The Curvature of the Lateral Chapels in San Carlo Alle Quattro Fontane

The Curvature of the Lateral Chapels in San Carlo alle Quattro Fontane Michael Hill National Art School, Sydney

Abstract

Leo Steinberg exposed the complex geometry of Borromini’s San Carlo

alle Quattro Fontane (1634-41) in his doctoral thesis of 1960, and

despite some reservations (Connors argues that many of the drawings

we see today were reworked after the church was built) his scheme

has been the basis for later interpretations. Nevertheless, something is

missing. Steinberg, like others before, presumed that the plan begins

with the diamond shape of the two triangles. From here one can follow

the formative steps, with one important exception – the rationale of the

inner arcs of the lateral chapels remains unclear. They are not

segments of a circle, parts of an oval, nor freehand arcs. The problem

arises because the equilateral diamond is not the beginning of the plan,

but stage two. The easiest way to construct such a diamond is to

interlock two circles of the same radius, with the centre of one placed

on the circumference of the other. The resultant cell provides not only

the co-ordinates of equilateral triangles but also the dimensions of the

plan. And, most significantly, its segments provide the curvature of the

lateral chapels. Before any symbolic significance (touched upon at the

end of the paper), the interpretative advantages of this proposition are

formal, providing a key to unlocking the developmental sequence of

Borromini’s spatial planning.

Introduction: The Importance of Geometry∗

In 1634 the Spanish Trinitarians commissioned Francesco Borromini to design a

new convent at the four fountains intersection in Rome, dedicated to San Carlo

Borromeo and the Holy Trinity. Despite a tiny site and barely secured funding, a

monastic ensemble was soon raised that would be the envy of every religious

order in the city.1 The ingenuity of the church in particular has been the subject of

much debate, with discussion often skirting the topic of the nature of the Baroque

style itself. What does it represent, a cross or an oval? How should its shifting

Cultural Crossroads: Proceedings of the 26th International SAHANZ Conference The University of Auckland, 2-5 July 2009 2

curves be understood? Interpretation was clarified by Leo Steinberg’s brilliant

doctoral thesis of 1960, which gained wide acceptance following its publication in

1977. Casting aside the erroneous plans that had misled earlier commentators,

Steinberg highlighted the importance of Alb. 171, the earliest surviving plan, and

demonstrated how the church evolved from an elongated Greek Cross to the

eventual synthesis of cross, oval, and octagon.2 He also made an extensive

exegesis of Alb. 173, hidden in the Vienna archive until 1958 and which seemed to

reveal once and for all the plan’s underlying geometrical structure. He summarised

this as follows:

1) Two triangles with shared base, perpendiculars erected over their

sides; 2) Two tangent circles inscribed, yielding the foci – and the short

segments – of an inscribed oval; 3) a double-rail rectangle tangent to

the oval; 4) Semi-circular chapels in the long axis articulated by four

columns; 5) Chamfered corners reducing the rectangle to an octagon;

6) Completion of the side chapels.3

The status of Alb. 173 was diminished when Joseph Connors persuasively argued

that it and others (including Alb. 168, 169, 175, and 176) were reworked or drawn

anew around 1660, when Borromini and the printmaker Domenico Barrière

decided to publish engravings of the monastery.4 At this point, Connors argues,

Borromini layered over the plan a geometrical armature, thereby exposing for the

educated reader the long held secret (already in 1650, the prior of the Trinitarians

had mentioned how often Borromini was harassed to explain his plan) of the

church’s recondite armature.5 For Connors, Alb. 173 is thus deceptive – more a

public relations document than a picture of the San Carlo’s spatial meaning.

Among Borromini’s drawings the true ‘ectoplasmic’ quality of the original plan is

instead better represented by Alb. 172, in which the constructional lines are all but

effaced.6 While Connors does not deny the existence of a geometrical armature,

the displacement of Alb. 173 from the conceptual stage implies its secondary

importance. Steinberg himself had been suspicious of the geometrical scheme he

so cogently outlined, arguing that Alb. 171 was drawn without ruler and compass;

moreover, even the crystalline geometry of Alb. 173 should be understood as a

regularisation rather than ideation of the form.7


The point, however, may be overdrawn. It is one thing to say that the ‘geometrical’

plans are post facto; it is another to suggest that they rationalise the plan in a

manner that distorts its conceptual basis, and imply in the process that Borromini

contrived a geometrical structure that would adhere to a shape conceived at a

separate non-geometrical stage. On close examination there seems no compelling

reason to reject the geometry of Alb. 173 as a good, albeit simplified,

representation of the ordered sequence by which design of the church was

constructed.8 Even though Connors is surely correct in arguing that Borromini

prepared or revised drawings for publication in the 1660s, the dating of the

drawings remains an open issue, and it is inconceivable that we are in the

presence of a complete sequence of preparatory studies (Borromini destroyed

many of his drawings before his suicide in 1667).9 Alb. 173 does indeed present an

