Eggs, turnips and chains: rhetoric and rhetoricians of architecture

Antonio Becchi A strange monarchy be able not only to write but also to think is nei- Another paper included in this volume appro- ther Latin nor English, nor Italian nor Spanish, priately calls to mind the work of Francis Ba- but a language […] in which silent things occa- con. I will adopt a position diametrically op- sionally speak to me, and in which one day I posed to the thoughts expressed there in order shall perhaps justify myself from my grave be- to underline what I consider to be crucial for fore an unknown Judge”1. the historiography of architecture understood “Things”, then, are the focus of attention, or as res aedificatoria. I take my cue from an rather (in Hofmannsthal’s words) “a language apocryphal letter addressed to Francis Bacon. in which silent things speak”. It bears a date that takes us back almost exact- Francis Bacon himself is also linked with a ly 400 years: 22 August 1603. The date is clear- scathing judgement that was formulated ly not random; on 17 August 1603, just five roughly a century ago by the author of a book days previously, the then 18-year-old Federico which, in its own field, is unsurpassed even to- Cesi and his friends , Anasta- day. I am referring to Raffaello Caverni’s Sto- sio de Filiis and Johannes van Heeck had ria del metodo sperimentale in Italia (1891- founded the in the Via 1900), which castigates the prophecies of Baron della Maschera d’Oro in . This apocryphal Verulam as follows: “Francis Bacon gave the letter, written at the beginning of the 20th cen- name Instauratio Magna to his new scientific tury, left an indelible mark on the ensuing kingdom, and he regarded himself as having decades. It was published in the Berlin newspa- been invested as its monarch for having per Der Tag (moderne illustrierte Zeitung) on planned the Encyclopaedia of every art and sci- 18 October 1902. ence in his book De augmentis scientiarum, I am referring, of course, to the famous Brief and for having minutely fixed the rules to be des Lord Chandos an Francis Bacon written followed in experimental method in his Novum by Hugo von Hofmannsthal. I recall it, in spite Organum. It is easy however to persuade one- of the fact that it has lost much of its freshness self that his monarchy was nothing but an emp- through repeated quotation, because I should ty name or, if you like, a kingdom that had al- like to attempt to consider it from the point of ready passed away. For if there is, in fact, no view of the correspondences with which we are such thing as science, and never has been, as concerned here: a letter published a century Bacon maintained, it follows that he divided up ago in Berlin (where the Max Planck Institute the burial niches in his Encyclopaedia without for the History of Science has its seat), ad- having anything to fill them with”2. dressed to Francis Bacon (the focus of our at- Here, too, I shall leave Caverni’s words to res- tention), and dated just a few days after the onate in the background without comment. fateful meeting in the Palazzo Cesi in Rome They speak for themselves. I would only add (not far from the Bibliotheca Hertziana), exact- that the empty burial niches [the loculi vuoti] ly four hundred years ago. I will transcribe a are a warning to us all in this research project, passage from Hofmannsthal’s letter without and convey one admonition in particular that is further comment, which will remain the cantus a real literary case. firmus of my considerations: “I felt at this mo- My considerations will focus on a field of re- ment with a certainty not wholly untinged with search that has not yet found its rightful place pain that I would write no English and no Latin in the order of things and that ekes out a mea- book in the coming years nor in succeeding gre existence on the margins of the official his- years, nor indeed in all the years of my life; […] toriography of architecture: mechanics in an because the language in which I would perhaps architectural context and, more generally, the

97 history of building construction. By this, I do venuto3; from the publications of the Instituto vince us that at last he has understood every- to play a major role in research and teaching. not mean the history of machines, nor even the Juan de Herrera to the book series Between thing. The opposite is the case: he shows that Invited to reflect on the historical approach in history of machines for building sites (on which Mechanics and Architecture (Birkhäuser) and he has not even begun to think about and, what teaching structural disciplines, Del Piero (pro- there is abundant literature), but the branch of Studies in the History of Civil Engineering is worse, to read and look at those things that fessor of Scienza delle costruzioni at the Uni- knowledge that is precisely defined in German (Ashgate). These are encouraging signs, but might have set him thinking. A smattering of versity of ) insisted vehemently that under the heading of “Geschichte der Bausta- they remain sporadic and isolated in nature, the vocabulary of the engineer, a handful of “the science of construction is the science of tik” and which in English is called the “history and it is still difficult for them to obtain the nec- quotations comme il faut, and a good dose of construction”(!) and not its history. In his view, of structural mechanics”. It is no coincidence essary institutional backing and the support amour propre make our author believe he has the historical approach represents a dangerous that I mention this field of research, of course. that is essential for research. found the solution that remains hidden to the derivative that abandons the rigour of the clas- The project “Epistemic History of Architec- rest of us. To find solutions, however, you need sical formal approach – the only method worthy ture” has its origins in a collaboration between Caricatures of thought first to identify the problems; and that is some- of consideration. two institutes, each with its own illustrious tra- To demonstrate this without seeming too elu- thing Fleckner has been unable to do. Del Piero’s febrile words underline the typical dition in fields of research that are apparently sive, I will give two examples – two bad exam- Among its various useful features, the article misunderstanding of a person accustomed to far removed from one another: the history of ples, both of which are revealing and to be presents an image (fig. 1) that is meant to ex- tautologies and afflicted with a worrying lack of architecture and the history of science (with avoided – which symbolically opened and closed emplify the statics scheme to which the author intellectual curiosity. This misunderstanding particular regard to the history of mechanics). the year 2003. refers. In its seemingly innocuous simplicity, was all the more glaringly revealed at a confer- The relations between mechanics and architec- The first example dates from January 2003, this concept of statics would surely leave mod- ence mounted to pay tribute to a scholar who ture will inevitably converge, therefore, in fu- when an article signed by Sigurd Fleckner was ern structural engineers perplexed; and it must has dedicated a large part of his life to advanc- ture investigations: a point of intersection in published in the authoritative journal Bauinge- make a historian’s hair stand on end, conscious ing and developing the “history of the sciences the history of thought that at present plays a nieur under the title “Gotische Kathedralen – as one is of the slow, laborious, hazardous and techniques of construction” and their modest role in architectural historiography. Statische Berechnungen”4. The subject of the progress of knowledge and – in this particular teaching, a scholar who has turned the docta This is indeed an empty or abandoned burial paper is stimulating, and the article is worthy case – of the first mechanical interpretations of curiositas into a lifestyle. niche, sometimes temporarily occupied by of closer reading, judging at least by what is the statics of arches. It goes without saying that The