Between architecture, science and technology: the Accademia della Vachia in Florence, 1661-1662

Hermann Schlimme The intercourse between building practice and et di chi ha Risoluto. It describes the activities natural philosophy – and especially mechanical of a discussion circle that existed from 1661 to science – has found new interest among schol- 1662 in Florence, a city which at that time was ars in recent times1. One aim of their research a major centre in the development of natural has been to overcome the division that exists science. In the present book, the academy will between the history of mechanics on the one be referred to as the Accademia della Vachia3. hand (which has traditionally been treated as Its members included the mathematician and part of the history of science) and the history of architect Cosimo Noferi, who pursued many of building technology, on the other hand, which is the topics discussed by the academicians in his generally subsumed in the history of architec- Travagliata Architettura (which has only re- ture. Indeed, in early modern times, no con- cently been published4); the mathematician stant or institutional link is evident between Domenico Fontani; Francesco Barzini and Gio- these two realms. Technology and building con- vanni Andrea Albizzini, who were professors struction were not official disciplines at the uni- for astronomy and philosophy respectively; Ja- versities; and the well-known 17th-century copo Ramponi and Giuliano Ciaccheri, building Italian professional associations and institu- engineers from the Parte Guelfa; and the sculp- tions tended to stress their own identity. One is tor and Accademico del Disegno Jacopo Foggi- familiar with scientifically oriented organiza- ni. The historical significance of the Accademia tions like the Accademia dei Lincei in Rome della Vachia, however, lies less in the impor- (1603–51, with long interruptions) and the Ac- tance of its individual members than in the fact cademia del Cimento in Florence (1657–67), that it was a forum where people of different where experiments were carried out in an ef- professional backgrounds collaborated. Some fort to comprehend the laws of nature. Con- of the members were followers of Galileo. The struction technology was institutionalized in manuscript contains evidence that links the craft guilds and also in the Parte Guelfa, the academy with Medici circles5. The academi- most important building authority in grand- cians met on Sundays as a rule, or at least this ducal Tuscany. Architects, painters and sculp- can be proved for the period from 30 October tors, on the other hand, had broken away from 1661 to 4 March 16626 (cf. table in appendix trade organizations. In Florence from the late listing all the problems). Every week, the acad- 16th century onwards, for example, they were emicians would set each other between one and organized in the Accademia del Disegno. Paral- three tasks or “problems”. Solutions were pre- lel to the creation and development of profes- pared for the following week, when they would sional associations and institutions, interaction be discussed. The manuscript contains 52 of was common between specific fields of expert- these tasks with all the solutions that were pro- ise and certainly of no less significance. En- posed. The academicians occupied themselves counters between disciplines often took place with mathematical problems (especially ones removed from the institutional context, howev- involving sections of cones and perspective er, and in many cases in private, as a result of geometry); with the construction of machinery which they are not so well documented. Never- and instruments of measurement; with techni- theless, numerous sources reveal the culture of cal issues relating to the erection of large-scale discussion at that time as an important field of sculptures; and with many areas of construc- study2. One point of reference in this respect is tion, from roofs, conversion work and fortifica- a hitherto unpublished manuscript in the Bi- tions to hydraulic, theatre and bridge struc- blioteca Nazionale di Firenze bearing the title tures. The academicians analysed the various La Risoluzione di più Problemi stati proposti branches of craft knowledge and sought to ex- nel Accademia del Sig. Abate Ottavio della tend technical learning, incorporating findings Vachia L’anno 1662 con i Nomi di chi propose from the natural sciences. The manuscript con-

61 tains rare source material, but the Accademia The manuscript Fondo Nazionale II_46: treatises on geometry and civil and military ar- same time, he recognizes the ingenuity of some della Vachia described therein is almost com- present state of research chitecture, was a pupil of our philosopher of the solutions to the geometric problems, but pletely forgotten today – unjustly so. For that The manuscript Fondo Nazionale II_46 com- [Galileo]. He was involved in an academy con- without going into detail. On page 118, Giovan- reason, it has been made the subject of this prises 159 pages of irregular format and of dif- cerned with geometry and to which various nozzi promises an essay on the academy (“Ne work; and in the second part of the book, a full ferent qualities of paper. The documents were compatriots belonged [citizens of the Grand darò un saggio”), but no such work was ever transcription is provided of the hitherto un- partially folded and bound in a cardboard cover Duchy of Tuscany]. The meetings were held in published. It is remarkable that even Maylen- published manuscript, with reproductions of 33 × 23 cm in size. The records of the academy 1660 at the house of Abbot della Vacchia, a Flo- der11, the standard authority on Italian acade- all the images it contains. In addition, commen- had evidently been compiled, therefore, to form rentine patrician. The members were the mies, does not allude to the Accademia della taries illuminate various aspects of the histori- a single manuscript. Internal information, such above-mentioned Noferi, Giuseppe Balatri, Ia- Vachia. In 1960, Michelangelo Muraro men- cal context. as dates and the summaries of individual tasks, copo Foggini, Orazio Vanni, Domenico Masini, tioned the manuscript and cited Nelli. Muraro, The present essay introduces the academy, its had also been added. One may assume that this Domenico Fontana, Gio. Battista and Paolo An- however, is much more interested in Noferi as a activities and members. It also provides a de- document was put together soon after the tonio Magnali, Domenico [sic] Barzini, Iacopo draughtsman and possibly as a painter, al- scription of the manuscript and the current events it describes, either by an academician or Ramponi, Filippo Morosi, Doctor Giovanni An- though he also gives an overview of Noferi’s state of research. Cosimo Noferi, a mathemati- by a person in close contact with the academy. drea Albizzini, and the experienced engineer work in the field of mathematics and technology. cian and architect who was strongly influenced by Galileo, played a decisive role as spiritus The manuscript contains 51 full-page illustra- Giuliano Ciaccheri. Problems from the realms In this context, he makes brief reference to the rector of the Accademia della Vachia. His biog- tions, many with a colour wash. A large number of geometry and architecture were posed in the Accademia della Vachia and shows three of raphy and his significance for the academy will, of them are by Cosimo Noferi. Furthermore, academy, and they were resolved by one acade- Noferi’s drawings without commenting on them 12 therefore, be outlined and evaluated. Examples there are well over 100 depictions incorporated mician. I have the files of the academy in my li- (problems 26, 31 and 42) . Other references to of the tasks that were posed will be presented in the written texts. All the illustrations – both brary [i.e. the manuscript, which is the theme of the academy can be found in notes to various and the working methods of the academy full-page and those in the texts – are repro- this essay]”8. texts and in manuals, without the name being analysed. In some cases, the constructional is- duced in the manuscript edition in this book. Nelli was mistaken in three respects: Francesco explicitly mentioned. In his work on the engi- sues raised by the academicians had a real The manuscript comes from the Nelli Collec- (not Domenico) Barzini was a member of the neer Bartolomeo Vanni (1662-1732), Luigi background and were related to projects like tion, in other words, from the private library of academy; Giuliano Ciaccheri, who later made a Zangheri refers to Giuliano Ciaccheri in a note, the building of the Ponte di Mezzo in Pisa or Giovanni Battista Clemente Nelli (1725-1793). career for himself as an engineer, was only 17 quoting the shelf mark of the manuscript under the Florentine palaces of the Corsini and Nelli’s father, Giovanni Battista Nelli (1661- years old at the time; and the problems were, as discussion here without actually naming the Medici-Riccardi. When a new roof was to be 1725), was master builder (architect) to the a rule, solved by a number of academicians, not academy13. Ciaccheri “studied at the school run constructed for San Giovannino in Florence, cathedral in Florence and a connoisseur of an- just by one. Nevertheless, Nelli’s statement is by pupils of Galileo”. With this statement in his the academicians publicly tested a newly devel- cient architecture. From him, the younger Nelli of enormous interest. He confirms the link be- article on Ciaccheri in the Dizionario Biografi- oped form of construction. The outcome of this inherited 1,000 architectural drawings and the tween the Accademia della Vachia and its guid- co degli Italiani (DBI), Zangheri is also clearly can still be seen today. A short report on the collection of manuscripts that his father had ac- ing light, Galileo; and he informs us about the referring to the Accademia della Vachia without trials has survived as well. The roof truss prob- quired from his teacher Vincenzo Viviani (1622- character of the “Gentiluomo Fiorentino” Ot- actually mentioning it by name14. In her Ciac- lem also has a bearing on the academicians’ 1703). In this way, the Vachia manuscript came tavio della Vacchia. From Nelli’s description, it cheri article in the Allgemeines Künstler- working methods and is discussed at length in into Giovanni Battista Clemente Nelli’s posses- also becomes apparent that the manuscript had lexikon, Susanna Partsch quotes this reference the present chapter. sion in 1733. From 1743, he extended his collec- already been bound when he inherited it as part and adds the information that Ciaccheri studied The interest of (natural) scientists in the every- tion of drawings and manuscripts to comprise of his father’s collection in 1733. architecture and engineering at this school15. day knowledge, skills and outlook of craftsmen more than 9,000 items, details of which are giv- In his survey of manuscripts in Italian libraries, In Partsch’s article on Jacopo Foggini in the – which goes back to Nicolaus Cusanus and en in a description of the collection dating from Mazzatinti lists the Accademia della Vachia and same encyclopedia, the author mentions the reached an initial peak with Francis Bacon – as 17567. In the Galileo monograph that Nelli pub- mentions the development of a chronometer academy by name, stating that Foggini “was well as the slowly developing exchanges that lished in Lausanne in 1793, which may be seen (problem 22)9. In 1919, Giovanni Giovannozzi attached to the Accad. Geometrica of the Abbot took place between the two realms will be de- scribed in their historical dimension, so that the as a description of science in the age of Galileo mentions the manuscript in an article about Della Vecchia [sic] in which the members dis- activities of the Accademia della Vachia may be and the following decades, Nelli also mentions Cosimo Noferi, but he provides no further infor- cussed geometric, architectural and mathemat- 10 16 understood in this context. In many respects, Cosimo Noferi and the Accademia della Vachia: mation about the academy . Giovannozzi gives ical problems” . though, the findings described here must re- “Cosimo Noferi, painter and architect, who has a very brief description of problems 22, 25 and The fact that relatively little interest has been main provisional for the time being. published a pamphlet on mathematics and who 37. He mixes up problems 35 and 37 and shown in the academy to date is attributable at at his death left unpublished many manuscript ridicules Noferi’s solution to number 35. At the a deeper level to a structural problem of our