ideal version of the plan, but it has not accrued redundant geometry – rather it has

been tidied up, so to speak, with the highlights emphasised.10 (In fact the major

thing wrong with Alb. 173, as will be discussed below, is that it depicts an

undersized church, indicating that Borromini wanted to make the church appear

less cramped within its site than it really was.) The idea that the geometry is

detachable from the church’s shape is itself perverse, as if ropes might not be

required to erect a tent. Borromini seems to have been one of those masters for

whom intention and technique were fused, which is to say that the conceptual

language of his spatial planning was already geometrical. If this were not the case

the dimensions of the seminal schemes of Alb. 171, which involve the ratio of 1:√3

(1.732), would be inexplicable. Moreover, while there is no explicit geometrical

armature in Alb. 172, it is nevertheless replete with constructional lines – ghostly

traces are visible of equilateral triangles, tangents framing the oval, bisecting lines

for the small circles, and so on, all of which can be articulated in reconstruction.

This is so even of the project-style drawing Alb. 170, which suggests that

whenever the plan was drawn the underlying geometry was too – in short, San

Carlo’s shape is difficult to achieve without geometry, and the ratios near

impossible.11 Thus reconstructing San Carlo’s geometry presents, as Alb. 173 so

memorably demonstrates, a composite and artificial – but hardly false – picture; or,

to put it a better way, an idea of the plan.


Figure 1. Reconstruction of Alb. 172.

Biangolo and the Lateral Chapels Nevertheless, something is missing. Scholars assume that the plan’s geometrical

armature, whether retrospective or not, begins with the diamond shape of the two

triangles, as seems to be apparent in Albs. 168, 169, 173, 175 and 176. From here

one can follow the steps in the formation of the plan – with one important

exception. The rationale of the arcs of the lateral chapels remains unclear. One

early commentator suggested they are both segments of a single large circle,

whose centre is the exact centre of the plan – but if that were so, the curvature of

the chapels would be more pronounced.12 To Steinberg, they appeared, once he

had discounted the idea that they echoed the interior cupola, to be drawn

freehand.13 Portoghesi, reprising Sedlmayr, sees the lateral arcs as segments of

two elongated ovals, which answer the semi-circularity of the longitudinal

chapels.14 This view requires that the short elbow-like curves – connecting the

straight diagonals to the shallow curves of the chapels – be segments of small

circles, which they quite clearly are not (it these four elbows which are in fact

drawn freehand). Whatever the case, the lateral chapels cannot be construed as

half ovals.

The problem arises because the equilateral diamond is not the beginning of the

plan, but stage two. The easiest way to construct such a diamond is to set the

compass at either end of the desired base, and draw two arcs, each of which will

be one-third the length of a larger circle. Such a method, which in one sense is an

elaboration of the means by which the longitudinal axis is formed, creates a cell-


like shape with a width to length ratio of 1: √3, which we can call, following Filippo

Juvarra and for want of a better term (the term vesica pisces, which is what many

would call the shape, is anachronistic), a biangolo.15 When the tips of the base line

are connected to the intersecting arcs above and below, end on end equilateral

triangles are created. If the triangles were all that Borromini wanted to inhabit the

plan, then the biangolo would be no more that an invisible means to an end. But

this is not the case, for the biangolo provides the curvature of the lateral chapels.

On each of the plans (Alb. 168-170; 175-76) that show the church in its final or

near definitive state biangolo segments correspond exactly to the arc between the

two innermost lateral columns.

Thus the first step for Borromini would have been to set the compass to the width

of 45 palmi, chosen, as we shall see, for its numeric symbolism and its fittingness

to the site, and construct a biangolo; thence follows the vertical axis and equilateral

triangles.

Figure 2. San Carlo, initial steps.


Figure 3. Inner line of San Carlo.

I hasten to point out that this line was not built, at least on the ground rather than

cornice level; rather it is part of the inner track for the setting of the columns. The

outer track, which corresponds to the walls of the actual church, is also formed by

the curvature of a wider biangolo, with each segment set about 2.5 palmi further

along the horizontal axis (making the wall to wall width of the plan 50 palmi). Thus

a second biangolo can be drawn, enveloping the first, which precisely describes

the outer lines of the plan’s lateral wings.

Figure 4. Inner and Outer lines of San Carlo.


In fact this outer track built was not built either, at least in the lateral chapel, for

there is a further recession to accommodate the side altar paintings. These curved

exedrae are also segments of a biangolo, with the centres set another 1 palmi

(according to Alb. 175 and 176) along the horizontal axis, making the total width of

the church’s horizontal axis 52 palmi.

