[9 879>?K *NOP LZE LJ J>.t C>D CJ F>D= +' BZCCJ F>D= >aD> 9>?K LZ >|D= 9>?K't C>?K > JH9 JE} m ENOP LZ LJ J> J>;E >|D= 9>?K ' B`D CJ F>D= +' J7 9d >aD>9>?K 97 9[9 JH9 BZ *'3'4'5' (m|9 =? BZ 9[9 JH9 mE) LZ >aD> 9>?K 97 LJ J> md =? BZ>aD> 9>?K JH9 mE ($aD> 5.2)67/180C. $ I 8?D :}D= C. $ I 8?D :}D=/ I =?7 Ab9> J>|9 JH`D JH9 mE L? Ab9> J>|9 J|zD= D= mE m|9 JH`D LJ J> m|9=? BZ > I 8?D :}D=./ I *'A' / *A =F BZ > I 8?D :}D= J>;E F>|zD= *N./ I *'B'/ 0B = G BZ > I 8?D :}D= J>;E F>|zD= *O./ I *'C' / *C = H BZ > I 8?D :}D= J>;EF>|zD= *P.)> 9[9 > I 8?D :}D= J7 9d J> 9>KOD J > JE} m LKeD= =d9 I7D= > JE}m JH9 mE LZ D=|9 B}?.. +>\D BE}? >aD> 9>?K JH9 mE . +>\D BE}? >aD> 9>?K JH9 mE+ CkD 9 LZE F>|zD= 9>?K ' LKeD= =d9 >E9 N?`D =d9 L? CJ F>D= >aD> 9>?K +u CZD=|? J7 F>\D J>ZD>:t $aD> 9>?K JH9 mE LKeD= =d9t $aD> 9>?K JH9 N?`D =d9.+ CkD9 J>;E > I 8?D :}D= CZ F>\D J>ZD>:t $aD> 9>?K JH9 mE mK: 87 > I 8?D :}D=J>;E 87 JH9 8D= D>7K.t $aD> 9>?K JH9 mE 9\D: >7? JHED= 87 > I 8?D :}D= 8D=D>7KJD= me? CJ.t $aD> 9>?K JH9 mE B9>: 87 > I 8?D :}D= J>;E 87 JH9 A>eD=8D= D>7K.-J D>?K BE}? >aD> 9>?K JH9 mE m|9 N\O :D= JH`D 9z I md. .ED= A J>KJJ>|D= :hD= CJ I BE}? >aD> 9>?K JH9 mE D>|:t $aD> 9>?K JH9 mE LKeD= =d9 mK.t$aD> 9>?K JH9 mE LKeD= =d9 9\D t $aD> 9>?K JH9 mE mD= mK(N?`D =d9 mK).t $aD>9>?K JH9 mE mD= 9\D (N?`D =d9 9\D).|? m\O =?? J>?K 9[9 GK? mD> LZ 9[9> L 8DBE}? >aD> 9>?K JH9 mE JH`D.68/180C[9 BE}? >aD> 9>?K JH9 mE C[9 BE}? >aD> 9>?K JH9 mE/?`K 9>KD 1?J )7C, /C1) 11 t 78, GKO mD> L L JHb 9[9 JH9 mE LZ > I 8?D :}D=J>;E 9[9 JH9 m L >aD> 9>?K JH9 mE.$aD> 9>?K JH9 mE LKeD= =d9 mK $aD> 9>?K JH9 mE LKeD= =d9 mKA, 1 JHb 9[9 JH9 mE A, 1 JHb 9[9 JH9 mEC[9 =d9 3'*'4' = 4'*'5' = 5'*'3' =120E. Cd J> N[9 mD> =d9 30E=?7 JH9 N >E9 O L?F>|zD= DC D=7D= 8D= UA;.B. $ I 8?D :}D= J>;E 9[9 JH9 B. $ I 8?D :}D= J>;E 9[9 JH9F = G = H = 0,82.l 9>E J?D L 9d J> L >aD> 9>?K JH9 mE LKeD= =d9 mK =D miD= 8D= 9[9> BO >I 8?D :}D= J>;E 9[9 JH9 