62 63 modern scientific system, divided as it is into scribed as a clergyman and addressed as tano), including the walnut doors to the two poldo de’ Medici sent the latter a list of the discrete disciplines. It is therefore not surpris- “frafratello” (a brother monk in a holy order), chapels of the Bonsi family28. books purchasable from the estate of Giovanni ing that historiography has only more recently “abbate” (as on the frontispiece of the manu- The Reverend [Reverendo] Domenico Fontani Andrea Albizzini. The list contains nearly 200 ti- probed the interaction between building con- script) and “eminentissimo Reverendo Si- (also written “Fontana”), a further important tles and includes works by Galileo and other nat- struction and natural science17. This phenome- gnore”. Della Vacchia’s estate included various member of the academy, was probably a mathe- ural scientists, plus architectural tracts by Vi- non has its roots in historical developments. items of landed property. These are not defined matician. Fontani posed four of the tasks involv- truvius, Palladio and Vignola, as well as a num- Becchi shows how, on the one hand, scientists more specifically, but they certainly included ing geometry and put forward solutions to 20 of ber of undefined mathematical instruments32. and mathematicians who developed the theories the house in which the academy met. The bulk the problems from all areas, but especially Giuseppe Balatri was evidently an expert for of mechanics, and on the other hand, engineers of this estate24 was bequeathed to his sister’s those that had to do with building. What inter- building matters. He submitted solutions to and technicians who were interested in mechan- sons, Giovanni Battista Magnali and Paolo An- ested him in particular was the underlying geo- eight of the tasks related to this field and posed ical questions had lost contact with each other tonio Magnali, both of whom had been members metric logic of the proposals, as in the solution two problems himself. These included joining as early as the first half of the 18th century18. As of the Accademia della Vachia. Giovanni Bat- to the roof-truss problem (described in detail two vaulted spaces to form a single vaulted a result, the history of mechanics and the histo- tista Magnali, who had evidently received an ed- below). The academicians, and especially space, without having to demolish the storeys ry of (building) technology often run parallel to ucation in mathematics, posed one geometric Fontani, tried to use empirical methods as little above (problem 12). No information is available each other without making contact. This divi- problem and proposed solutions to three others, as possible in their work and to calculate their on the academicians Filippo Morosi (who posed sion is overcome by Renn/Valleriani in their including the geometry of a stage space (prob- solutions on the basis of natural laws as formu- the problem of the roof trusses discussed at study of the discussions that took place between lem 8a). Paolo Antonio Magnali posed problem lated by Galileo and Torricelli. An example of length in this essay), Domenico Masini33 and Galileo and the masters of the Arsenal in 36, which involved the geared transmission for a this is the calculation of the cross-sections of Orazio Vanni34. Venice19, and by Becchi in his work on Bernardi- very large carriage. water pipes (problem 28). One knows that Jacopo Ramponi and Giuliano no Baldi’s Exercitationes (1621)20. The present The architect-stonemason, woodcarver and Francesco Barzini was a professor of astronomy Ciaccheri, however, were both building engi- analysis of the Accademia della Vachia may be sculptor Jacopo Maria Foggini (*Florence, at the Studio Fiorentino, the university of Flo- neers. Jacopo Ramponi was an engineer for the regarded as a continuation of these studies. As 1610/1620; †Florence, 28 January 1684), an un- rence, and he wrote 12 books on various aspects Parte Guelfa, the building authority in the one sees from the example of the Vachia, down cle of the more eminent sculptor Giovanni Bat- of that subject29. He proposed solutions to two Grand Duchy of Tuscany35, and evidently spe- to the present day in many cases, little attention tista Foggini, was one of the most active mem- tasks. One involved keeping the overflow from a cialized in the construction of fortifications. He has been paid to the discussions that took place bers of the Accademia della Vachia. Foggini re- fountain in equilibrium with the supply from had profound and detailed knowledge in this between architects, artists, engineers, mathe- ceived his training in Antonio Novelli’s school three pipes. In the second, he developed an ap- field and posed two tasks related to this subject maticians and natural scientists, all of whom and in Rome25. From 1643 to 1647, he was a paratus to measure the rate of flow of rivers (problems 13 and 23). Giuliano Ciaccheri (Giu- played a decisive role in advancing building con- pupil of the Accademia del Disegno. In 1648, he (problem 25). liano di Giov. Piero Ciaccheri36, *Florence, 1644; struction especially in the 17th century. As a re- was elected a member of the academy, and down Born in Florence, Giovanni Andrea Albizzini †Florence, 17 July 1705 ante) was one of the sult, these aspects have slipped into a no-mans- to his death, he held the offices of conservatore, was a lecturer [lettore] for logic (1659-1660) and young members of the academy. Contrary to land between the histories of technology, art festaiolo, consigliere and console26. From 1652 a reader or associate professor [professore stra- what literature on this subject may suggest (see and science. to 1656, Foggini was chairman [sindaco] of the ordinario] for philosophy at the University of above), Ciaccheri belonged to the academy, but Fraternity of Wood Carvers of San Giuseppe27. Pisa (Accademia Pisana) from 1660 to 1666. not explicitly in the role of a student. On the The members of the Accademia della Vachia21 In 1644, there is evidence of his presence as a There is also evidence of his presence there as a contrary, he posed and resolved problems like Ottavio della Vacchia, in whose house the acad- stonemason during the erection of a library in student in 165830. Albizzini, who was addressed all the other members. Among the tasks he for- emicians met, is described by Nelli as belonging the Badia. Foggini’s works include the tomb of as “dottore” at the Accademia della Vachia, is mulated was the development of an appliance to to a patrician Florentine family22. The date of Heinrich von Starhemberg (†1650) in Santo especially associated with the proposition and measure the speed of flow of water. No distinc- della Vacchia’s birth is not known precisely. He Stefano al Ponte in Florence, carvings on the resolution of geometric problems. In his chroni- tion was made in the academy between teachers must have died, however, sometime between Medici coaches and a large Ecce homo for Bal- cle of the University of Pisa (1791-1795), Ange- and students anyway. Everyone learned from May 1669 and May 1670, because his will, drawn dinucci (1654). Foggini carved crucifixes for the lo Fabroni described Albizzini as one of the out- everyone else. In his description of the Accade- up on 22 May 1666 by the Florentine notary main altar in the Church of S. Pietro d’Alcan- standing minds of his time, who argued against mia della Vachia, Giovanni Battista Clemente Francesco Patriarchi, was attested every year tara in Montelupo Fiorentino and for Abbot Aristotelian teachings and who took Galileo as Nelli referred to Ciaccheri as a professionally by the civic keeper of records in Florence, and Baldacchini. In the years 1668-1671, he execut- his model31. In 1666, probably following Albizzi- experienced engineer37, which is what he was this took place for the last time on 23 May ed various works for the Theatine Church of ni’s death, his books were sold off. On 30 Sep- later to become. In 1673, the municipal authori- 166923. In his will, Ottavio della Vacchia is de- San Gaetano (formerly Santi Michele e Gae- tember 1666, the Pisan correspondent of Leo- ties awarded him the title of engineer, and he