Figure 5. San Carlo completed: altar recesses, columns,

and adjacent chapels.

I have set out graphically each stage in the construction of the plan, and, although

it is tedious to describe, a summary of the scheme is necessary to highlight the

theory here being advanced (needless to say, the numbered stages are my own,

not Borromini’s): 1) establish scale and horizontal axis, set the compass to 45

palmi, draw biangolo and vertical axis; 2) within the biangolo intersection, bisect

arcs for diagonal axes; inscribe base to base equilateral triangles; 3) within

resulting diamond, construct an oval, following Serlio’s method; 4) rectangle

tangential to oval and another parallel to it, by a width midway between broad

segment of the oval and point of the diamond (3 palmi); 5) establish semi-circular

apses (with 10 palmi radius) on the long axis; 6) rule diagonals, commencing from

the intersection of the apse semi-circles and rectangle, then running parallel to the

diamond and ending at the long side of the rectangle; 7) complete plan with

freehand curves to the lateral segments of the biangolo; 8) second biangolo, five

palmi wider than the first, to establish the outer track of the plan; 9) repeat steps 5,

6, and 7; 10) final biangolo to establish altar exedrae, a further 2 palmi wider (a

depth that is provided by the extending the inner diagonals of the plan down to the


horizontal axis); 11) sixteen columns, just under 3 palmi in diameter, in four

groups, underscoring the cross. Biangoli therefore announce three periods in the

plan. Of course the biangoli are not drawn in full, as Borromini is interested only in

their dimensions and their lateral segments. However, it is useful to keep their full,

twin-circled, representation in mind, as Borromini may have done, because as the

plan is developed the secondary spaces, such as chapels and corridors, take their

cue from the biangolo’s wider elaboration.

Biangoli and the Development of the Plan Apart from explaining the curvature of the lateral chapels, highlighting biangoli in

San Carlo’s plan helps us to reconstruct the earlier planning phases, when the

shape was developed in relation to the site. The first surviving draft of the

monastery is Alb. 171, which shows the plot destined for the church measuring,

once the slight angle of the Strada Felice (now via Quattro Fontane) is squared off,

approximately 65 x 82 palmi. The initial idea for the church, barely visible under the

later revision, is a sort of elongated Greek Cross, with the long axis centred on the

site, and an octagonal chapel in the top corner (the Cappella Barberini, dedicated

to the Madonna).16 Borromini, however, needed to accommodate a sacristy, so he

blocked off one of the lateral chapels and shifted the central vertical axis south

about 6 palmi. The squared space that remains for the church measures 52 x 82

palmi, less once wall thickness is deducted; it is at this point that Borromini laterally

compressed the cross into a shape that would sit within the biangolo. The inner

width (which will define the cornice supporting the pendentive zone) in the second

scheme of Alb. 171 measures 45 palmi, and the length, 78 palmi, a ratio of exactly

1: √3. At this stage the biangolo supplies only the proportions and not the shape,

for in squashing the initial lobed cross Borromini has arrived at a flat walled form in

the side chapels – my eyes, at least, can detect no lateral curvature in the any of

Alb. 171’s pentimenti.


Figure 6. San Carlo: Development of the church in relation

to site.

The second scheme of Alb. 171 is a tight fit and looks as if it has been shunted on

both sides. The solution is Alb. 172, where Borromini makes the church smaller

still: he narrows the longitudinal apses from 25 to 20 palmi in diameter; he pinches

the diagonal bays (which in Alb. 171 were not straight, although it is unclear

whether Borromini preferred convexities or concavities), drawing in the four central

columns so that they now stand as points on a 34 palmi sided square; finally, and

crucially for the present argument, he installs the curvature of the biangolo into the

design by setting the lateral arms onto its shallow arcs. The lobed cross of the

initial scheme in Alb. 171 is reestablished: indeed, although they are differently

shaped, the wall length of longitudinal and lateral chapels is the same, about 33

palmi, as is the inter-columniation.

This is more or less what was built, but Borromini still ran out of room: even

shortening the longitudinal axis, compared to Alb. 172, by 3 palmi (the width to

length ratio line is 45 to 75 palmi, or 1:1.67) did not prevent the high altar exedra

from projecting beyond the site and into the corridor behind.17 When he later drew

a plan intended for publication (Alb. 173) he solved the problem by shrinking the

church nearly 10%, so that its width is 41 palmi, its length 70 palmi (thus returning

to the precise biangolo proportion of 1: √3); while ample space is found for the high

altar exedra behind and even miniature vestibule in front.18 In other drawings (Alb.