N, O, P 8D= F = G = H = 1, D=>o7 BZ m] F>dD= JE >aD> 9>?K JH9mE B`D 1/0,82 = 1,22 BD IE L? J>9 J.69/180C. 1 C. 1 >aD> 9>?K JH9 mE 97 m| >aD> 9>?K JH9 mE 97 m|D= JHcD D= JHcD/HED= >aD> 9>?K JH9 mE LKeD= =d9 mK, m|D= JHcD J>K9 9[9 CJ F>D= IED= IED=L? CJ F>D= JE} m 9d >aD> 9>?K JH9 mE BZ ;BbF. /H9 BD 97 ;BbF LKeD= =d9 L?JH9 mE J> 87 A>eD= 9>7 ;BbF. )K BO > 8?D :}D= :}D= GK? |9 F = G = H = 1 J>a JH9BD 97 ;BbF 8D= 1,22 m|D= AbD> LcD= JHcD LZ JH9 D> 8D= 0,7 m|D= AbD> md. Cd J>L =D miD= >aD> 9>?K JH9 mE 97 m|D= JHcD 8D= e L7D (J>7O J> 9>E m|D= ;B?F).C[9> L m|D= e L7D D>| >aD> 5.5: 'O JH9 BD AB 8D= 1,22:, JH9 D> C 8D= 0,7:(: BZ m|D= AbD> m|D= JHcD 9D L), GK7O 9KD= JHcD J\C*' 8[D AbD> *'C = *' 9J JH9BD AB J}? *3, *4 . ,K7O 9KD= JHcD J\C*' 8[D AbD> *'A = *'B 9J JH9 D> C J}? *1, *2.BD 9KD= JHcD 9d J\C *J, *2, *3, *4 J}E J>ZD> m|D= e L7D. 1 JHb 9[9 J?F m?C J>K99[9 m|D= 9ED= m|9 N[9 mD> D>| >aD> L.$aD> 9>?K JH9 mE LKeD= =d9 9\D $aD> 9>?K JH9 mE LKeD= =d9 9\DA. 1 JHb 9[9 JH9 mE A. 1 JHb 9[9 JH9 mEC[9 =d9 3'*'5'= 97E10' ; 4'*'5' = 4'*'5' =131E25'. Cd J> L JH9 *'3' J>;E J=7E= 1:8 LZJH9 *'4' J>;E J= 410x 7:8.70/180B. $ I 8?D :}D= J>;E 9[9 JH9 mE B. $ I 8?D :}D= J>;E 9[9 JH9 mEF = H = 0,94, G = 0,47. l J?D L, D=|? J7 I :D= > I 8?D :}D= GK? |9 F = H = 1, G =0,5. )>| LO >aD> 9>?K JH9 mE m] m|9 F>dD= JE 1,06 BD IE L? J>9 J.C. 1 C. 1 >aD> 9>?K JH9 mE 97 m| >aD> 9>?K JH9 mE 97 m|D= JHcD D= JHcD+ l|D= JHcD J>K9 CJ F>D= IED= IED= L? CJ F>D= *'3'5' 9d >aD> 9>?K JH9 mEBZ ;BbF. l :Z? 97 JH9 BD 8D= 1,06:. l :Z? JH9 D> 8D= 0,94:. (: BZ m|D= AbD>97 m|D= JHcD) ($aD> 5.7). + l|D= JHcD J>K9 CJ F>D= IED= IED= L? CJ F>D=3'*'4' LZ 4'*'5' 9d >aD> 9>?K BZ ;B?F.l :Z? JH9 BD 8D= 1,06:,m :Z? JH9 D> 8D=0,35:.$|D= JH9 BD 97 ;BbF >F L? *'3' >7O *'5' CJ =d9 70 JKs J>;E ;BbF J>K9 CJF>D= IED= IED= L? 3'*'4' >7O 4'*'5'. $7O Dd? 9[9> A>[9, JH9 BD 97 ;BbF DZO LKeD==d9 L? *'5' >7O *'3'.