64 65 1. Santo Spirito, Florence, courtyard with vertically cracked columns repaired with slender iron rings (Bibliotheca Hertziana, photographic archive).

was a member of the Capitani di Parte Guelfa. 2. Diagram illustrating arranged them in the Travagliata. All this sug- peripatetic [Aristotelian] arrogance with wis- Ciaccheri designed and rehabilitated buildings; Torricelli’s theory, explaining gests that Noferi was born around 163544. He dom and circumspection and with a few, brief the phenomenon that slender iron 47 he was involved in bridge construction and was rings can prevent further vertical could not have been a direct pupil of Galileo, as words” . regarded as a specialist for hydraulics38. Ciac- cracking of heavily loaded Noferi himself claims to be or as Nelli says he If Noferi, like Albizzini (see above), advocates cheri purchased the first volumes of Lorenzo columns (graphic reconstruction was, since Galileo died in 1642. Noferi was sim- Galileo and roundly rejects Aristotle, this is at- by Hermann Schlimme). Magalotti’s Saggi di naturali esperienze del Ci- ply a very staunch adherent of Galileo’s ideas. tributable at least in part to the polemic effect of mento immediately after their publication. This In the proem to the first part of the Travaglia- Galileo’s own writings and biography. The lat- underlines his deep interest in applying the ta, Noferi says: “I will not just lay down the ter’s break with the Greek philosopher and sci- findings of natural science to building construc- rules for the things I aim to do; I will lecture on entist, especially in questions of mechanics (and tion – entirely in accordance with the aims of them and prove their validity through their un- thus of building), was not as pronounced as it the Accademia della Vachia. derlying geometric and natural logic. These dis- subsequently seemed. For example, Bernardino courses, therefore, are not devised by some sim- Baldi, in his commentary of Aristotelian me- Cosimo Noferi – spiritus rector ple practician, but by a speculative philosopher; chanics, had anticipated many important ideas of the Accademia della Vachia and I will prove that the architect has to be a contained in Galileo’s science of materials48. Cosimo Noferi, a mathematician, architect and person trained in this way”45. Furthermore, as far as his interest in the knowl- artist based in Florence39, was an important In other words, Noferi announces that he in- edge and views of craftspeople is concerned, source of ideas for the Accademia della Vachia. tends not only to describe the techniques and Galileo does not mark the beginning of this It is thanks to him that the organization can be phenomena involved, but also to investigate the process. He stands at the end of a long line of located today in the context of cultural history. underlying natural and geometric reasons for development. Noferi was probably little known during his life- them. He argues that the architect should view time. In retrospect, however, he may be regard- his discipline with the eyes of a natural scientist. Philosophers and craftsmen ed as one of the first architects to adopt the ap- Noferi’s concept is certainly based on episodes As one knows, the interest shown by natural proach followed in the emerging natural sci- like Galileo’s discussions with the workers in the philosophers for craftsmanship, knowledge and ences and to seek to apply it in the realm of Venetian dockyards, the Arsenale. Galileo pro- building technology was an important point of building. We know that Noferi died young, but ceeded from the experience of the workers that departure for modern natural science. Crafts- that he lived until at least 166340. He was fully if one increased the scale of a structure, it was manship and technology were not part of the acquainted with the work of Galileo and Torri- not sufficient simply to enlarge the individual canon of the seven liberal arts [Artes Libe- celli. Noferi published a treatise on geometry in constructional elements proportionally. They rales]49 that had been handed down from antiq- 166041 and left behind at least twelve manu- had to be increased more than proportionally in uity and remained valid throughout the Middle scripts42. In the first part of his four-volume cross-section. This analysis of workers’ experi- Ages. Discussion of the manual arts was consid- manuscript treatise Travagliata Architettura43 ence was the starting point of Galileo’s science ered demeaning, unworthy of a free man. At the (Galileiani 122-125), he deals with vaults, roofs of materials, which he describes in his Due latest from the mid-15th century, however, and foundations. The frontispiece contains a nuove scienze (1638)46. philosophers began to take an interest in un- self-portrait of the author, who claimed to be 27 Noferi explicitly declares his anti-Aristotelian written technology and the knowledge of daily when he wrote this work. Since Noferi mentions position and his intention to accept explanations life. In his Idiota Dialogues, dating from the the testing of innovative roof trusses [cavalletti] of phenomena only after taking account of summer of 1450, the humanist and theologian in the new structure for San Giovannino in Flo- everyday experience. The architect “should Nicolaus Cusanus (Nicholas of Cusa) criticized rence – which was also one of the problems ad- consider the forces, the movements, the the one-sided concentration of men of learning dressed by the Accademia della Vachia (see be- weights, the proportions, the time and what the on book knowledge, and the exaggerated defer- low) – the date of this treatise cannot be earlier intellect suggests to him, in order to examine a ence they showed to auctoritates like Aristo- than 1662, although the fourth part of the certain phenomenon [accidente]. This will be tle50. The two men of learning in the dialogues of Travagliata can be dated with certainty to 1658. the path he should follow to reach such perfec- Cusanus, the orator and the philosophus, exem- This is not necessarily a contradiction, however, tion that, though others may indulge in mere plify this type. Unexpectedly, though, they rise since one cannot be sure that Noferi wrote his idle talk and have more eloquence and memory, above their pride in learning and begin to take a treatises in the order in which he subsequently he [the architect] will be able to quieten any deep interest in the views of the craftsman and