170, 175-176), a different strategy of distortion is employed: Borromini maintained

the actual size of the church, but lengthened the plot on which it stands by 10

palmi, with the consequence that the dormitory was shifted east and the garden

diminished.19 In Borromini’s mind, the relationship of the size of church and the

dimensions of its site was never reconciled.

Figure 7. San Carlo dimensions as constructed.

Demonstrating the genesis of the plan in the manner above raises an interesting

possibility. I have proceeded from the inner dimensions (that is, 45 palmi) and

worked outwards. However, what if we worked from the outer dimensions (52

palmi) and then inwards? The reason for suggesting such a sequence is that the

width of larger biangolo fits precisely within the boundaries between sacristy and

cloister allotted to the church. The result is a far simpler geometrical construction.

The 52 palmi cell yields the curves of the altar recesses and equilateral triangles,

whose sides come close to providing the diagonals of the plan. Once the smaller

biangolo is inscribed it is simply a matter of drawing the semi-circular apses on the

vertical axis and the small free hand curves to the lateral chapels to arrive at the

definitive shape. It shows that the plan is but a modification of the initial scheme in

Alb. 171.


Figure 8. San Carlo, hypothetical scheme.

Against this method, and in favour of beginning with the smaller dimension, is the

particular numerical value of 45 palmi. Steinberg noted that since the early

eighteenth century St Peter’s and San Carlo were often compared: the former

could contain the latter within one of its piers, while the diameter of its dome, 186

palmi, is same as the circumference of San Carlo’s.20 Given that the earlier dome

was designed by Michelangelo, Borromini’s hero, it would seem likely that the

coincidence was contrived by Borromini himself. However, the legend is skewed:

by my calculation San Carlo’s oval dome is approximately 136 palmi in

circumference, which even allowing for the difference between plan and

construction (within the standard deviation of 5%), is not remotely close to the

required length.21 The source for the story that Steinberg cites is a stucco account

for the church, which mentions 186 palmi length of ‘Ornamento sotto il

gocciolat[oia]e della cornice principe della ch[ies]a f[att]a a stampa con rose’

[ornament under the drip profile of the main cornice of the church, relief-moulded

with rosettes].22 This cornice is a continuous band duplicating the inner track of the

ground plan; it supports the pendentive zone, which in turn supports the dome. The

number 186 thus refers not to the dome, but to the perimeter of San Carlo’s plan. If

Borromini did wish for this particular concordance with St Peter’s, then creating

circumferential length of the plan to exactly to fit the magic number 186 would have

required some guiding method. This I would suggest is the biangolo – one drawn

with a radius of 45 has a length of 188 palmi (4rπ/3, where r = 45). In fact, 186

palmi is achieved with a radius of approximately 44.5, which turns out to be almost

exactly the width of the church as constructed (9920mm = 44.4 palmi).


Significance Beyond the formal analysis I do not make any grand claims for my theory.

Borromini’s complex geometry and fondness for ovals has led to speculation about

his knowledge of scientists such as Kepler, who discovered the elliptical basis of

planetary orbits, and Galileo, who famously remarked that the secret language of

nature was one of geometry.23 I cannot see my argument affecting one way or the

other such views, although it clearly revises – not replaces, which is too

oppositional – San Carlo’s traditional characterisation as ovular, first advanced in

Borromini’s own time, and continuing as the default category until Steinberg, Blunt,

and beyond.24 Apart from this, the principal significance of this paper is the light it

sheds upon Borromini’s procedure. The biangolo is a basic construction in practical

geometry, of such note that it was referred to in a surveying text-book of 1616

simply as la prima del primo, the beginning of the beginning.25 As Alb. 171 reveals,

at an early stage of planning he had the idea of using the biangolo’s dimensions as

a means of adapting an undulating Greek Cross to the awkward and cramped site.

Once established, he took structural cues from the biangolo’s form – hence the

curvature of the lateral chapels. The proportioning idea gradually assumed control

over other parts of the plan, such as the chapels and exit corridors, all aligned to

the vertical axes of biangoli rotated 45°.

Connors called the plan a sacred theorem. I think puzzle is a better word;

Borromini has solved (although not to the extent he would have liked) the problem

of a small and irregular site, fitting in a church, sacristy, corridors, spiral stair, and

two chapels. And there is no stacking like furniture in a removal van; each space

flows from the other, justified by the overarching method of geometry. This

continues to the last element, so far not considered in the paper, namely the

façade. One might expect that its central convexity is concentric with the semi-

circular apse, as if it were an extension of the geometrical operations going on in

the church itself – this in fact is how the façade is imagined in Alb. 169.26 But

Borromini has to account for the line of the street, about 4° degrees off

perpendicular to the vertical axis of the church. So he rotates the compass to the

south, establishes a new perpendicular, and tilts the façade accordingly. Again,

Borromini legitimises the recalcitrant site with geometry.