+ C[9> L =D miD= ;BbF 8D= m|D= e L7D:t l? L? ;BbF DC JHED= CJ F>D= 3'*'5' 9d JH9 BD AB = 1,06: JH9 D> C = 94: J7D? AC. 'O * BZC J\C GK7O 9KD= JHcD 8[D AbD> *A 9J C J}? !. 'O * BZC J\C GK7O9KD= JHcD 8[D AbD> *A 9J C J}? !. ,K7O 9KD= JHcD J\C C, 8[D AbD> C! 9J AC J}? ".D= JHKD= JH9 A" 9J AB, C J}? *4,*1 BO *3, *2 m? ND= *4, *1 GK7 *. BD J\C*1,*2, *3, *4 BZ 8D J\C9KD= JHcD D? J?F J}E J>ZD> m|D= e L7D.$aD> 5.8- l? L? ;BbF 9dJH9 BD AB = 1,06:; JH9 D> C = 0,35:. /7 BO:*2A = *4B = C/4 *1C = *2 = - = AB +(C/2) ($aD> 5.9)71/18072/180$aD> 9>?K JH9 N?`D =d9 mK $aD> 9>?K JH9 N?`D =d9 mKA. 1 JHb 9[9 JH9 mE A. 1 JHb 9[9 JH9 mEC[9 =d9 3 '*' 5' = 90E, 4' *' 3' = 4' *' 5' = 135E. (>aD> 5.12)B. $ I 8?D :}D= GKO |9 B. $ I 8?D :}D= GKO |9F = G = H = 1C. $aD> 9>?K JH9 mE 97 m| C. $aD> 9>?K JH9 mE 97 m|D= JHcD D= JHcD+ l|D= JHcD J>K9 CJ F>D= IED= IED= L? CJ 3*4 >7O 4*5 9d >aD> 9>?K JH9 mE BZ;BbF . l :Z? JH9 BD 97 ;BbF 8D= 1,3:, m :Z? JH9 D> 8D= 0,54: (: BZ m|D= AbD> 9773/180m|D= JHcD). $|D= JH9 BD 97 ;BbF >F L? JH9 *'3' >7O *'5' CJ =d9 22E30'.($aD>5.13) + C[9> L =D miD= ;BbF 8D= m|D= eL7D D>| >aD> 5.14./H9 BD AB =1,3:, /H9 D> C = 0,54:- = *1C = *3 = 1,42:H = *2A = *4B = 0,1874/180$aD> 9>?K JH9 mE N?`D =d9 9\D $aD> 9>?K JH9 mE N?`D =d9 9\DA. 1 JHb 9[9 JH9 mE A. 1 JHb 9[9 JH9 mE#?D= D>| >aD> 9>?K JH9 mE mD= mK.B. $ I 8?D :}D= GKO |9 B. $ I 8?D :}D= GKO |9F = H = 1; G = 0,5C. $aD> 9>?K JH9 mE 97 m| C. $aD> 9>?K JH9 mE 97 m|D= JHcD D= JHcD+ l|D= JHcD J>K9 CJ F>D= IED= IED= L? CJ F>D= 3'*'5' 9d >aD> 9>?K JH9 mE BZm|D= JHcD.+ l|D= JHcD J>K9 CJ F>D= IED= IED= L? CJ F>D= 4'*'5' >7O 5'*'4' 9d>aD> 9>?K JH9 mE BZ ;BbF. l :Z? JH9 ;BbF 8D= 1,06 :, D=>?`D= 7EL? JH9 3' DK DCJHED=, >E9 IED= IED= L? CJ F>D= 3'*'4'; D=>?`D= 7EL? JH9 5' DK DC JHED= >E9IED= IED= L? CJ F>D= 4'*'5'. l :Z? JH9 D> 8D= 0,35 : (: BZ m|D= AbD> m|D=JHcD) ($aD> 5.16)+ C>E F>_F L =D miD= ;BbF 8D= eL7D D>| >aD> 5.17.75/18076/18077/18078/180C[9 Lb : L 9[9 BE}? >aD> 9>?K JH9 mE C[9 Lb : L 9[9 BE}? >aD> 9>?K JH9 mE79/180C[9 GKO |9 L >aD> 9>?K JH9 mE C[9 GKO |9 L >aD> 9>?K JH9 mE1. /H`D >aD> 9>?K JH9 mE 9[9 J>ZD> CD=, 9[9 D7D >E7 L.L.... LD L Aj >?K JH`D CJ 9JA>? 