misunderstanding, of which Del Piero be- some vagabond, who comes upon it by chance, promised in the editorial note: “This specialist Fleckner is ignorant of them; probably he does came the mouthpiece, stems from the suspicion driven there by curiosity or by necessity. paper has been scientifically assessed and re- not want to know about them. This is demon- that historical analysis is a soft option, a short One might object that the literature on this viewed”. The article does indeed seem to prom- strated with great clarity by the contents of his cut to relieve “conceptual fatigue” and to trans- subject has grown in recent years, with new au- ise significant new findings, as the author article and the attached bibliography. form the hard core of the discipline into a frag- thors and new research programmes entering stresses. In the introduction and in the text it- The second example is as follows. On December ile popularization of hagiographic character. the limelight. Although I understand the rea- self, one finds the following thesis: “According 2003, a seminar was held in on the There are even those who believe that the his- sons for this objection, I still think that the re- to the present state of research in the history of “Teaching of Scientific Disciplines in the Cur- tory of scientific concepts can be no more than ality is very different – apart from the effects of art, the erection of Gothic cathedrals was main- rent Curriculum of the Faculties of Architec- “anecdotal”. One is aware that this misunder- a Fata Morgana that may deceive the unwary. ly based on empirical knowledge without struc- ture and Engineering” to mark the 72nd birth- standing has had many advocates over the past It is true that several recent projects seem to tural calculations. This paper supports the the- day of Salvatore Di Pasquale. The seminar was century – some distinguished, others less so – indicate a promising development in this line of sis that structural calculations were also car- seen as a good opportunity to review the 40- whose hand was admittedly strengthened by research: from the one launched by Patricia ried out in accordance with the demands of year period of research and teaching during some rather unedifying examples of the histori- Radelet de Grave and Edoardo Benvenuto in modern construction and as demonstrated by which Di Pasquale became the main protago- ography of science. It is hard to believe, 1992, entitled “Between Mechanics and Archi- the buttressing system”. nist of a new way of understanding mechanics though, that this dismissal of the methods of tecture”, to that dedicated to the formation of One cannot help being slightly perplexed by applied to architecture and its teaching within historical analysis could be reaffirmed with an Archive of the Art and Science of Construc- such formulations, torn between a sense of faculties of architecture and engineering (not such assurance as something obvious, especial- tion (founded in Genoa in 1999); from the First headiness and dismay that a person might feel only in Italy). Giampiero Del Piero’s interven- ly by those who ought really to represent the International Congress on Construction Histo- who has managed to escape the rapt gaze of an tion at the seminar, however, made it clear how dignity of their spiritus rector. ry (, January 2003), to the activities eccentric dreamer. Once one has read the pa- much still remains to be done to educate uni- Historiography, then, is regarded as something sponsored by the Construction History Society, per, any feeling of headiness is gone; but one is versity teachers and researchers in this broad- spurious (at least by some distracted and mis- the Sociedad Española de Historia de la Con- still left with a sense of dismay. In his article, er view of knowledge, where historical insights informed representatives of academic culture), strucción and the Associazione Edoardo Ben- our Magellan of historiography wants to con- would seem predestined, by their very nature, instead of being a wonderful opportunity to in-

98 99 1. From FLECKNER 2003, fig. 10. corollary of the spuriously “rigorist” position of 2. From RENN ET AL. 2000, fig. 4. a convenient setting already at hand for exper- Giampiero Del Piero. In fact, the two authors 3. From RENN ET AL. 2000, fig. 5 imentally verifying a method similar to that de- mutually justify each other and represent the (detail). scribed by Galileo on a scale comparable to that two faces of the same problem. This reciprocal of ballistics, the usual context in which projec- justification does not denote the soundness of tile motion was considered at that time”8. their positions, but the risk of falling into the Note 11 (p. 311) explains the genesis of this in- trap of cultural caricatures. terpretation: “Henrik Haak, who constructed It is essential that the new project “Epistemic the apparatus for our reproduction of the his- History of Architecture” does not fall into the torical experiment, has directed our attention same trap. It was born from the need to over- to the fact that the inclined planes depicted by come the limitations, the pigeonholing, imposed Guidobaldo immediately before and almost im- by the traditional disciplines, which have for- mediately after the protocol represent a roof gotten that they are tools in the service of construction”. knowledge, and have too often been trans- Haak is therefore the mediator between me- formed into the arrogant vestals of gleaming chanical and architectural historiography, but vestigate the genesis of the concepts and struc- white sepulchres. the problem remains unresolved, rather like ture of the formal apparatus commonly used by something of secondary importance that is the calculatores. Del Piero cannot yet have The Haak case worth only a marginal note. For a better under- found time to investigate the problem with very To illustrate one of the many possible forms of standing of what has happened, one must re- much attention and to read the texts that could collaboration “between mechanics and archi- turn to 1841, the year in which Guglielmo Libri have opened up new perspectives of thought. tecture”, I should like to dwell briefly on what I published a partial transcription of the manu- Yet little effort would have been needed to en- call the “Haak case”. The name of Henrik Haak script page in question and the respective rich his stock of knowledge. It would be is mentioned in an article I consider of great drawings9 (fig. 4). Neither the roof truss nor enough, for example, to consider the judge- importance. It was published in the “Preprints the text at the top left of the page is mentioned ment of Gottfried Wilhelm Leibniz that Clifford of the Max Planck Institute for the History of in the transcription. The two spheres of inter- Truesdell wanted to adopt as an emblem of the Science” (Preprint 97, 1998) and, two years lat- est are divided by an invisible line that never- review Archive for the History of Exact Sci- er, in the periodical Science in Context6. The theless seems quite concrete and apparently ences: “Utilissimum est cognosci veras inven- paper reproduces a manuscript page by unbridgeable, brutally cutting the manuscript tionum memorabilium origines, praesertim Guidobaldo del Monte7, to which the authors in two. Over the years, other scholars have earum, quae non casu, sed vi meditandi in- devote a magisterial analysis. The subject is the commented on this passage, and more recently notuere. Id enim non eo tantum prodest, ut law that describes the trajectory of projectiles it has been subjected to a new and original in- Historia literaria suum cuique tribuat et alii ad and the interpretation proposed by Guidobaldo terpretation10, in which the roof becomes a pares laudes invitentur, sed etiam ut augeatur del Monte, who compares the trajectory to the “metaphor” for an inclined plane. Here, the ars inveniendi, cognita methodo illustribus ex- line described by a chain [catenella] suspended conjunction of mechanics and architecture oc- emplis”. Let us hope that Del Piero is able to between two points. The comment referred to curs between the