Figure 9. Façade analysis: Alb. 169 (left) and Alb. 177

(right).

The dominance of geometry is noteworthy.27 It is the plan’s organic circuitry, which

must be manipulated if even a single component is to change. Even in the 1660

plans, when everything but façade had been built, the graphic dialogue between

geometry and detail remains vital, with divergence from one plan to the other at the

micro-level of wall, niche, and column base. San Carlo’s plan is a perfect example

of Borromini’s belief in the power of the compass to create symmetry, recalled by a

confidant in these words: ‘The beauty of building, like music, depends on numbers,

so that all the parts have such a proportion that with a single opening of the

compass, without ever moving it, everything is measured.’28 Of course, Borromini

opened and closed the compass many times; but he only had to set it to scale

once, when establishing the initial radius of 45 palmi, or whatever was the size of

the biangolo at that stage of planning – thereafter, almost every element is scaled

automatically, by geometry. The drawings for San Carlo are unbelievably rigorous in their construction, and

their countless pentimenti suggest a relentless search for perfection. Even in the

tiny components, such as the jambs giving onto the niches or the orientation of

column bases, an elaborate rationale can be detected, which I freely admit has

often left me floundering to reconstruct. A drawing of the entire church precinct,

with every constructional line visible, is fantastically complex, too much so perhaps

to be of any use, but not fanciful; every line is needed, every line is in fact there in

some form or another. One recalls contemporary descriptions of Borromini as living

only for his art, who would draw all night rather than sleep.29 To good purpose, for

the plans of San Carlo comprise something like a self-contained graphic world.


If the biangolo has any significance beyond its demonstrable presence within the

construction of the plan, it would surely relate to the Trinitarian dedication of

church, the topic Steinberg illuminated.30 The symbolic parallels are obvious: the

biangolo is the creative basis of form, the beginning of the beginning; its dimension

√3 embodies Trinitarian irreducibility; and it spawns the equilateral triangle, the

Trinity’s emblem. At the very least, we know that interlocking circles to form the

biangolo also results in a variation on the emblem for the Trinity: adding an

additional circle to the two required for a biangolo creates a trefoil with a three-

pointed cell in the centre, a three into one motif that Paolo Aresi had featured as a

Trinitarian symbol in his Imprese sacre (Milan, 1625) and which appears as a

stucco moulding on San Carlo’s lavabo niche (near the old sacristy) and as

wrought-iron portalumi installed at the base of the dome.31

This paper has examined the idea of the church’s footprint, seen from above. If we

turn our heads upward, we see the other half, or what is implied, for the lantern

calls in response to the ground plan, like heaven to earth.32 The inscription at the

base of the dome lantern reads: SANCTISS. TRINITATI. BEATOQ. CAROLO.

BORROMEO. D. AN. SAL. M. DC. XL [To the Most Holy Trinity and Blessed Carlo

Borromeo, year of the Lord, 1640]. Above the inscription, on the lantern ceiling, is

an image of the Dove, framed in an equilateral triangle and suspended within an

aureole of light created by the lantern windows below. Poetically, the lantern is a

valve connecting here to the beyond: through it the Dove enters, unlocking the

majesty of the plan and sending a spiritual pulse throughout the room. The idea of

San Carlo as an interior reverberating with sacredness was advanced in Fra

Juan’s 1650 account of the convent, likely written with the imprimatur of Borromini

himself.33 Often cited, but not as far as I know translated, the passage merits

quoting at length – while no doubt imbued with a fair share of self-promotion, and

in parts owing something to Procopius’ description of the St. Sopia (particularly