66 67 uneducated layman. (In this context, idiota analysis of craft techniques as a path to recog- crafts, but of those that were newly emerging. craftsmen, it was enough to know under what means a brush-maker.) The layman admits that nizing the laws of nature57. To identify this more Bacon said that experiences in the crafts [arti] conditions mortar hardened, but not to ask why something can be learned from books, but that general cultural background to the Accademia that have no practical use and are of no interest it happened. Bacon’s ideas met with under- one can reach God only through a direct obser- della Vachia, it is worthwhile taking a closer to the craftsmen themselves are all the more in- standing, however, especially in the Nether- vation of the world – for instance, the world of look at Bacon. teresting for studying the history of nature62. lands70. It was no coincidence that the second manual work51. To be able to philosophize about Bacon considered the technology of his time to edition of his Novum Organum was published such direct observations, however, book knowl- Francis Bacon (1561-1626) be very advanced. He wanted to make it the ba- there71. Some copies of the 1620 editio princeps edge was essential, according to Cusanus. What Francis Bacon, a son of Sir Nicholas Bacon, who sis for a liberation of philosophy, which he per- soon reached Italy, too. In a letter written in was needed, he suggests, was to reinforce the was Lord Keeper of the Great Seal in England ceived as imprisoned in the self-referential in- 1625, Cassiano dal Pozzo, who belonged to the Quadrivium and hence the role of mathematics during the reign of Queen Elizabeth I, was tellectual isolation of scholastic tradition. As an entourage of Cardinal Francesco Barberini (a within the Artes Liberales52. In the last dia- trained as a barrister, and rose through the le- example of the technological advances of his nephew of Pope Urban VIII and the papal logue, Idiota de staticis experimentis, the lay- gal profession to become Lord Chancellor un- time, Bacon refers to the relocation of an legate in France), referred to Francis Bacon’s man discusses experiments carried out with a der James I. His writings are varied and volu- obelisk63. He obviously had in mind Domenico books with great enthusiasm72, and several of common measuring instrument like a set of minous, with a particular focus on scientific Fontana’s famous transport and re-erection of these works were sent to dal Pozzo in 163473. scales. In addition to studying the colour of method, the natural sciences and the classifica- the Vatican Obelisk in the Piazza San Pietro, an The Biblioteca Apostolica Vaticana in Rome blood or urine, for example, weighing them tion of knowledge. With his well-known Novum exploit published to a monumental scale in folio contains three copies of Bacon’s Instauratio could help physicians to diagnose disease; or Organum, published as part of the Instauratio in 159064. In acts requiring physical exertion of Magna (1620): the Barberini copy and two oth- heartbeat and breathing rates could be meas- magna in 162058, Francis Bacon initiated an ex- this kind, manpower was always supported by ers74. Possibly Bacon’s publications were also ured with the aid of a weight-operated water perimental approach to the understanding of machinery. Bacon, however, suspected that peo- known to the Accademici della Vachia. The Eng- clock. The traction power of a magnet could be nature. In the now much lesser-known Catalo- 4. Description of the Acqua Felice, ple would think the intellect was capable of do- lish scientist, however, was merely summarizing defined in terms of mass by weighing the ob- gus Historiarum Particularium, published as Rome. Representation of the main ing everything on its own without further assis- a tendency that had culminated in Italy in the jects that the magnet can attract and hold53. Al- an appendix to the Novum Organum59, Bacon water supply pipes (house tance, whereas he himself considered that the person of Galileo Galilei. Galileo had also at- connection). Ink and grey wash; 65 though Cusanus had presumably never con- called on natural philosophers systematically can be dated to 1696/1697; f. 8r intellect could achieve nothing on its own . He tracted a large number of adherents, such as ducted such practical experiments himself, he and comprehensively to document and study of a manuscript bound in the copy also criticized the exaggerated devotion to an- Evangelista Torricelli and Benedetto Castelli. forged a link between philosophy and craft the knowledge of the mechanical arts and of Francesco FONTANA, Relazione tiquity, which he thought would inhibit To see how the knowledge of artisans was inves- work that would seem to be unprecedented for crafts, which he saw as a pool of ready-made ex- dello stato vecchio, e nuovo progress66. The relocation of the obelisk tigated by a scientist during the period immedi- 3. Evangelista Torricelli, dell’Acqua Felice [...], Roma 1696, Meccanica dei Solidi 2 (BNCF, the time. He even proposed compiling a sepa- periments in the realm of nature. Bacon even Bibliotheca Hertziana, Max- prompted Bacon to voice some critical remarks, ately preceding the Accademia della Vachia, it is Ms., Gal. 147). rate book containing all the experiments in provided a documentation programme for no Planck-Institut für though. He lamented the fact that technology interesting to look at a model study by Evange- which scales were used54. What is important in less than 130 fields of knowledge, with almost a Kunstgeschichte, Rom, was simply exploited, and not investigated in an lista Torricelli. It is also instructive to compare unpublished. this discourse is not the general interest shown dozen building crafts, including the historia effort to understand the underlying principles this almost ideal example with another, more in building construction or techniques; that (description) of quarrying, carpentry, wrought- of nature67. A mere documentation of the complex one, namely Benedetto Castelli’s trea- would not be particularly surprising in any iron work and the production of glass, bricks, “what” of craftsmen’s knowledge was only the tise on the movement of water, and everyday epoch. The crucial aspect here is the interest mortar and cement60. first step for Bacon. As the second step, he technical knowledge on this topic. shown in a craftsman’s knowledge and outlook Bacon no longer adhered to the Aristotelian called for the transformation and elaboration of on life. In the 15th and 16th centuries, Leonar- concept that human intervention in nature de- the reasons behind the experiments through Evangelista Torricelli (1608-1647) do da Vinci, Giulio Agricola, Louis Vives, stroys the existing order of things. Instead, he the intellect68. Bacon criticized the fact that At the end of his life, the scientist Evangelista Bernard Palissy, François Rabelais, Andrea advocated a study of craft knowledge, believing progress in the crafts was not systematic and Torricelli succeeded Galileo as mathematician Vesalio, Giacomo Aconcio and Humphrey that nature reveals its true characteristics more that as a result of this, discoveries were largely to the Grand Duke of Tuscany. In early modern Gilbert, to mention but a few, repeatedly precisely not when it is studied in its original random. He therefore sought to work systemat- times in Florence, columns that were cracked in crossed the border between craftsmanship and state, but when it is exploited by the human ically in a bid to make progress predictable69. their length were often successfully repaired by the liberal arts55. Francis Bacon summarized mind, as occurs in craft activities: “[…] the pas- Existing knowledge was thus subject to new encircling the shafts with slender iron rings. these reflections in his influential work Instau- sages and variations of nature,” Bacon said, questions. For example, Francis Bacon reflected Examples of this can still be seen today, as in ratio Magna of 1620, underlining their impor- “cannot appear so fully in the liberty of nature, on why bubbles occur in water or why lime- the portico of the Cappella Pazzi, Santa Maria tance for the development of society56. Bacon as in the trials and vexations of art”61. He also based mortar solidifies. Hitherto, it had not Maddalena dei Pazzi and the basilica of Santo called for a systematic documentation and urged a study not only of the existing, organized been usual to pose questions like these. For Spirito (fig. 1). Torricelli was astonished to see