lines, in an unspoken form. understand this historical idiom. the manuscript as follows: “At the end of one of Let us now try to imagine the same manuscript Having ascertained the intellectual fragility of Guidobaldo’s notebooks there are two drawings falling into the hands of an architect or an ar- certain apodictic positions, perhaps we could which possibly depict an inclined plane used for chitectural historian (a rather fanciful hypothe- recommend to their devotees a reading of the such an experiment, together with a protocol sis, I admit, but I shall let it stand if only for its recent book by Karl-Eugen Kurrer5, in which which perfectly resembles the description of absurdity). The architect would immediately Goethe’s Adagio is modified but sustained with Galileo’s second method mentioned in the Di- recognize the roof truss, of course, and would excellent arguments: namely, that “the history scorsi (see figures 4 and 5) [in the present pu- perhaps more or less understand the text relat- of structural mechanics is structural mechanics blication figs. 2 and 3]. A closer inspection of ing to the cable [fune]. Furthermore, he or she itself”. We would recommend the same book to Guidobaldo’s drawings shows that they actual- would be extremely interested in those parts of Sigurd Fleckner, who represents the natural ly represent a roof which may well have offered the manuscript (fig. 5) that were ignored in the

100 101 4. Guglielmo LIBRI, Histoire comments quoted above. In this way, the archi- nent parts (rafters, king post, tie beam, struts). 5. From RENN ET AL. 2000, fig. 4 Leon Battista Alberti in his De re aedificato- des Sciences Mathématiques tect would discover that Guidobaldo is here He goes into detail. For example, he notes the (detail). ria12. Once again, then, mechanics; and once en Italie [...], vol. 4, Paris 1841, pp. 397-398. dealing with the gradient of a channel designed bisection in the joint between rafter and strut again, architecture; once again, a text that his- to bring water to a mill and, by analogy, with and accurately marks the absence of junction torians of mechanics have read, hitherto ignor- the gradient of roofs: in other words, the ques- between the tie beam and the king post, which ing the part that concerned architecture, and tion of roof slopes, which was to be a recurrent presupposes a precise mechanical interpreta- which architectural historians have simply not theme in architectural treatises of the period. tion of the structural behaviour of the roof read at all, because it concerned structural me- If the architect in question were a little more truss itself. Guidobaldo draws with a “black- chanics. curious, he or she would go even further and smith’s eye”, so to speak, in what is perhaps an The Haak case is a particularly eloquent exam- note that the structure designed by Guidobaldo improvised but not insignificant way that re- ple of how the separation of canons and, in is far from schematic. Indeed, it is a precise de- calls the “constructional” clarity of Giovanni many respects, the separation of codes, forces scription of the structural details of a roof Battista da Sangallo in the marginal drawings the history of construction and (in a quite spe- heuristic tools of our ancestors, eggs, turnips truss. This is immediately recognizable if one he inserted in the editio princeps of the treatise cial way) the history of architectural mechan- and chains have been transformed by expert compares it with those structures reproduced of Vitruvius11. ics, into a terrain vague of knowledge, into an tightrope walkers into toys, into the compo- in the manuscripts of Taccola, Oreste Vannocci This is a small example through which one can inhospitable and desolate swamp. There the nents of a sophisticated game. Biringuccio, Pellegrino Pellegrini and, to stick follow the history of the “discovery of scientific building site (of whatever kind) is located, a lab- The great fascination exerted by Giovanni to Guidobaldo’s lifetime, Giorgio Vasari. discovery”. It extends from the publication of oratory of ideas between theory and practice, a Poleni’s famous Memorie istoriche della gran Guidobaldo designs not just an inclined plane, the treatise of Guglielmo Libri, who reads space for the verification of mechanics rather cupola del Tempio Vaticano13, in which the au- not even a generic roof truss with its compo- Guidobaldo’s text and recognizes its impor- hastily defined as “rational”. thor describes the analogy between an arch and tance for his own purposes (the history of This no-man’s-land, this free zone, which is, in a catenary curve (fig. 6), has had some surpris- mathematics), through the appreciation of in- principle, exempt from disciplinary idiosyn- ing effects, both overt and covert, in which it is numerable other scholars, down to modern crasies, remains terra incognita. Neither me- difficult to distinguish bavardage from scientif- scholars who broaden their investigation to in- chanical nor architectural historians have ven- ic hypothesis. In the context of some vaulted clude the roof truss and interpret it more gen- tured into it: the former because they do not structures in the Traianeum in Pergamon, for erally as an inclined plane. The question we find it “mechanical” enough; the latter because example, Klaus Nohlen asks whether the Ro- must now ask is whether it is not time to read they do not find it “architectural” enough. The mans were not already using the catenary to this manuscript, too, as a detail – perhaps sig- fact remains that the separation between them define the curvature of vaulting14, while Hans- nificant, perhaps not – in the history of con- is academic and exists only on paper, not in fact. georg Bankel conjectures that the catenary struction. Should we not also read it as source curve was used as a guide in defining the material for the history of mechanics and for The jugglers’ chains scamilli inpares15. The fascination of the cate- the history of construction – all the more so, I will now move on to the second part of my re- nary leads him to write that “one could also since it is not an isolated case, but one of many flections, the part that more directly concerns imagine a sagging chain directly on a vertical examples? the eggs, turnips and chains of my title. Here, drawing surface, a method which to my knowl- To give some idea of how this simple suggestion too, I should have liked to preface my argu- edge has not yet been considered. With two might be fruitful in opening up new research ments with some remarks about the remote nails, a piece of fine chain, and a base divided perspectives, I should add that Bernardino Bal- past, with certain premises that affect the pres- into equal sections, a curve can be quickly de- di da Urbino was a pupil and friend of ent. But since the space at my disposal is limit- signed”16. Guidobaldo del Monte. In his commentary on ed, I shall make only very cursory mention of In the late 1940s, Oscar Broneer17 also spoke of the Mechanical Problems of Aristotelian tradi- this latter aspect. the chain, boldly linking it with the definition of tion (the umpteenth Renaissance comment on It is interesting to note that the question of the the entasis of columns (a thesis revived more these problems that architects ought to read chain has also become a rhetorical topos in the recently by other authors). At the same time, with due attention), Baldi would take the roof historiography of the 20th century. Architects Riccardo Gizdulich believed he could see a cate- truss as a pretext to illustrate the mechanical and archaeologists alike have amused them- nary revolved by 90° in the profile of the Ponte implications for architecture, as an elegant but selves by seeing hanging chains in all sorts of Santa Trinita in Florence. Broneer’s prophetic playful reference to the treatment offered by places, whether rightly or wrongly. From the emphasis recalls that of Bankel: “The much de-

102 103 6. Giovanni POLENI, Memorie istoriche della gran cupola del Tempio Vaticano e de’ danni di essa, e de’ ristoramenti loro, divise in libri cinque, Padova 1748, Tab. D.