how it produces in the viewer an insatiable desire to see it again), its imagery

nevertheless suggests something of the spiritual-poetic language of artistic

intention.34

… when [visitors] are inside they cannot do anything other than gaze

upwards to the vault, for everything is disposed in such a way that each

calls to the other, and for those who look upon it each part seems to

glance at the other.… And the more one regards the church the more


pleasure it gives, so that one wants to see it again and leave already

wanting to return.... It seems to me that this is somewhat in imitation,

one might say, of the divine. You recall what St Peter said of the

blessed angels? ‘The Holy Spirit was sent from heaven, which even the

angels want to see.’ [1 Peter, 1,12] … How can the angels yearn and

wish to see the Holy Spirit, when being already blessed they always

see and enjoy it. St Gregory the Great answers this, ‘While this is true,

you also know that the vision is of such quality that they nevertheless

desire to see it.’ [Lib. Moral, 18.28] … Which is to say that, ‘Everybody

in the world, before they see things, wants to see them, and after

having seen them, they are satisfied. But the divine essence is so

enjoyable that when it is seen, satisfying and fulfilling in its exquisite

sweetness, it is not enough, so that one wants to see it again and

again, always finding in it something new.’ The fabric of this church,

when it is seen by these foreigners, seems to suspend their minds,

because they stare at it so fixedly, and after seeing it return to see it

again; and not only many times on the one visit, but also a great many

times on many different days. If one were satisfied and had had

enough after they had seen it, just as if they had seen worldly things,

we would not return many times to see it.… It is true that [other great

Roman churches] are magnificent buildings, but after seeing them once

there is no need to see them again. This church of San Carlo is never

boring, and always seems new, just as Bede said about the Divine

Essence. This church seems shaded with divinity, so sacred that it

gives pleasure, and seeing it creates the desire to see it again…35

What has of course been left unsaid until now is that the plan’s generative cell,

divested of its interlocked circles, is in the form of a mandorla, a shape seen

enthroning Christ, the Virgin, or the Trinity in countless paintings and sculpture.

Indeed, with chapels and corridors axially arranged to create four corners, the plan

as a whole is quinquepartite, like those medieval mandorle that have four

evangelists buttressing the Pantocrater – one could even liken San Carlo’s semi-

circular apses to Christ’s circular halo above and the world beneath his feet. So far,

the term has been avoided because I wanted to focus on the formal construction of

the plan, and mandorla is not a word encountered in contemporary geometry texts.

But Borromini could always operate on more than one level, understanding


biangolo as a mandorla, or vice versa. As a variation of this sacred frame, San

Carlo thus takes the form of a vessel cradling the Trinity – a gift offered, a truth

revealed. Indeed on the presentation drawing (Alb. 172), Borromini drew at the

intersection of axes the Trinitarian cross among a radial spray, the creative spark

from which springs the whole.

Endnotes

∗ Note 1: All dimensions are in palmi romani; 1 palmo = 223.4 mm. Citation of drawings as Alb. 171, 172, etc. refers to Albertina Museum, Vienna, Graphische Sammlung, Az. Rom. Note 2: Reconstruction drawings by the author. Note 3: The author would like to thank Fabio Barry and Peter Carl for detailed readings of the paper. 1 The sequence of construction on the monastery, as testified by the Prior’s account of 1650, is as follows: dormitory 6 July 1634, completed August 1635; cloister began February 1635, finishing June 1636; church began 23 February 1638, consecrated on 26 May 1641. Fra Juan de San Buenaventura, Relatione del Convento di San Carlo alle Quattro Fontane (ca. 1650), J. M. M. Garcia (ed.) (Rome: Polifilo, 1999), 59-60. The curved façade was added in the 1660s. 2 L. Steinberg, Borromini’s San Carlo alle Quattro Fontane: A Study in Multiple Form and Architectural Symbolism (Phd Diss., New York, 1960) (New York: Garland, 1977), 73-94. E. Hempel, Francesco Borromini (Vienna: Kunstverlag, 1924), 38-41, published the anonymous oval plans Alb. 165, 166, and 167, as Borromini’s early ideas for San Carlo, which proved to be major red herrings (see Steinberg, Borromini’s San Carlo, 72). 3 Steinberg, Borromini’s San Carlo, 89. 4 J. Connors advanced this view in numerous articles (e.g., ‘A Copy of S. Carlo alle Quattro Fontane in Gubbio’, Burlington Magazine, 137 (Sept. 1995), 590), and fully spelt out the relationship of Borromini and Barrière in his introduction to Borromini’s Opus Architectonicum (Milan: Polifio, 1998), lvii. As it turned out, Barrière made no prints of the church; however, around 1725, Sebastiano Giannini made one of the plan showing the geometry as depicted in Alb. 173 (although without the centre oval), intended for the projected third volume of Opera del Francesco Borromini, dedicated to San Carlo: J. Connors, in R. Bösel and C. Frommel (eds.), Borromini e l’Universo Barocco (Milan: Electa, 2000), vol. 2, 122. 5 The widespread curiosity in Borromini’s design is reported by Fra Juan di San Buenaventura, Relatione del Convento di San Carlo alle Quattro Fontane (Rome: Polifilo, 1999), 56. 6 Connors, in R. Bösel and C. Frommel (eds.), Borromini e l’Universo Barocco, vol. 2, 118-19. Connors had earlier commented approvingly on Steinberg’s reservations: Review of Steinberg, Journal of the Society of Architectural Historians, 38, 3 (1979), 284. Connors’ view was seconded by Martin Raspe: ‘it is highly doubtful that the underlying lines [of Albs. 168-173] really belong to the planning process.’ Martin Raspe, ‘The Final Problem: Borromini’s Failed Publication Project and his Suicide’, Annali di Architettura, 13 (2001), 135 n. 15. 7 Steinberg, San Carlo, 91-93. 8 Likewise Paolo Portoghesi, who, while accepting that Alb. 173 was done after the fact, is confident that it reveals both the logic of the plan and the triangulated heart of the church as a whole: Portoghesi, Storia di San Carlino alle Quattro Fontane (Rome: Newton and Compton, 2001), 121. 9 On the destroyed drawings, see Raspe, ‘The Final Problem’, 131. In the catalogue essay on San Carlo, Connors hardened his position on the drawings, although he has inadvertently included a project drawing (Alb. 170) in his set of 1660s plans: ‘Questi disegni geometrici [Alb. 168-70, 173, 175-77] sono spesso stati identificati come progetti per la