68 69 that a slender iron ring could successfully with- 5. Description of the Acqua Felice, rough sketches of the relevant geometry (fig. 3). nection pipes (cf. fig. 4). The operators of the stand the heavy loads that a column had to bear. Rome. Representation of the main This episode highlights certain aspects of an ap- water-supply network were perfectly aware water distribution pipes running Paolo Galluzzi analyses Torricelli’s considera- below the Via Pia between the proach based on the natural sciences and the that quite different amounts of water could flow tions in conjunction with Vincenzo Viviani’s fountain near Santa Susanna way this can be applied in building. On the one through a pipe of a given diameter. The method studies on the structural concept of the cathe- and the Quattro Fontane. Ink hand, Torricelli questions and quantifies a tech- of providing the guaranteed quantity of water 75 and colour wash; can be dated to dral dome in Florence . Torricelli did not sim- 1696/1697; f. 3r of a manuscript nology that quite evidently functions and that for the lump sum payment was laid down in an ply accept this at face value, though; he tried to bound in the copy of Francesco would not lead to further questions on the part edict dating from 1598, which stipulated that explain what actually happened in physical FONTANA, Relazione dello stato of those involved in the building work. On the the water in the aqueduct had to be maintained vecchio, e nuovo dell’Acqua Felice terms. Torricelli begins his explanation with an [...], Roma 1696, Bibliotheca other hand, Torricelli is interested in craft and at a constant level: “[…] so that all users enjoy analysis of a beam leaning against a wall (fig. 2, Hertziana, Max-Planck-Institut building techniques that lie outside the seven precisely the water quantity conceded to left), and he assumes that there is nothing to für Kunstgeschichte, Rom. liberal arts. He overcomes the divisions be- them”80. As a rule, this was effected by in- stop the beam from sliding down the wall. Tor- tween these different realms and ultimately stalling an open fountain or basin from where ricelli then tries to deduce the force A that seeks to make knowledge interchangeable. the water was distributed via smaller runs (cf. would be necessary to prevent the beam sliding fig. 5). In addition, the connections to individual away from the wall under its own weight P; and Benedetto Castelli (1578-1643) buildings had to be at a predetermined height, he finds that loads P and A are in the same pro- The reciprocal relationship between science and which was the same for all consumers and to portion to each other as the straight lines “a” everyday applied technology or common knowl- which no change was permitted. One knew, and “b”. (The notation “A”, “P”, “a” and “b” was edge is more complex, however, as the example therefore, that in addition to the diameter of the introduced by the author.) Torricelli imagined of the Roman water supply shows. Bernardo pipes, a difference in height between the stor- the vertical column cracked along its length as Castelli was a Benedictine monk who had stud- age basin and the house connection played an four such beams (fig. 2, centre) which have to ied in Padua under Galileo. In 1626, he became important role in controlling the amount of wa- be restrained by the iron ring from sliding out- a professor for mathematics at the Sapienza in ter supplied. Since this difference in height was wards into a more oblique position. The heavy Rome and papal adviser for the supervision of the same for all consumers, the diameter of the load P has to be contained by the iron ring, rivers in the Papal States. At the beginning of pipe really did reflect the quantity of water sup- which also has to resist force A. Forces P and A his treatise on the movement of water, written plied. This procedure was adopted from antiqui- are in the same proportion to each other as the in 1628, Castelli explicitly refers to the common ty, when the charges for the volume of water half-height of the column “a” is to the half-width methods used by engineers to calculate quanti- were calculated in exactly the same way, as of the crack “b”. In this way, a method of calcu- ties of water. He complains that their calcula- Frontinus describes in a treatise written in the lating the requisite thickness of the iron ring tions in the case of rivers and fountains were first century AD on the water supply in Rome81. can be obtained. Since a crack in a column would based exclusively on the cross-sectional dimen- Neither in this treatise nor in the edict of 1598, be much narrower than that shown in the sions of pipes or streams, overlooking the fact however, is there any physical explanation of sketch, the contrasting force A would be very that the speed of flow is just as important. In the phenomenon. Since a connection with a low- small (fig. 2, right). Torricelli sums this up with this respect, though, Castelli himself is telling er end outlet meant a greater supply of water – the following words: “Now, I say, preventing im- only half the truth and probably based his own and a higher one meant less water – it was pos- mediately any disorder, that any minimal force studies more on contemporary technology than sible to cheat simply by cutting off or setting the is enough to hinder it [the sloping line of the he is prepared to admit. supply pipe at a lower level. The edict of 1598 beams], and that, if we leave the aperture large, After the Acqua Vergine had been repaired in implicitly takes account of this fraudulent prac- there is a position where it needs a force that is the second half of the 16th century78 and the Ac- tice. Frontinus describes the various opportuni- equal to the weight; and there can be a position qua Felice had been rebuilt in part79, Rome en- ties for fraud and deals with the problems of [with a much larger aperture] where we need a joyed a supply of running water again, to which house connections at different heights: “As far force a thousand times greater than the private consumers could be connected. There as the dislocation of the water supply is con- weight”76. were no meters and no taps; the water simply cerned, one should ensure that they [the house Torricelli explains this at some length in a flowed continuously into the houses or into connections] are all at the same level and that no manuscript preserved in the Biblioteca Na- fountains. A lump-sum charge was made based water supply is positioned at a lower level and zionale in Florence77, where one also finds his on the diameter of the standardized house con- another at a higher level. Located at a lower lev-