bated question whether the curvature in an- 7. James STIRLING, Isaaci Newtoni the image of the former is easy to find, where- cient buildings is to be regarded as an arc of a Enumeratio Linearum Tertii as the second is a good deal harder (as well as Ordinis; sequitur Illustratio circle or a parabola has thus found a new solu- Ejusdem Tractatus Auctore being included in a text that is hard to come by tion. It is neither. It is in essence a catenary, Jacobo Stirling, Paris 1797, and difficult to read)? No, Poleni tells us some- which in a curve as slight as this would be indis- Tab. C, fig. 39. thing more: while Stirling is interested only in tinguishable from a parabola”18. Our discussion the Gedankenmodell, which sums up what we of this problem could, of course, continue at have just been saying, Poleni is interested in some length, recalling the important and more the model as trait-d’union with the mechanical convincing works of Dieter Mertens19 or Lothar interpretation of construction, an interpreta- Haselberger20. tion that takes the problems of the building site I cannot dwell on the question, but it should be into account. borne in mind that fashions condition our inter- Hence the motif of the apparently insignificant pretations and even lead us to draw bizarre and addition: the spheres are not suspended in the exhilarating conclusions. With regard to air, but rest on two bases, which could be the Broneer’s hypothesis, for example, one should heads of columns, for example. These heads ask whether sufficient account has been taken are not horizontal but necessarily inclined. of what Pietro Cataneo wrote in I quattro pri- That means that the reverse catenary arrange- mi libri di architettura (1567), where he ex- ment of the spheres presupposes an impetus plained that the entasis of the column could be towards the outside (in other words, it could be obtained with a long, thin and very flexible affirmed that the tangents of the catenary at wooden batten21. This solution may have its the points of suspension are obviously not ver- roots in remotest antiquity; and it is so much chains and return to those of the exponents of tical). This is a seemingly banal observation, simpler and more convincing (even if less bril- mechanics, in the hope that one day a detailed but it impinges on one of the great problems of liant and symbolic) than the catenary that it historical and critical survey of the various sys- the theory of vaulting: the possibility of defin- was revived by Andrea Palladio22, who claimed tems of catenary construction will be attempt- ing a building that does not cause impetus load- to have invented it himself, maintaining that he ed. Poleni reconstructs the transition from the ing on the supports. The round arch, for in- had illustrated it years before Cataneo. No intuition of Robert Hooke and David Gregory stance, long enjoyed a privileged existence and trace of this solution is to be found in Hasel- to the formulation of James Stirling, right was extolled in architectural treatises because berger’s study Old Issues, New Research, Lat- down to the pages of the Memorie istoriche. it was “firmissimus”: “Ergo rectis arcubus, qui est Discoveries: Curvature and Other Classical This transition is far from self-evident, howev- sese facile tueantur, cordam non exigimus”27. Refinements23, though the author does consider er, if we study the details closely. Let us consid- This, as we know, is mistaken, but it is very se- some Renaissance texts. Gorham P. Stevens24, er the image reproduced by Poleni and the ductive. In the case of the catenary curve, in- on the other hand, confirmed its widespread original one provided by Stirling26 on which the genuously adopted as a panacea for all ills con- diffusion many years earlier, though he re- former is based (figs. 6 and 7). First of all, one nected with the theory of vaulting, this proper- mained trapped in the fascination of “mathe- observes that the focus of attention is a series ty is excluded in principle. In order to guaran- matical” constructions: “The method employed of spheres in equilibrium. The Gedankenmo- tee the constructional equilibrium of an arch in Italy today: the Italian architects of today dell is very clear, even though inevitably far re- designed according to the catenary principle, take a long wooden straight edge, bend it to the moved from the reality of construction, with its one has to ensure the absorption of lateral desired entasis, and then draw the curve. The bricks, stones, mortar and friction. What is ten- loading on the imposts28. method cannot be used for large columns, for sion in the chain (a better model than the cable, If one goes further back in time to Galileo, in the inequality of a long strip of wood causes ir- as Guidobaldo del Monte stresses) is here com- the Seconda Giornata of the Discorsi e Di- regularities of curvature. At best, it is but a pression between the tangent spheres. Is that mostrazioni Matematiche29, one finds a cele- rough method and will not, therefore, be fur- all? Is it, therefore, right for historians to recy- brated passage relating to solids of equal re- ther considered in this paper”25. cle this image repeatedly – substituting the sistance and the “problem of the beam”, in Let us now leave aside the archaeologists’ name of Poleni for that of Stirling – given that which Galileo explains how to design a parabo-

104 105 la. This well-known passage reads as follows: “I on its free end is a parabola (this is the source 8. Jean ERRARD DE BAR-LE-DUC, use an exquisitely round bronze ball, no larger of the quotation above), with an axis parallel to Le premier livre des instruments mathematiques mechaniques, than a nut; this is rolled [tirata] on a metal mir- the longitudinal axis of the beam. This is a cor- Nancy 1584, Tab. 32. ror held not vertically but somewhat tilted, so rect if only partial indication. Galileo adds that that the ball in motion runs over it and presses a homogeneous suspended chain subject to its it lightly. In moving, it leaves a parabolic line, own weight assumes a parabolic form. In this, very thin, and smoothly traced. This [parabola] however, he is mistaken; the form it assumes is will be wider or narrower, according to whether not that of a parabola, but of a hyperbolic co- the ball is rolled higher or lower. From this, we sine. The application of the catenary to struc- have a clear and sensible experience that the tural optimization, however, could not be more motion of projectiles is made along parabolic valid. Galileo does not proceed beyond this lines, an effect first observed by our friend, point, but he does come close to the solution of who also gives a demonstration of it. We shall another problem related to structural optimiza- all see this in his book on motion at the first tion: namely, the transition from the catenary meeting. To describe parabolas in this way, the to the “best form” – not of the beam, but of the ball must be somewhat warmed and moistened arch. by manipulating it in the hand, so that the Precisely this distinction between the two traces it will leave shall be more apparent on types of structural behaviour – that of a beam the mirror. The other way to draw on the prism and that of an arch – leads to the last example the line we seek is to fix two nails in a wall in a I wish to describe. If one goes back a little in horizontal line, separated by double the width time, to the year 1584 to be more precise, one is of the rectangle in which we wish to draw the faced by yet another variation on the problem semi-parabola. From these two nails hangs a of the use of chains in architecture. I refer to an fine chain, of such length that its curve [sacca] invenzione contained in Errard’s Premier li- will extend over the length of the prism. This vre des instruments mathematiques mechan- chain curves