chiesa, ma in realtà sono stati eseguiti oltre venti’anni dopo e tendono a idealizzare quanto costruito…’: J. Connors, in R. Bösel and C. Frommel (eds.), Borromini e l’Universo Barocco (Milan: Electa, 2000), vol. 2, 110. As I see it, the dating of the relevant drawings, with the exception of Alb. 171, remains murky, mainly because Borromini did not ‘finish’ his drawings. For example, Connors sees Alb. 172 as the only definitive drawing belonging to the planning/construction phase of the church, namely 1634-38, yet it includes the characteristic triple curved façade, which Connors declares only emerges in the 1640s (in Bösel and C. Frommel (eds.), Borromini e l’Universo Barocco, vol. 2, 110). 10 The case of Sant’ Ivo’s drawings are related, but different: the original plan (Archivio di Stato, Rome), drawn ca. 1640, is oriented around a hexagon; in contrast, a later plan, ca. 1659, shows the design based upon an equilateral triangle (Alb. 509). Julia Smyth-Pinney argues that Borromini, in an effort to secure funding from Alexander VII to complete the upper reaches of the church, deliberately altered the geometric rationale to present the conceptual basis of the church in more accessible terms: Julia Smyth-Pinney, ‘Borromini’s Plans for Sant’Ivo alla Sapienza’, Journal of the Society of Architectural Historians, 59, 3 (2000), 312-37. 11 Because of the large number of measurements, Alb. 170 is normally described as a project drawing. Yet for what? It depicts the church sited on a plot 92 palmi in length, not 82 palmi as constructed and as shown in Alb. 171/172/173, and with the garden correspondingly shortened by 10 palmi. 12 V. Fasolo, ‘Sistemi ellittici nell’architettura’, Architettura e Arte Decorative (1939), 318, summarised in Steinberg, San Carlo, 22. 13 Steinberg, San Carlo, 89. Steinberg came closer to the truth when he suggested that the the curves of the lateral chapels were parts of a large oval: idem, 150. 14 Portoghesi, Storia di San Carlo, 121; Connors has the same view: ‘Un Teorema Sacro: San Carlo alle Quattro Fontane, in M. Kahn-Rossi and M. Franciolli (eds.), Il Giovane Borromini: Dagli esordi a San Carlo alle Quattro Fontane (Skira: Milan, 1999), 469. 15 Juvarra’s showed the biangolo cell in his itinerary of figures, Appunti di Geometria (ca. 1709), in Salvatore Boscarino, Juvarra architetto (Rome: Officina Edizioni, 1973), pl. 79. The form does not seem to have had a proper name in Borromini’s time: Serlio demonstrated the construction of the oval via the device, but described in with a descriptive phrase, due cerchi, che uno tocchi il centro dell’altro: Serlio, Tutte l’Opere del Architettura, bk 1 (1537), 14; nor did Scamozzi when he gave the interlocked circles centre position in his tableau of geometry (Vincenzo Scamozzi, L’idea dell’Architettura Universale (Venice, 1615), part 1, bk 1, 32). The term Vesica Pisces [lit. = fish bladder], did not enter the architect’s vocabulary until the nineteenth century, and that mainly in English (OED notes the first use in 1809). The vesica would become bloated with meaning: for example, Ray Lawler, Sacred Geometry: Philosophy and Practice (London, 1982), 33-35. 16 Connors identifies an earlier phase of small cruciform with convex walls (‘Un Teoremo Sacro’, 466). 17 The measured inner line width and length of the actual church is 9920 x 16580 mm, that is 44.5 x 74 palmi. However, if the 1: √3 proportions of Alb. 172 were applied, the length would be 76.5 palmi. 18 Steinberg, taking his measure from the sacristy, thought the site had been increased by 3 palmi. Alb. 173 does not have a scale, but one can be applied by comparing the relative position of the components in the other scaled drawings. A scale can also be inferred by taking into consideration the length of the site, 198 palmi (Fra Juan, Relazione, 51) relative to the plan’s horizontal axis. The undersizing of Alb. 173 was thus unnoticed by Steinberg, among others. 19 This figure has been calculated by comparing the scales in Alb. 170, 175, and 176. There is no scale in Alb. 169; the scale in Alb. 168, which Portoghesi (Storia di San Carlo, 54) dates as wholly of the 1660s, appears to be in a measure smaller than the Roman palmi (according to its scale, written in ink rather than the pencil of the rest of the sheet, the site is 132 wide at the horizontal axis: yet we know that the maximum width of the site is 127 palmi, and approximately 122 at the half way mark). 20 Steinberg, San Carlo, 44.