70 71 6. Convent of St Anna, Rome; in the Via Pia, Rome (figs. 6, 7). The example 7. Convent of St Anna, Rome, cones and perspective geometry, for example) the background one can recognize shows the degree of complexity that everyday stone slab indicating the level and new findings in the natural sciences (like the facade of San Carlino of the water supply pipe (photograph Hermann Schlimme). technical knowledge could attain. Not only the (photograph Hermann Schlimme). flow mechanics and the laws of falling bodies) to engineers of the time, but also the general pub- resolve technical questions, especially in the lic without any special education would have re- fields of building construction and surveying. garded Castelli’s statement that the amount of Vignola’s second rule of perspective was re- water received does not depend solely on the versed, for example, to allow the layout plan of cross-section of the supply pipe as something a fortification to be reconstructed solely from a perfectly obvious. Having said that, though, one perspective drawing (problem 27). The acade- must add that Castelli goes beyond the level of micians also developed a geometric construc- everyday knowledge by systematically ques- tion process for the creation of perspectively tioning relationships of this kind which seem so foreshortened stage sets, thereby replacing the clear at first sight. usual form of construction, using cords extend- ed through space (problem 8a). Sometimes the The Accademia della Vachia: innovation arch bridge in Pisa with a span of no less than problems seem to have been made deliberately and the application of scientific knowledge 124 braccia (70 metres), the still unfinished complicated to justify the application of new Wholly in accordance with the concepts of structure collapsed into the river, together with knowledge, as in the case of determining the di- Galileo, Torricelli, Castelli and Noferi, the acad- the cradling. In a letter dated 2 January 1644, ameter of the water pipes for a fountain (prob- emicians were concerned with questioning and Torricelli described Alessandro Bartolotti, the lem 28). If one wishes to coordinate the supply deepening technical knowledge – knowledge re- master builder responsible for the work, as an and outlet of a fountain in such a way that the lated to building construction in many cases – architect who had been “too audacious” [ar- basin always remains well filled but never over- that had been gained by empirical methods. It chitetto troppo ardito]85. Bartolotti had, in fact, flows, the water level can be controlled simply was quite common for buildings to undergo ex- boldly tried to advance building technology by a by using a connecting pipe. This effect can, of tensive conversions or for “new structures” to process of trial and error, and not through the course, also be achieved by testing pipes of dif- incorporate almost the entire fabric of a former application of new knowledge based on calcula- ferent diameter until one finds the appropriate building. That was certainly the case with the tions and the laws of physics, as had been the proportions; but the academicians were con- Palazzo Farnese in Rome (from 1534 onwards), trend since the time of Galileo. Torricelli, for ex- cerned with determining the right diameter by for example84. The complex knowledge required ample, had questioned tried-and-tested tech- means of calculations based on hydromechanics, to implement such measures was not contained niques (like those applied in repairing longitudi- a newly developing discipline in those days. in architectural treatises, however. Today, it is nal cracks in column shafts) in respect of their Their solutions were inspired especially by the scarcely possible to reconstruct this knowledge, basic physical parameters, and he had made the findings of Benedetto Castelli (1628) and the ap- el, it provides more water; located at a higher which was based on experience and implicit to findings quantifiable. Bartolotti, in contrast, plication of Torricelli’s overflow law86. level it supplies less water, since the water is the individual measures. The Accademia della used methods that had never been tested be- Problem 28 plays a key role: it is an example of drawn to the connection at the lower level”82. Vachia is one of the few sources for such bodies fore, directly and to full scale. The bridge was fi- the transition from empirical methods to a sys- The significance of differences in level was of knowledge, thanks to the tasks its members nally erected between June 1658 and March tem of calculating the dimensions of construc- everyday knowledge, therefore. Castelli, who set each other. In one case, in which reference is 1661 in a three-arch form on existing founda- tional elements. Only in this instance, though, makes express reference to engineering knowl- probably made to the Palazzo Medici-Riccardi, tions. The Accademia della Vachia nevertheless did the academicians make a preliminary calcu- edge, must have been aware of this, too. The en- two large vaulted spaces had to be joined to addressed the question of broad-span bridges lation. In the case of the roof trusses in San Gio- gineers would scarcely have withheld such in- form a single vaulted space without demolishing again with a theoretical, exploratory approach. vannino (fig. 22), in contrast, the timber beams formation from him. To prevent fraud, from the floors above with their complex layout One of the principal issues was the shape of the have much greater dimensions than was normal 1767 onwards, the correct level of water connec- (problem 12). Like all the other problems men- arch. The academicians rejected an oval form, at that time (fig. 8). In this way – empirically in tions had to be marked by a stone plaque fixed tioned on the following pages, this one is de- which though easily constructed, has its struc- effect – one could overcome the potential dan- visibly to the public face of every building83. scribed in detail in the manuscript edition in the turally weak points (problem 6). gers of an unfamiliar form of construction for Such a plaque can still be seen today fixed to the second part of the present volume. The aim of the academicians was to apply new which no values existed based on experience facade of the Carmelite convent of S. Anna in In January 1644, in an attempt to erect a single- mathematical knowledge (relating to sections of (see chapter below).

72 73 8. Interior of San Giovannino, Florence; former Jesuit church (Bibliotheca Hertziana, photographic archive).

Mathematics and especially geometry played namely “counting boxes”, with a geometric sys- an important role in the academy. A lot of the tem. The task involved dividing a rectangle into mathematical-geometric problems were related four equal areas: three trapezia and a smaller to issues of contemporary interest. Problem 16, rectangle (see illustration to problem 3 in the for example, is a complex task relating to hyper- manuscript edition in the second part of the bolas as they were treated in the universities in book). Giuseppe Balatri expressly resorted to those times87. Cosimo Noferi, who had already the usual method of counting boxes, while published a treatise on parabolas88, evidently Fontani pursued an innovative approach and wished to gain as much information on hyberbo- tried to find a geometric solution. On closer ex- las as possible through his work at the academy. amination, though, his proposal also proves to That, at least, would explain why he took every be a cleverly concealed counting of boxes. Al- opportunity to turn the discussion to the hyper- bizzini alone succeeded in developing a geomet- bola or addressed this topic in addenda to his ric solution. solutions (problems 9, 15, 16, 24 and 47). At the same time, the academicians solved a number of The Accademia della Vachia: exchanges tasks that were based mathematically on ex- between technical bodies of knowledge tremely simple precepts by pursuing an often With Jacopo Foggini, the academy also had a complex line of approach – partly through a sculptor among its members. Two of the prob- process of iteration (problems 9 and 15). In the lems, therefore, were directly concerned with course of this, one becomes aware of a range of sculptural matters (problems 18 and 26). The mathematical devices to which the academicians first of these involves the creation of a monu- repeatedly turned. Many problems were solved mental figure that can move in a circle. Achiev- by using geometric mean values (where a : b = ing movement in art – and thereby evoking a b : c); for example, where they were concerned sense of wonder [maraviglia] – had met with in- with converting linear proportions to superficial creasing interest since the 16th century. This proportions, or superficial to cubic proportions. development found special expression in the hy- In addition, there were other rules based on dropneumatic automatic figures that had been geometric mean values that were derived from placed in courtly gardens since the early 17th Euclid, such as Thales’s law or laws relating to century. An outstanding example of this, partic- height or to chords and tangents. As part of the ularly in the context of the present work, is the history of mathematics, the mathematical tasks garden of the Medici villa in Pratolino, where a are of interest only in exceptional cases. For series of automatic figures and scenic appli- that reason, they are treated more or less de- ances driven by water and cogwheels had been scriptively in the commented source material in installed. Special aspects of the task the acade- the second part of the book. Far more important micians set themselves in problem 18 were a ful- is the fact that the academicians explored both ly automatic method of functioning and the di- mathematics and technical problems. As a re- mensions. Noferi solved the task by adapting sult, the historically interesting case of the pre- the mechanism normally used to drive water liminary calculation of the cross-sections of wa- mills. ter pipes came about almost by itself. The Accademia della Vachia would seem pre- Even in the case of mathematical questions, destined to solve a task set in the area where though, the systematization of everyday knowl- sculpture and mechanics overlap. Problem 17 edge was always a topical issue, as in problem 3. involves the development of lifting gear (a In a real situation, the academicians replaced building crane) with which heavy loads – in this the method commonly used to determine areas, case, preassembled roof trusses – could be

74 75 13. Illustrations of French forms of roof construction: “A” and lower “B” (to be read as “D”) (Sebastiano SERLIO, Il settimo libro d’architettura di Sebastiano Serlio bolognese. Nel qual si tratta di molti accidenti, che possono occorrer’al architetto [...], Frankfurt/Main 1575, p. 199).