in a parabolic shape, so that if we iques32, an extraordinary book that places the mark points on the wall along the path of the “architectural machine” in the classic reper- vention was a solution to this problem33 (fig. 8): dome is compared to a skull, which is not an egg chain, we shall have drawn a full parabola. By toires of machinery that were widespread in an arch made monolithic. In other words, it is and yet recalls an egg in its “structural” char- means of a perpendicular hung from the centre the Renaissance. Here, Errard raises the ques- an architectural oxymoron, which assumes the acteristics: “Although (in truth) no mechanical between the two nails, this will be divided into tion of the distinction I have just drawn: be- most intuitive connotation of the chain; that is cognitions are yet evident of certain strange ef- equal parts”30. tween the beam and the arch. A beam may re- to say, the sum of individual elements firmly fects, in spite of the fact that it is beyond doubt In these few lines, the seduction of the semble an arch if it has a curved profile; but it linked together. An arch of this kind will not ex- that a random act of violence in one part may Gedankenmodell of the catenary reaches its does not ipso facto become an arch in the true ert any outward impetus, because the “lapides produce a disturbance in another different climax and creates a close link between me- sense of the term. At most, it is a beam in the inter se concatenati sunt”. This is a metaphoric part: so it sometimes happens that the skull, chanics and architecture. The passage could be form of an arch. This fine distinction consists shift in the Gedankenmodell of the catenary, of when struck on the right side, remains frac- interpreted as a significant shift in the defini- not in the form, which remains identical, but in which wonderful prefigurations can be found in tured not in the same part, but on the left side, tion of the falling trajectory of projectiles, as the mechanical behaviour. Resting horizontally Leonardo da Vinci’s Taccuini. and vice versa, when struck in that part, is frac- was brilliantly proposed in the above-men- on two columns, a rigid beam forms part of a tured in the other: the which case, called by tioned study31. But one can also perceive a for- trilithic system that does not create lateral im- Skulls, eggs and turnips Hippocrates an accident (as we would translate midable connection between two problems that petus. Moreover, like the arch, the beam may In the case of the egg, too, Poleni’s work Memo- it), is referred to as a counter-fracture by many were to be related only much later and in consist of a number of small elements combined rie istoriche (1748) can be taken as an indirect surgeons: and this happens all the more easily rather a rash way in the case of Gizdulich and together, just as an arch is composed of vous- reference. Special mention should be made of a in those of advanced age, who having almost no the Ponte Santa Trinita in Florence. soirs. To form a beam, however, these elements passage unjustly ignored by scholars (though sutures left in their skull, come to have this al- Galileo states that the “best shape” (in terms of have to be firmly wedged together, otherwise more original and interesting that the well- most in one piece. Is it not to be suspected, solids of equal resistance) of a cantilever loaded the whole structure could collapse. Errard’s in- known one I have already quoted), in which the therefore, that some strange accident (in some

106 107 sense of similar kind) may happen in build- vex, or back, of this bark. The bark, as Signor each man’s intellect would be discerned. Taking analysis. His Idea dell’architettura univer- ings?”34 Viviani says, like all the bark of trees, is every- an egg, therefore, all those masters sought to sale40 contains the following description after a Poleni no doubt arrived at the analogy of the where of the same thickness; so how does it, ac- make it stand upright, but not one of them reference to the dome of S. Maria del Fiore: skull through intensive discussions with his cording to him, withstand such large weights could find the way. Whereupon Filippo, being “This strength and equality of the vault in the friend Giovanni Battista Morgagni, a famous placed on the convex and maintain its constan- told to make it stand, took it graciously, and giv- form of a dome we can ascertain from the expe- anatomist and pathologist with whom he had cy? As we follow his comments, he adds that a ing one end of it a blow on the flat piece of mar- rience of natural things, and especially from conducted experiments on the cardiac muscle. half-barrel vault is built twice as thick at the ble, made it stand upright. The craftsmen the egg; which by its nature having so thin a The anatomical analogy forms part of an illus- base (up to a height of approximately two protested that they could have done the same; skin, and being so weak, nonetheless cannot be trious tradition, to which Alberti had given a thirds), so that the middle part of the arch, but Filippo answered, laughing, that they could broken by human strength, as also Pliny says; decisive impetus. In this case, though, it ac- which pushes on the imposts, will find there also have raised the cupola, if they had seen the for by pressing [it] at both ends [it cannot be quired a novel technical emphasis. greater resistance, and counterpressure. What model or the design”38. broken], as is demonstrated by the vaults of The skull is per se a good model for a dome, i.e. will the architects learn? What will masons do The choice of the egg says a good deal more domes that have the form of a semi-circle or are for a structure that should, if possible, be “thin” when they have to deal with a half-barrel vault? than is expressed in these lines: in the case of steeper in profile, and the flat parts [along the (the example of the Pantheon was much ad- Is the shell able to support very great weights, Columbus, it is a reference to the rotundity of sides of the egg], or segments that form less mired, but would not be reproposed in the same and is it not thicker up to two thirds? Conduct- the earth; in the case of Brunelleschi, to the ro- than half a circle; as may also be deduced from technical and structural terms), but that is also ing careful surveys and tests to this end round tundity of the dome. Was it not the same Alexander Aphrodisias. And we have proved resistant, thanks to its form. The problem is al- Brunelleschi’s cupola is not difficult; it is not Brunelleschi who used clay, wax, wood and that three eggs placed upright on a table, with ways the same, namely to deduce from the na- science similar to that required by speaking of even winter turnips to explain to his workmen a little wax on both ends, have supported the 36 9. Ignace Gaston PARDIES, ture of things (whether one is talking about a a half-barrel vault […]” . 