9J GK7 9>iD= ($aD> 5.20).2. C>E F>_F 9J H?`D= F>D JH`D >aD> 9>?K JH9 mE. +>DLJ B?K 97 LJ J> 8 CJ F>D= JHKD= =?7D 9J, GKO |9 L 8D= 9[9 9>C D> ($aD>5.21).3. #>? Ab9> J>|9 JH`D >aD> 9>?K JH9 mE.t C[9 m|D= :dD= m|9 A IED= IED= L?9[9 JH9 mE *'3', *'4', *'5' LZ 9[9 m|D= Ab9> J>|9 A IED= IED= L? mE}D m|9 =>? Ab9>J>|9.t C[9 9> I Ab9> J>|9 9pD= =>? J>;E 9>?K 97 m|D= :dD= ($aD> 5.22).4. l|D==}9> Aj >?K LJ B?K 97 CJ 9J JH`D >aD> 9>?K JH9 mEl|D= =}9> =}9> m|9 A IED=80/180IED= L? >aD> 9>?K JH9 mE 97 m|D= 9>_E >aD> LKeD= DCJH`D 9[9 CJ F>D= JE} mJ|zD= D= LZ 9d 9[9 9}D> IED= IED= L? 9[9 JH9 N, O, P. $aD> LKeD= 9d >7? m|D= 9>_ED`D J|zD= D= J7 9d 2 A?K =}9> CJ 9J 9>E C? BE}? >aD> 9>?K JH9 mE. ($aD> 5.237;$aD> 5.238). 5. C>E F>_F L H;D LZ HkD= 97 8[D> HkD= J>;E D>| GKO |9 JHED= >aD>9>?K LKeD= =d9 ($aD> 5.24 , $aD> 5.25).6. &>? 9D J>?J 9>E F>_F :hD= 9[9 BE}? >aD>9>?K JH9 mE A>[9 :7 JH`D 9z I Bj J>KOJ L >aD> 9>?K JH9 mE )=EZ? H7 9>E F>_F:hD= > JH9 mE JH[? D>| >aD> 5.26.81/18082/18083/18084/180C[9> L >aD> 9>?K JH9 mE C[9> L >aD> 9>?K JH9 mEC>D BE}? >aD> 9>?K JH9 mE C>D BE}? >aD> 9>?K JH9 mE&>? 8?K :?D >aD> 9>?K JH9 mE 97 LJ J> J7 9>D CJ JHED= 9[9 BE}? >aD> 9>?KJH9 mE JH`D. 1?9 9>D F>~? JKs J>K9 LZE >aD> :}D= 9K J}E 97 LJ J> LZ JKs J>;E O`K9K J> >?D CZ 9>D BE}? >aD> 9>?K JH9 mE 9>E J>b9> >F. $aD> 9>?K JH9 mE LKeD==d9 mK J> >?D 9K J}E 97 LJ J> J>;E 87 CJ mK Hf HZD=, 9\D m?, >aD> 8?K :?DmF, : :D=. 1a LO >aD> 9>?K JH9 mE LKeD= =d9 mK m|9 I :D= D>?K, D>J BZ m?L? 9[9 LJ J> 9d 9K J}E F>9 J}F J>;E 9~ 87 9>?K ($aD> 5.27). l? L? D>D= LJ J>85/1809d 9K J}E BZ D>D= A>? >aD> >F, 9d :}D= D>| >aD> 5.28 J>a BE}? >aD> 9>?K JH9 mELKeD= =d9 mK I A>eD= J> >?D Hf 9K J}E La CJ I m|D= D_J I 8 JHhD= D>7K. &>?md J7 D`D :hD= BE}? >aD> 9>?K JH9 mE LKeD= =d9 9\D I A>9 F>9 m|9 D>|9 m?CJH`D ($aD> 5. 