21 The length of the oval as constructed by Borromini consists of two 120° circular segments with a radius of 13 palmi, plus two 60° segments with a radius of 39 palmi (thus, 52π/3 + 156π/6 = 136). 22 Steinberg, San Carlo, 45. The document was published in Pollak, 90. Steinberg is blurred in his reference to this story (he clearly did not check the measurement of San Carlo’s dome). On page 45 he says ‘the circumference of S. Carlo’s cupolar cornice measures exactly 186 palmi’, making it unclear whether he means the dome cornice or the cornice supporting the domical substructure. On p. 84, he refers to ‘the circumference of S. Carlino’s dome’ equalling St Peter’s. The widespread fame of St Peter’s diametric span comes from Vasari. 23 For example, A. Blunt, Borromini (London, 1979), 47-9; M. Simona, ‘Le Geometrie del Borromini’, in Kahn-Rossi and Franciolli (eds.), Il Giovane Borromini, 453-4; J. Connors, ‘Un Teoremo Sacro’, 469. 24 Portoghesi, Storia di San Carlo, 149-171, provides a thorough review of the critical history. The categorisation of San Carlo’s space as ovular began in Borromini’s own day and continued among the bulk of the formative art historians, including Gurlitt (1887); Schmarsow (1897); Gnudi (1923), who calls it an ellipse rather than oval, no doubt in allusion to Kepler; and Hempel (1924). 25 Bernardo Ricchino, Schemi Geometrici per le Lezioni di Agrimensura (1616, Milan, Cast. Sforzesco), reproduced in Kahn-Rossi and Franciolli (eds.), Il Giovane Borromini, 62. 26 As Alb. 169 shows the façade perpendicular to the long axis of the church, it is likely one of the revisionist plans of the early 1660s. Did Borromini harbour thoughts that this was the ideal of the façade, against which the angled version was the imperfect accident? 27 For Wittkower, the priority of geometry meant Borromini was outside the Renaissance tradition on modular/column based planning: R. Wittkower, Gothic versus Classic: Architectural Projects in Seventeenth-Century Italy (London, 1974), 90. Given Borromini’s outstanding knowledge of antiquity, this view of Borromini is problematic, as is Wittkower’s corollary, namely that Borromini’s planning is medieval. Proportioning according to the width/length ratio of 1:√3, or 1: √3/2, called ad triangulum, remained common in the Renaissance, occurring at Milan Cathedral (famously celebrated in Cesare Cesariano 1521 edition of Vitruvius) and Alberti’s San Andrea in Mantua, among other examples. 28 Reported in a letter of Virglio Spada (7 October 1656) to Cesare Rasponi (Archivio di Stato di Roma, Fondo Spada 494 int. 3, f.42r) quoted in Thelen, ‘Sui disegni di Borromini’, in Bösel and Frommel, Borromini e l’Universo Barocco, 73. 29 F. Baldinucci, Notizie dei Professori del Disegno (Florence, 1681-1728), vol 5, 139; a French visitor to Rome in 1677 recalled that ‘luy faisait passer des nuits entières a ressuer sur quelque partie d’un nuoveau dessein’: in H. Thelen, ‘Sui Disegni di Borromini’, in Bösel and Frommel, Borromini e l’Universo Barocco, vol. 1, 72. 30 Steinberg, San Carlo, 287-331. 31 Thanks to Fabio Barry for the reference to Aresi. 32 Steinberg, San Carlo, 247; Portoghesi, Storia di San Carlo, 119. 33 See Montijano Carcia’s introductory remarks, Fra Juan, Relatione del Convento di San Carlo, 25. 34 For example, ‘No one ever became weary of this spectacle [of the interior of Sancta Sophia], but those who are in the church delight in what they see, and, when they leave, magnify it in their talk.’ Procopius, De Aedificiis, in, The Church of St. Sophia Constantinople (New York, 1894), 28. 35 Fra Juan, Relatione del Convento di San Carlo, 72-73.

Documents

The Curvature of the Lateral Chapels in San Carlo Alle Quattro Fontane