10. Ignace Gaston PARDIES, the constructional idea he had in mind? As An- weight of a metal mortar weighing over 150 La statique ou la science des chain, subject to the natural law of gravity, or a Despite the incontrovertible appeal of skulls La statique ou la science des tonio Manetti narrates with regard to the cupo- pounds”41. forces mouvantes, Paris 1673, skull as a resistant structure) guidelines for and bark, the analogy par excellence remains forces mouvantes, Paris 1673, la of Santa Maria del Fiore: “There are many At that time, Galileo was also considering the p. 149. their artificial reconstruction; i.e. for construc- the egg. Its incredible resistance to longitudi- p. 151. stones and concealed [stones] in the angles resistance of the egg42. Gaston Pardies, too, tion contro natura (stones suspended over a nal compression had been the subject of scien- which are not evident to anyone, while others dwells on the same theme in his La statique ou void tend to fall), and secondo natura (a partic- tific enquiry since antiquity. This is attested by can be seen. Those that can partially be seen la science des forces mouvantes43, going into a ular arrangement of the constituent elements a passage from Pliny the Elder, taken from a are long macigno beams. When he [Bru- wealth of detail. Pardies investigates the guarantees the stability of the whole). The long investigation devoted to the egg37: “Firmi- nelleschi] discussed these with the stonema- strength of the egg, offering explanations and strategy is simple and effective: to comply with tas putaminum tanta est, ut recta, nec vi, nec sons, they could not understand him at all. [He then making a huge and surprising leap to the nature by governing it; and to govern nature by pondere ullo frangantur, nec nisi paululum in- made some models for them] in soft clay and world of architecture. Here is the first part of complying with it. flexa rotunditate”. then in wax and wood. Actually those large the passage in question (fig. 9): “However, it is Thin-walled and yet resistant by virtue of its At some point – it is difficult to say precisely turnips, called “calicioni” (large goblets), as well to remark that no body ever breaks un- form, the cranium is undoubtedly a good exam- when – the egg also became a recurrent image which come on the market in winter, were use- less its parts are overdrawn [subjected to too ple to follow. Another example taken from the in relation to architectural construction. For ex- ful for making the small models and for ex- much tension]; and if a glass that resists tension natural world could also be adopted as a model ample, one recalls the anecdote in which, plaining things to them”39. breaks when one wants to bend it, it is by means in architecture: the bark of trees, as Vincenzo strangely enough, both Filippo Brunelleschi Among other edible analogies, one recalls of this inflexion: namely, more effort is needed Viviani suggested in the late 17th century35, in- and Christopher Columbus share a role. In Leonardo’s “oranges”, in other words, domes to exert pressure on the convex parts than curring the criticism of the irascible Bar- Brunelleschi’s case, the egg is cited by Vasari that, in collapsing or cracking, behave like would be needed by pulling the glass straight at tolomeo Vanni (1662-1732): “The same author with regard to the famous dispute about how to squashed oranges; or the “pomegranates” of the two ends, as we will be able to see in the con- [Vincenzo Viviani] informs us that this form of raise the cupola of Santa Maria del Fiore in the three mathematicians Jacquier, Le Seur tinuation of this discourse. It is for this reason vault [barrel vault] is the most ancient, as if Florence: “They would have liked Filippo to and Boscovich, who use the analogy of this fruit that we find so prodigious a resistance in an egg they [the ancients] had learnt it from nature it- speak his mind in detail, and to show his model, in their analysis of the dome of the Vatican that we would like to crush by pressing it from self by observing that, since it enjoys a circular as they had shown theirs; but this he refused to Basilica. Boscovich was to return to the same end to end between our two hands: something form, even the thin bark that surrounds the do, proposing instead to those masters, both image in the Scrittura dedicated to the tiburio that would seem all the more surprising to trunk of a tree, if sawn in half and laid on the the foreign and the native, that whosoever of Cathedral. those who don’t know the reason for it”44. ground with the concave part below, is able to could make an egg stand upright on a flat piece It was Vincenzo Scamozzi, however, who took Viviani, too, had read and annotated these support very large weights placed on the con- of marble should build the cupola, since thus the decisive leap in the direction of mechanical pages45, and from this (together with his read-

108 109 ing of Scamozzi’s treatise) he derives the idea one might come to the conclusion that this fabric 1 “Ich fühlte in diesem Augenblick mit tionale de France, Paris, MS Lat. 10246, nezia 1567 (1st edition: 1554), book 5, te, ma alquanto inclinato, sì che la palla einer Bestimmtheit, die nicht ganz oh- 1587-1592. chapter 11. nel moto vi possa camminar sopra, cal- of comparing the dome of Santa Maria del of mechanics and architecture should finally find ne ein schmerzliches Beigefühl war, daß 8 RENN ET AL. 2000, p. 311. 22 Andrea PALLADIO, I quattro libri del- candolo leggiermente nel muoversi, la- Fiore to an egg. Pardies goes beyond this, how- patient weavers: among theoreticians of me- ich auch im kommenden und im folgen- 9 Guglielmo LIBRI, Histoire des Sci- l’architettura di Andrea Palladio, Ve- scia una linea parabolica sottilissima- ever. His remarks on the “prodigieuse résist- chanics, among architects, architectural histori- den und in allen Jahren dieses meines ences Mathématiques en Italie [...], vol. nezia 1570, book 1, chapter 13. mente e pulitissimamente descritta, e Lebens kein englisches und kein latei- 4, Paris 1841, pp. 397 et seq. 23 Lothar HASELBERGER, “Old Issues, più larga e più stretta secondo che la ance de l’œuf” give rise to a curious mechanical ans and historians of science, in the context of a nisches Buch schreiben werde: [...] 10 RENN ET AL. 2000. New Research, Latest Discoveries: proiezzione si sarà più o meno elevata. interpretation of architecture (fig. 10): “In this rigorous, systematic and far-sighted “Epistemic nämlich weil die Sprache, in welcher 11 See MS Corsini 50.F.1, Biblioteca Curvature and Other Classical Refine- Dove anco abbiamo chiara e sensata e- way columns can be made of wooden planks, History of Architecture”. nicht nur zu schreiben, sondern auch zu Corsiniana (Rome). Facsimile in Ingrid ments”, in Appearance and Essence. sperienza, il moto de i proietti farsi per denken mir vielleicht gegeben wäre, D. ROWLAND, ed., Vitruvius. Ten Books Refinements of Classical Architecture: linee paraboliche: effetto non osservato which will be very strong; because if they are To achieve this, however, one would need to weder die lateinische noch die engli- on Architecture. The Corsini Incunab- Curvature, Conference proceedings, L. prima che dal nostro amico, il quale ne joined together like the staves of barrels, by overcome, once and for all and in a resolute and sche, noch die italienische oder spani- ulum. With the annotations and auto- Haselberger, ed., Philadelphia 1999, pp. arreca anco la dimostrazione nel suo li- sche ist, sondern eine Sprache […], in graph drawings of Giovanni Battista 1-68. bro del moto, che vedremo insieme nel giving them a slight curve, and surrounding incisive manner, the growing pains that have welcher die stummen Dinge zuweilen da Sangallo, Roma 2003. 