9. Cosimo Noferi, Tomo primo hoisted to the top of a wall. Just as a mill mech- ical subject. The academicians addressed ques- della Travagliata Architettura, anism (see above) was applied in a different con- tions of time measurement (problem 22) above Quarto discorso, Quinta Figura (BNCF, Ms., Gal. 122). text, so Noferi enlarged the pivoting trestle all because of doubts in the precision of the pen- 10. Formulation of problem 14 commonly found in sculptors’ workshops (as he dulum. Shortly afterwards, the development of with sketch, files of the Accademia explicitly states) and used it as the basis for the apparatus for measuring the speed of flow of della Vachia (BNCF, Ms., Fondo design of a crane. water became the subject of problem 25. Here, Nazionale, II_46, f. 45v). Many of the solutions from the realm of me- too, discussions focused on the precision of 11. Cosimo Noferi, Tomo primo chanical engineering are of interest because the measurement; and again, in seeking to con- della Travagliata Architettura, Quarto discorso, Prima Figura academicians sought to spread the expenditure tribute to the advance of science, the academi- (BNCF, Ms., Gal. 122). of energy evenly over the various working phas- cians proved to be on the cutting edge of cultur- 12. Francesco di Giorgio, roof es of an appliance (e.g. by means of flywheels). al developments. truss without horizontal beam In many cases, though, the apparatus could (Inscription in Italian: “Trave scarcely have functioned properly. Doubts of Communications within the Accademia armata senza bordone”) (from Codice Torinese Saluzziano this kind are justified in respect of the alterna- della Vachia 148, published in Francesco tive forms of propelling a ship (problem 35), The most important innovation within the acad- DI GIORGIO MARTINI, Trattati driving a carriage without draught animals (36), emy, however, was that persons of different di architettura, ingegneria e arte the remote control of a bucket and chain (42), training collaborated directly with each other. militare, C. Maltese, ed., vol. 1, Milano 1967, f. 22v / tav. 40, pile-driving equipment (43) and the mechanical The usual standards prevailing at the universi- detail). fanning device (49). However, the concepts of ties were adopted as the plane of communica- remote control and the use of springs as a tion between members. The literature on which means of storing energy to operate machines the solutions were based was quoted – Euclid (49) are innovative for their time. and Apollonius93, for example (with references to the book and proposition), or Galileo, Torri- The contemporary relevance of the Accademia celli, Castelli and Vignola94. That also shows della Vachia: measuring instruments how familiar the academicians were with these Until the late 17th century, precision was not ing, especially the development of ball mecha- sources. While the prospective engineer Ciac- the decisive factor for private clocks: they were nisms, helped to achieve an ever-greater degree cheri made his quotations in this form, Jacopo not required to be more accurate than those in of precision in astronomic observations and new Ramponi did not relate his proposals to source public towers around which everyday life was scientific findings89. In 1581, Galileo had recog- literature. His solutions for the entrances to organized in towns. Until late in the 17th centu- nized the isochronous quality of the pendulum. fortresses (problem 13), however, go beyond the ry, these public clocks employed a relatively im- In 1602, he conducted further experiments90, treatise on fortifications by Lorini. Although precise regulating movement, consisting of and in 1641, he conceived the use of a pendulum this dated back to 1592, at the time of the acad- counterbalanced weights that rotated back- with clockwork. The pendulum clock marked a emy it was still the standard work. Like wards and forwards. This mechanism was re- major advance for science. Christiaan Huygens Galileo95, the academicians used contemporary placed only gradually by clockwork with the (1629-1695) built the first clock according to this sine tables, with values ranging from 0 to more precise pendulum. On the other hand, principle in 165691. Drawings by Vincenzo 100,000. This corresponds to five digits after the clocks used for scientific purposes, such as re- Galilei and Vincenzo Viviani dating from 1659 decimal point according in modern tables (prob- search into the celestial bodies and their move- were meant to prove Galileo’s pre-eminence in lem 15a). At the universities, it was usual to ments, or for measuring intervals of time in sci- arriving at this invention. In the same year at write the proof of mathematical theories in entific experiments, had to have a regular the very latest, Johann Philipp Treffler (1625- Latin. The academicians did not follow this movement. They also had to be synchronized as 1698), who was born in Augsburg but who lived practice consistently. far as possible with the standard of astronomi- at that time in Florence as master clockmaker Drawings were an important means of commu- cal time: the length of time the earth takes to re- to the grand duke, also built a pendulum clock92. nication within the academy. Apart from volve about its axis and around the sun. In the At the time when the Accademia della Vachia Domenico Masini, who merely posed two tasks, 16th century, various innovations in clockmak- was active in Florence, this was obviously a top- all the other academicians used drawings to for-

76 77 14. Problem 14; solution by Cosimo Noferi; files of the Accademia della Vachia (BNCF, Ms., Fondo Nazionale, II_46, f. 47r; coloured reproduction in the manuscript edition contained in this book: plate 5).

mulate their ideas. The mode of drawing for 16. Problem 14; anonymous geometric subjects, using characteristic letter solution; files of the Accademia della Vachia (BNCF, Ms., Fondo codes, is adopted from the editions of Euclid. In Nazionale, II_46, f. 50r). building, orthographic projection was called for and theoretically developed by Alberti, Antonio da Sangallo the Younger and Raphael. Their aim was to replace the combination of perspec- tive and orthographic projection in construc- tional drawings96. Whereas this new form of representation increasingly gained ground in the realm of building, perspective views re- mained the norm for depictions of machinery until the beginning of the 18th century97. This practice of representation was adopted in the Accademia della Vachia, too. In other words, in the medium of drawing, members observed the conventions of the time.

Testing innovative roof trusses in San Giovannino, Florence, 1661-166298 The academicians della Vachia did not conduct 15. Problem 14; solution by experiments along the lines of the Accademia Jacopo Foggini; files of the del Cimento, where natural phenomena were Accademia della Vachia (BNCF, simulated under controlled conditions. In the Tuscany to raise the roof of the church and to in- built between 1660 and 1665. Noferi was also in Ms., Fondo Nazionale, II_46, 100 f. 48r). Accademia della Vachia, the opposite happened: troduce a light timber vaulted ceiling (fig. 8). direct contact with the Medici family (see earli- fresh knowledge gained in the emerging natural Between 1660 and 1665, the roof of the church er), and it is conceivable that the interest of the sciences was applied to technical problems. The was in fact rebuilt101. academicians in investigating the problem was innovative constructional aspects of the roof Although the Accademia della Vachia is not aroused through this channel102. Above all, over San Giovannino are not so much directly mentioned in the source material relating to the though, the academicians’ formulation of the dependent on natural science as on prevailing new roof construction for San Giovannino and task they set themselves reflects the conditions trends in the approach to knowledge in general, conversely the church is not mentioned by name laid down by the grand duke (who allowed the as recapitulated by Bacon (see above). For the in the manuscript describing the activities of the roof to be raised by only a small amount) and roof over the church of San Giovannino in Flo- academy, the two are certainly connected. The the timber structure actually erected in the rence, the academicians developed a new kind of decisive link in this respect is Cosimo Noferi’s church. truss construction (problems 14, 17 and 37). Travagliata Architettura, mentioned earlier, Problem 14 in the Accademia della Vachia man- Bartolomeo Ammannati had begun work on the where the author speaks of the roof trusses that uscript is formulated as follows: “Given the former Jesuit church99 and the adjoining con- “one wishes to use in San Giovannino”, provid- curved line ADB of the vaulted ceiling that is to vent in 1579. The church had been limited in ing illustrations of them as well (fig. 9 “A”). The be built and the slope of the roof FE, which in height in order not to dominate the Palazzo roof trusses in Noferi’s illustration resemble the the position CD are at a distance of one braccio Medici on the opposite side of the road. Amman- actual construction surviving in the church (58.4 cm) from each other, the roof truss must nati was therefore obliged to cover the interior (figs. 22-24) and are also like those proposed by be installed in such a way that it does not hinder with a flat ceiling. On 1 May 1655, thanks to the Domenico Fontani in the Vachia manuscript (fig. the building of the above-mentioned vaulting”103 mediation of the later Cardinal Leopoldo de’ 20). In addition, various details correspond to (fig. 10). The roof had to start a considerable Medici and the Duchess of Parma, the Jesuits each other: the academy met in the years 1661 distance below the crest of the vaulting, so that were granted permission by the Grand Duke of and 1662, and the new roof of the church was it was not feasible to insert the usual horizontal