29). $aD> 9>?K JH9 mE N?`D =d9 mK, N?`D =d9 9\D J>|D= :hD= m? L?D>D= LJ J> 9d D>?K LcD= JHcD, 9KD= JHcD DCJHED= 9[9 CJ F>D= IED= IED= D>7K.)K 9>D CJ F>D= JE} m NEP IED= IED= L? 9[9 CJ F>D= 9>7 LcD= JHcD J>a >aD>9>?K JH9 mE 97 LcD= JHcD BZ LcD= JHcD. 1a LO L?9 :D= >aD> mzD =?~D >zD HJ D>?KIE L? :D= ;BbF. )K 9>?K :Z? 97 LJ J> J>;E F>|zD= O BD, J>a D`D 9>D BE}? >aD>9>?K JH9 mE N?`D =d9 9\D, Ab9> J>|9 J>;E F>|zD= *O HiJ D=D m? CJ D7, >aD> 8?K:?D I 9\D m? >zD ($aD> 5.308).#D > JE} m LKeD= =d9 LZE LJ J> #D > JE} m LKeD= =d9 LZE LJ J>86/1801?9 9>D L JHb LZ 9>?K 97 9[9 JH9 JE} m >F Bj I BZC 9>E L?9 8?K :?D JH`D>aD> 9>?K JH9 mE : >zD, mF >zD LZ J> >?D Hf D_J 9[9 9K J}E 97 LJ J>. 1a LO, JKsJ>;E 9K J}E LJ J> JKs J>;E O`K 9K J> >?D CZ =D > JE} m I7E 9>E >F Bj. />eD=J>|D=, L? D>D= LJ J> 9d :}D= A>? >F J7 D`D 9>D =9 > JE} m JHhD= L? =d9 97A>?, 9[9 9}D> 97 > JE} m JHhD= L? 9[9 9}D> 97 A>?. CcD L? D>D= A>? :}D= JHJHcD J7 D`D 9>D =9 JE} m JHhD= L? J\C97 A>? JH, 9[9 9}D> 97 > JE} m JHhD= L?JH9 m? ND= 97 LJ J> (>aD> 5.31).C[9> :D= >aD> 9>?K JH9 mE C[9> :D= >aD> 9>?K JH9 mE/7 m] 8?J, CJ mE}D J>D= (>7O CJ 9}D>) m|9 N[9 mD> 8? >7? m?C, C? >aD> F>D=(C? CJ) B}? m|9 N[9 mD> 8D= 9[9 9}D> 97 Dd, La LO L?9 :D= >aD> 9>?K JH9 mE9pD= GKO L :D= 9[9 m?C, 9[9 9}D> LZ 9[9 CJ JHED= A>eD= =?7D.A. D= >aD> 9>?K JH9 mE 97 m?C A A. D= >aD> 9>?K JH9 mE 97 m?C A/ > JE} m LKeD= =d9 97 m?C A (3A,4A,5A) D>| JH`D >aD> 5.32 J7 :D= B}? L JHb97 m?C A JHED= A>eD= =?7D J>;E 9[9 8|9 I7K:t C>D BE}? >aD> 9>?K JH9 mE, L 9[9JH9 mE.t 3[9 mD> JE} m JH9 mE 97 m?CA 8D= 9[9> D>\D JE} m LKeD= =d9 L? > I8?D :}D= 97 >` JH9 mE .N'A = NA.F; O'A = OA.G; P'A = 5A.Ht lJ 9[9 JE} m JH9 mE B`D 9[9 JH9 mE LZ N[9 mD> A' BZ >aD> 9>?K JH9 mE 97 A (>aD>5.33).87/180B. D= >aD> 9>?K JH9 mE 97 1 mE}D J>D= B. D= >aD> 9>?K JH9 mE 97 1 mE}D J>D=t )K mE}D J>D= 9d L JHb 8J As IE L? JH9 JE} m J7 N[9 mD> >aD> 9>?K JH9 mE 2 m?CmK CiJ 97 mE}D J>D= H? D? >aD> 9>?K JH9 mE 2 m?C md J7 9d >aD> 9>?K JH9 mE97 mE}D J>D=. 