24 Gorham P. STEVENS, “Entasis of Ro- primo congresso. La palla poi, per de- them with some iron rings, these hollow left their mark on our research and on that of zu mir sprechen, und in welcher ich 12 Bernardino BALDI, In mechanica man columns”, Memoirs of the Ameri- scrivere al modo detto le parabole, biso- columns would be capable of supporting very others into the ars aedificandi. This research, vielleicht einst im Grabe vor einem un- Aristotelis problemata exercitationes. can Academy in Rome 4 (1924), pp. gna, con maneggiarla alquanto con la bekannten Richter mich verantworten Adiecta succinta narratione de autoris 121-152. mano, scaldarla ed alquanto inumidirla, heavy loads. Ancient architects apparently took as I have suggested, suffers from three main werde.” Hugo von HOFMANNSTHAL, vita et scriptis, Mainz 1621, pp. 101- 25 STEVENS 1924, p. 126. ché così lascerà più apparenti sopra lo this into account in their construction of ills. Firstly, it is threatened by those who deny “Brief des Lord Chandos an Francis 104. See Antonio BECCHI, Q. XVI. 26 James STIRLING, “Methodus dispo- specchio i suoi vestigii. L’altro modo, Bacon (A.D. 1603, diesen 22ten Au- Leonardo, Galileo e il caso Baldi: nendi quotcunque Sphaeras in Forni- per disegnar la linea, che cerchiamo, columns, which they made round and slightly or ignore the value of history for the develop- gust)”, in Der Tag, moderne illustrierte Magonza, 26 Marzo 1621, Venezia 2004. cem. Et inde Demonstratur Proprietas sopra il prisma, procede così. Ferminsi 46 bulging [at the centre]” . ment of scientific knowledge. Secondly, it is im- Zeitung, 18 October 1902 (English 13 Giovanni POLENI, Memorie istoriche praecipua Curvae Catenariae”, in ad alto due chiodi in un parete, equidi- Once again, then, the question of entasis is ad- paired by a toothless historiography that is in- translation by Peter Spring, 2005). della gran cupola del Tempio Vaticano idem, Lineae Tertii Ordinis Neutonia- stanti all’orizonte e tra loro distanti il 2 “Francesco Bacone dette al suo nuovo e de’ danni di essa, e de’ ristoramenti nae, sive Illustratio Tractatus D. Neu- doppio della larghezza del rettangolo su dressed; once again a text on mechanics deals capable of coming to grips with the problems Regno scientifico il nome d’Instauratio loro, divise in libri cinque, Padova toni De Enumeratione Linearum Ter- ’l quale vogliamo notare la semiparabo- with problems of architecture. In analysing and that is accustomed to cooking an insipid Magna, e si credè di dover esserne in- 1748. tii Ordinis. [...], Oxford 1717, pp. [11]- la, e da questi due chiodi penda una ca- 14 these issues, one would have to reread the cor- epistemic broth in which documentary sub- vestito Monarca, per avere architettata Klaus NOHLEN, “Concameratio: eine [14]; Stirling’s essay was studied in its tenella sottile, e tanto lunga che la sua l’Enciclopedia d’ogni scienza e arte nel leichte Wölbschale in Pergamon. War original edition (1717), but the picture sacca si stenda quanta è la lunghezza respondence between Evangelista Torricelli stances of uncertain origin float. Thirdly, it is libro De augmentis scientiarum, e per den Römern die Kettenlinie für die shown here was copied – for conserva- del prisma: que-sta catenella si piega in and Michelangelo Ricci on the problem of rendered sterile by a sort of ping-pong between aver nel Novum Organum minutamen- Formgebung von Wölbungen be- tion reasons – from an edition published figura parabolica, sì che andando pun- 47 te divisate le regole da seguirsi nel me- kannt?”, in Bautechnik der Antike, in 1797. See James STIRLING, Isaaci teggiando sopra ’l muro la strada che vi “cracked” columns , already considered by academic disciplines and by a perverse pigeon- todo sperimentale. È facile però per- Conference proceedings, A. Hoffman, Newtoni Enumeratio Linearum Tertii fa essa catenella, haremo descritta Truesdell in his essay The Rational Mechanics holing of studies in which so-called experts di- suadersi che quella sua Monarchia non E.-L. Schwandner, W. Hoepfner and G. Ordinis; sequitur Illustratio Ejusdem un’intera parabola, la quale con un per- of Flexible or Elastic Bodies, 1638-178848 and vide the exploration of a network of themes era altro che di un nome vuoto, o se si Brands, eds., Mainz 1991, pp. 166-171. Tractatus Auctore Jacobo Stirling, Pa- pendicolo, che penda dal mezo di quei vuole, di un regno già trapassato. Se, in- 15 Hansgeorg BANKEL, “Scamilli in- ris 1797, table C, fig. 39. due chiodi, si dividerà in parti eguali.” analysed by Paolo Galluzzi in a paper that still among themselves: to you the holes, to me the fatti, scienza veramente non ci è, e non pares at an Early Hellenistic Ionic 27 Leon Battista ALBERTI, Leonis Bap- GALILEI 1638, Seconda Giornata. Eng- has a lot to teach us49. cords. ci è stata mai, come vuole Bacone, egli Propylon at Knidos – New Evidence for tistae Alberti Florentini viri clarissi- lish translation from , divisa dunque nella sua Enciclopedia i the Construction of a Curvature”, in mi de Re aedificatoria opus elegantis- Two New Sciences, Including Center of If we consider that a few years later Leonhard By carving up disciplines in this way, one plays loculi senza avere di che riempirli.” Appearance and Essence. Refinements simum, et quam maxime utile, Firenze Gravity & Force of Percussion, transl., Euler was to clarify the “buckling problem” with the mesh and the openings in the net, but Raffaello CAVERNI, Storia del metodo of Classical Architecture: Curvature, 1485, book 3. with introduction and notes, by S. Dra- (buckling of a compressed beam) by analysing the essential elements are allowed to fall sperimentale in Italia, vol. 1, Firenze Conference proceedings, L. Haselber- 28 The problem had already been point- ke, Madison, Wisc./London 1974, pp. 1891, p. 118 (English translation by Pe- ger, ed., Philadelphia 1999, pp. 127-138. ed out by David Gregory, “Catenaria. 142 et seq. the force des colonnes, and that soon afterwards, through the gaps and slip away as if they were ter Spring, 2005). 16 BANKEL 1999, p. 135 and fig. 6.13. Ad Reverendum Virum D. Henricum 31 RENN ET AL. 2000. the great mathematician Louis Lagrange was to something irrelevant. As a result, architecture 3 See Antonio BECCHI, Massimo CORRA- 17 Oscar BRONEER, “Measurements and Aldrich S.T.P. Decanum Aedis Christi 32 Jean ERRARD DE BAR-LE-DUC, Le tackle the question of entasis mathematically, is divorced from its history in the shortsighted DI, Federico FOCE and Orietta PEDE- Refinements of the South Stoa at Oxoniae”, Philosophical Transactions premier livre des instruments mathe- MONTE, eds., Construction History. Re- Corinth”, American Journal of Ar- 19 (1695-1697), pp. 637-652, p. 641: “Ex matiques mechaniques, Nancy 1584. citing architectural literature on the subject view of those who don’t understand the premis- search Perspectives in Europe, Firenze chaeology 53, no. 2 (April-June 1949), praecedente Corol. 5. colligitur quali vi 33 See Antonio BECCHI, “Chambre H. (Vitruvius, Vignola, Palladio, François Blondel), es of ars inveniendi. 2004. pp. 146 et seq. arcus, muros quibus insistit extra pro- Per una storia del costruire”, in Degli 4 Sigurd FLECKNER, “Gotische Kathe- 18 BRONEER 1949, p. 147. pellit; nempe haec eadem est cum parte archi e delle volte. Arte del costruire dralen – Statische Berechnungen”, 19 Dieter MERTENS, “Zur Entstehung vis Catenam sustinentis, quae secun- tra meccanica e stereotomia, A. Becchi Bauingenieur (January 2003), pp. 13- der Entasis griechischer Säulen”, in dum directionem Horizontalem trahit. and F. Foce, eds., Venezia 2002, pp. 17- 23. Bathron. Beiträge zur Architektur und Quae enim in Catena introrsum trahit 127, pp. 41-48. 5 Karl-Eugen KURRER, Geschichte der verwandten Künsten. Festschrift für vis, in arcu Catenae aequali, extrorsum 34 “Benchè (a parlar con tutta la verità) Baustatik, Berlin 2002. H. Drerup, H. Büsing and F. Hiller, propellit.” di certi strani effetti di scissure non si 6 Jürgen RENN, Peter DAMEROW and Si- eds., Saarbrücken 1988, pp. 307-318. 29 Galileo GALILEI, Discorsi e dimostra- abbiano ancora evidenti meccaniche co- mone RIEGER, “Hunting the White Ele- 20 Lothar HASELBERGER and Hans SEY- zioni matematiche, intorno a due nuo- gnizioni, non ostante egli è fuor di dub- phant: When and How Did Galileo Dis- BOLD, “Seilkurve oder Ellipse? Zur ue scienze attenenti alla mecanica & i bio, che una disordinata violenza in una cover the Law of Fall?” (with an appen- Herstellung antiker Kurvaturen nach mouimenti locali, Leiden 1638. parte può produrre lo sconcerto in dix by Domenico Giulini), Science in dem Zeugnis der Didymischen Kurven- 30 “Io ho una palla di bronzo esquisita- un’altra diversa parte: siccome accade Context 13, nos. 3-4 (2000), pp. 299-419. konstruktion”, Archäologischer Anzei- mente rotonda, non più grande di una tal volta, che il cranio percosso nella 7 Guidobaldo del Monte, Meditatiuncu- ger (1991), pp. 165-188. noce; questa, tirata sopra uno specchio parte destra, non nella parte medesima lae Guidi Ubaldi [...], Bibliothèque Na- 21 Pietro CATANEO, L’architettura, Ve- di metallo, tenuto non eretto all’orizon- resti fesso, ma nella sinistra, e vicende-

110 111 volmente che percosso in questa, si fen- quella, che richiede il parlare d’una vol- parte, di macigni lunghi; che quand’è ne jamais, que quand ses parties sont trop da in quella: il qual caso, chiamato da ta a mezza botte [...].” Bartolomeo Van- parlava agli scarpellini, a nessuno modo tirées; & si un verre qui résiste à la Ippocrate (tradurremo così) sfortuna, ni, Discorso Sopra i difetti, e Vizi delle lo potevano intendere. E quando con traction se casse quand on le veut faire da molti Cerusici viene detto Contrafis- fabbriche (...), Archivio di Stato di Fi- terra molle e quando con ciera, quando ployer, c’est que par le moyen de cette sura: e ciò molto più facilmente avviene renze, MS f.212. See Luigi ZANGHERI, con legnami, e in vero lo serviva molto inflexion, on tire les parties convexes in coloro, che per l’età avanzata non ed., Avvertimenti e discorsi di Bartolo- quelle rape grandi, che vengono la ver- avec plus d’effort qu’on ne sauroit faire avendo quasi più suture nel cranio, ven- meo Vanni, Ingegnere Mediceo (1662- nata in mercato, che si chiamano cali- en tirant droit le verre par les deux gono ad aver questo quasi tutto d’un 1732), Firenze 1977, p. 62. The same re- cioni, a fare e modegli piccoli ed a mo- bouts, comme l’on pourra voir dans la pezzo. Non è dunque da sospettarsi, che marks are also to be found in Bartolo- strare loro.” Cf. Antonio MANETTI, Vita suite de ce discours. C’est pour cela nelle Fabbriche ancora alcun strano ac- meo Vanni, Pareri di Bartolommeo di Filippo Brunelleschi, preceduta da qu’on trouve une si prodigieuse résist- cidente (in qualche maniera di simil ge- Vanni intorno alle fabbriche degli ar- La novella del grasso, critical text edi- ance dans un œuf qu’on voudroit écra- nere) accader possa?” POLENI 1748, col. chi, de’ voltami, e delle cupole, Bibliote- tion by Domenico De Robertis with in- ser en le pressant de bout en bout entre 115 (English translation by Peter ca Riccardiana (Florence), MS 2141 troduction and notes by Giuliano Tan- les deux mains: ce qui paroist bien sur- Spring, 2005). (English translation by Peter Spring, turli, Milano 1976, pp. 97 et seq. English prenant à ceux qui n’en savent pas la 35 Vincenzo VIVIANI, Formazione, e 2005). translation of Antonio MANETTI, The raison.” PARDIES 1673, p. 148 (English misura di tutti i cieli [...], Firenze 1692, 37 Caius PLINIUS SECUNDUS, Historia Life of Brunelleschi, introd., notes and translation by Peter Spring, 2005). p. 18. naturalis. See Caius Plinius Secundus, critical text edition by Howard Saal- 45 See Isabella TRUCI and Marta ZAN- 36 “L’Autore [Vincenzo Viviani] medesi- Historia naturalis ex recensione I. man. English translation of the Italian GHERI, eds., La collezione galileiana mo ci informa, che questa volta [quella Harduini et recentiorum adnotationi- text by Catherine Enggass, University della Biblioteca Nazionale di Firenze, a botte] sia la più antica, come che dal- bus, vol. VIII, I, Torino 1832, book 29. Park/London 1970, pp. 92 et seq. vol. 3, 2, Roma 1994, p. 301. la natura medesima l’imparassero nel- 38 “Egli arebbono voluto che Filippo 40 Vincenzo SCAMOZZI, L’idea della ar- 46 “Ainsi l’on peut faire des colonnes de l’osservare, che godendo essa della for- avesse detto l’animo suo minutamente e chitettura universale, Venezia 1615. planches de bois, qui seront tres-fortes; ma circolare, fin la sottile scorza, che mostro il suo modello, come avevano 41 “Questa forza, & egualità della Volta à car si on les joint ensemble comme les circonda il fusto d’un albero segato nel mostri essi modelli e disegni loro; il che Cupola la potiamo conoscere anco con doiles des barriques, en leur donnant mezzo, e messo a diacere col concavo non volse fare, ma propose questo a’ l’esperienza delle cose naturali, e spe- une petite courbure, & les environnant per di sotto e valendole a sostenere maestri e forestieri e terrazzani, che chi cialmente dal vuovo; il quale per sua na- de quelques cercles de fer, ces colonnes grandissimi pesi posati sul convesso, o fermasse in sur un marmo piano un uo- tura havendo un scorzo cosi sottile, e ainsi creuses seront capables de sup- schiena di tale scorza. La scorza che di- vo ritto, quello facesse la cupola, ché debole, niente di meno non è forza hu- porter de tres-pesants fardeaux. Il y a ce il Sig.re Viviani, come sono tutte le quivi si vedrebbe lo ingegno loro. Fu mana, che lo possi rompere, come disse apparence que les anciens Architectes scorze degli alberi, è da per tutto della tolto uno uovo, e da tutti que’ maestri anco Plinio; perche strignendolo per il ont eû égard à ceci dans la construction medesima grossezza; e come ella per il provato a farlo star ritto, nessuno sape- capo, e punta, che dimostrano i Volti di des colonnes qu’ils ont fait rondes & un suo detto, resiste a così gran pesi posti va il modo. Fu loro detto a Filippo ch’e’ mezo cerchio, ò apuntati, & i suoi lati peu renflées.” PARDIES 1673, pp. 151 et sul convesso e manterrà la sua costan- lo fermasse, et egli con grazia lo prese, quelli scemi, ò manco, che di mezo cer- seq. (English translation by Peter za? Mentre noi seguitiamo la sua lettu- e datoli un colpo del culo in sul piano del chio; come si può trarre anco da Ales- Spring, 2005). ra, soggiunge, si lavora la volta a mezza marmo lo fece star ritto. Romoreggian- sandro Affrodiseo: e noi habbiamo fatto 47 See Gino LORIA and Giuseppe VAS- botte, e giù basso ne fianchi, sino a due do gl’artefici che similmente arebbono prova, che tre vuova fernate in piedi sù SURA, eds., Opere di Evangelista Torri- terzi in circa dell’altezza, la fanno fare fatto, rispose loro Filippo ridendo che una tavola, conun poco di cera da ambi i celli, vol. 3, Faenza 1919, pp. 91 et seq. il doppio più grossa, affinchè il rima- egli averebbono ancora saputo voltare capi, hanno sostenuto il peso d’un mor- 48 Clifford A. TRUESDELL, “The rational nente dell’arco di mezzo, che gravando la cupola, vedendo il modello o il dise- taio di metallo di più di 150. libre di mechanics of flexible or elastic bodies, spinge alle bande, trovi quivi maggior gno.” Giorgio Vasari, Vita di Filippo peso.” SCAMOZZI 1615, part 2, book 8, 1638-1788”, in Leonhardi Euleri Opera resistenza, e contrasto. Che cosa impa- Brunelleschi, in Giorgio VASARI, Le vi- p. 320 (English translation by Peter Omnia, vol. X-XI, ser. secunda, Zürich reranno gl’Architetti? Che faranno i te de’ più eccellenti architetti, pittori, Spring, 2005). 1960, p. 53, note 1. Muratori avendo fra mano le volte a et scultori italiani [...], Firenze 1550 42 Galileo GALILEI, Le opere, Firenze 49 Paolo GALLUZZI, “Le colonne fesse mezza botte? La scorza è valevole a so- (English translation by Peter Spring, 1968, vol. VIII, pp. 604 et seq. degli Uffizi e gli screpoli della cupola: il stenere grandissimi pesi, e non è sino a 2005). 43 Ignace Gaston PARDIES, La statique contributo di Vincenzo Viviani al dibat- due terzi più grossa? Il fare le attenti 39 “E sonvi molte pietre, e delle nasco- ou la science des forces mouvantes, tito sulla stabilità della cupola del Bru- ricognizioni, e le sessioni di proposito ste negli angoli, che none apariscono a Paris 1673. nelleschi”, Annali dell’Istituto e Museo intorno alla gran Cupola del Brunelle- nessuna evidenza, e di quelle che appa- 44 “Cependant il est bon de remarquer di Storia della Scienza di Firenze, A. 2, sco, non è fatica, non è scienza simile a riscono, e di quelle che appariscono in que nul corps absolument ne se romp fasc. 1 (1977), pp. 71-111.

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