1b : mE}D A'B'JH`D >aD> 5.34./7 N[9 mD> >aD> 9>?K JH9 mE 97 m?CA' LZ B'I7K md D? A' L? B' J7 m|9 mE}D J>D= A'B't )K mE}D J>D= IED= IED= L? CJJH9 mE DZE md J>a 9> 9D N[9 mD> CJ m?C J>K9 mE}D J>D=, GK7 >aD> 9>?K JH9mE 97 m?C L7 N[9 mD> A IED= IED= L? JH9 mE. l?C 9cD B}? F>~? J>K9 m|D=J>D= L7 A LZ 9d A>E~D= 9[9> 8D= A>E~D= 9[9> J>J =?7 >7? m?C D>\D L? > I8?D :}D= 97 JH9 mE. 1b :: /H`D >aD> 5.35, m N[9 mD> A''' J7 9> 9D N[9 mD> JE}m m?C A' I7K md A GK7 A' m|D= J>D= IED= IED= *' 3' . 1 JHb m??C ' m|9 JbD> 8D=A'' = A N F.C. D= >aD> 9>?K JH9 mE 97 CJ >aD> F>D= C. D= >aD> 9>?K JH9 mE 97 CJ >aD> F>D=D= >aD> 9>?K JH9 mE 97 CJ B9 =?[9 ABC!# J>K9 CJ F>D= IED= IED= L?CJ F>D= 5*3 , J7 =D CJ F>D= ABC!# JHhD= L? CJ F>D= 3*5. /\C* JHhD= L?m?C A 97 >aD> F>D=, 9}D> A# JHhD= L? JH9 *3, 9}D> AB JHhD= L? JH9 *5 ($aD>5.367). />;E 9[9> :D= m?CLZ mE}D J>D= J7 9d J> :D= : :ZD= >aD> F>D= ABC!#/HXD> Jh :hD= D> I7K:+ 1 m?CA'(0, 0). + 1 m?CB'(0, 7).+ 1 m?CC'(>, 8).+ ,K7 C' A m|D= J>D= IED= IED=L? *'3'. lJ C'' = A.+ 3[9 mD> #' JH`D *'3' J>E~ C]D *'#' = C+ 1 m?C! (C, 7)+ )? !'L? ' J7 m|9 >aD> F>D= 9D :D= ($aD> 5.368).. D= >aD> 9>?K JH9 mE LJ J> 9d :}D= >aD> >F . D= >aD> 9>?K JH9 mE LJ J> 9d :}D= >aD> >Ft C>D =9 JE} m JHhD= L? =d9 97 A>? >F BD, 9[9 CJ 97 A>? >F BD DC JHED=9[9 CJ F>D= JE} m. D= >aD> 9>?K JH9 mE 97 A>? >F BD JH|9, I7K md :D= mD9[9 A>? D>, F>D L[J, B HD= (DK 9d)L.L... t /H`D >aD> 9>?K JH9 mE A>eD= J> >?DF>D A>KJ 97 LJ J>. /O 8 9[9 D_J J>7, Je B}? F>D J>O. $aD> 5.38 JHaD> 8ZO 9[98|9 :D= >aD> 9>?K JH9 mE 97 CJ A>? >F.!. D= >aD> 9>?K JH9 mE 97 LJ J> 9d 9[9 CJ F>D= m? ND= !. D= >aD> 9>?K JH9 mE 97 LJ J> 9d 9[9 CJ F>D= m? ND=l? L? 9[9 LJ J> 9d 9[9 CJ F>D= m? ND= J>a D`D 9>D CJ F>D= m? ND= BZCCJ F>D= JE} m. $aD> 5.39 JHaD> 8ZO 9[9> L >aD> 9>?K JH9 mE 97 LJ J> 9d CJF>D= m? 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