78 79 17. Problem 37; solution by 18. Problem 37; solution by Cosimo Noferi; files of the Filippo Morosi; files of the Accademia della Vachia (BNCF, Accademia della Vachia (BNCF, Ms., Fondo Nazionale, II_46, Ms., Fondo Nazionale, II_46, f. 120r; coloured reproduction f. 121r; coloured reproduction in the manuscript edition in the manuscript edition contained in this book: plate 26). contained in this book: plate 27).

tie beam [catena]. It had long been common 19. Problem 37; solution construction, since the free ends of the rafters building practice to place the timber roof beams by Giuseppe Balatri; files function like levers and impose additional strain of the Accademia della Vachia and posts directly on top of the vaulting in order (BNCF, Ms., Fondo Nazionale, on the joints between the higher tie beam and to save space. One finds this in medieval church- II_46, f. 122r). the rafters109. The academician Giovanni An- es in Lombardy, for example104. During the Re- drea Albizzini possessed a copy of Baldi’s publi- naissance, roofs were laid directly over large cation in his private library110. Serlio had depict- barrel vaults like the one over the nave of St Pe- ed forms of roof construction comparable to the ter’s in Rome105. This technique could not be capra – but with a much steeper pitch – in his used in the task described in problem 14, how- architectural treatise (fig. 13, “A” and lower ever, nor in San Giovannino, because in these “B”, to be read as “D”), describing them as the cases the wooden vaulting had to be built after- common type in France. Unlike Baldi, though, wards, as the problem description suggests. Serlio does not go into the structural aspects111. Before discussing the academicians’ proposals It is nevertheless clear from the illustration that for this special problem, though, it is instructive the higher tie beam had to be connected to the to take a brief look at the form of roof truss rafters with braces. This was structurally effec- [capriata] commonly used in Italy at that time. tive and reduced the length of the lever arms It consists of two rafters [puntoni], which form formed by the free ends of the rafters. the roof line, and a horizontal tie beam [catena, asticciola] between the feet of the rafters. The Problem 14. The academicians’ proposals tie beam bears the resulting horizontal forces for roof trusses and restrains any tendency of the rafters to The proposed solutions will be analysed now. spread. A central vertical column or king post Where the authors provide descriptions of their [monaco] connects the ridge with the horizontal own solutions, these are quoted in full and beam and is stabilized by two oblique struts translated either in the main text or, more com- [saette], which support the rafters. In the 14th therefore, to look at roof trusses throughout monly, in the notes. In addition, a commentary and 15th centuries, the relationship between the Italy – both built and drawn – where this ele- of the descriptions is given. The main purpose of king post and the tie beam was the subject of ment has been omitted. Francesco di Giorgio this is to understand the academicians’ mode of extensive discussions in manuscripts and trea- Martini was one of the first to propose some- thought and the strategies they used in arriving tises about architecture. These considerations thing of this kind (Codice Torinese Saluzziano at their solutions. The analysis begins with focused on the question of whether the vertical 148; fig. 12). In his solution, the entire system is Noferi’s proposals (fig. 14) and the accompany- post imposes a load on the tie beam, or whether stabilized by the combination of king post and ing descriptions. After recapitulating the prob- conversely the tie beam is held up by the post. struts. In his Travagliata, Noferi drew a two- lem, Noferi proceeds to describe his three solu- By the time the Accademia della Vachia came monaco roof truss (fig. 9 “D”), which would tions, the first of which (fig. 14, 1.°) is more or into existence, the roof truss was understood to seem to reflect the same idea. Indeed, one can- less meant to illustrate the problem once function in the latter form106. The academicians not preclude the possibility that Noferi was ac- again112. The second solution is based on the also adopted this view. When Noferi later pre- quainted with Francesco di Giorgio’s manu- idea of the capra (see above): “The second roof sented the trusses for San Giovannino in his script or one of the numerous copies108. Many of truss is made with interconnections like those Travagliata Architettura, he also described a the proposals put forward by the academicians which form scissors. The rafters of this [roof common roof truss (fig. 11 “A”), stating explic- were based on the so-called “capra”, a recog- truss] are not just connected at the junction K, itly that the vertical post should not impose any nized term used in the first half of the 17th cen- but also at the two points M and L of the collar load on the tie beam. To avoid this, he under- tury to describe a common roof truss in which beam ML; and as in the case of the other [first] lined the need for the gap that was usually the horizontal tie beam does not start at the foot roof truss, the rafters should press against the formed between the two members107. of the rafters, but half way up, creating a figure proposed supports, which have to be made of It was not feasible to use a normal tie beam in in the form of an A. In his Exercitationes dating chestnut or oak, and they have to be clamped to- the roof of San Giovannino. It is instructive, from 1621, Baldi advises against this form of gether as [described] above and should be

80 81 20. Problem 37; solution 21. Problem 37; rudimentary concept for the joints: the swallow-tail truss, in This at least explains Noferi’s line of thought: by Domenico Fontani; files sketch by Domenico Fontani; files which the collar beam is connected to the since the struts are no longer available to sup- of the Accademia della Vachia of the Accademia della Vachia (BNCF, Ms., Fondo Nazionale, (BNCF, Ms., Fondo Nazionale, rafters, functions only if the doubled rafters are port the long rafters, he introduces beams as a II_46, 7f. 123r). II_46, f. 116v). joined together with iron straps. These appear substitute to support the rafters in the middle. to be shown in Foggini’s drawing. These new beams connect the middle of the The anonymous solution (fig. 16) combines a rafter with the wall below eaves level. In the number of countermeasures. The two rafters first solution (fig. 17, left), the end of the for- are in the nature of two cranes that jut out inde- mer tie beam is still present. In the second solu- pendently of each other and are tied together at tion (fig. 17, right), the former tie beam is cut the ridge. The rafters are supported by shorter back more radically and does not interact with and slightly steeper beams. The rafter con- the new beam119. In contrast to the struts of a struction is tied to the wall with a number of normal roof truss, this new element is inclined iron straps and vertical members. As in Noferi’s in the opposite direction, thereby reducing the solution, this is designed to form a counter- horizontal thrust from the rafters. The idea is weight. It seems that Noferi adopted this solu- essentially true, and the solutions seem feasible. tion for his own proposal to problem 37. Probably Noferi thought that the weight of the entire masonry at the top of the wall – between Problem 37. The academicians’ proposals the eaves and the position where the new beam When the roof-truss question arose again in was to be inserted – would act as counterweight, January 1662 (1661 according to the Florentine resisting any outward thrust from the roof con- calendar) in problem 37, it was in an altered struction as a whole. It seems likely that Noferi form. Problem 14 involved the erection of a new was thinking along these lines, because he also roof with new roof trusses, whereas problem 37 proposes using the weight of the masonry of the was concerned with the continued use of an ex- top of the wall as a counterweight in other solu- isting roof structure. Here, as in problem 14, tions – to problems 14 and 33. He would seem to based on stone slabs as shown in the figure”113 the roof steeper, which would allow the use of a light timber vaulting was to be inserted in a roof be indebted to the anonymous solution to prob- (fig. 14, 2.°). common roof truss with extended rafters (fig. space, for which it was necessary to reduce the lem 14 (see above). Noferi acknowledges, how- Noferi uses the word forbicioni (scissor-like 14, 3.°)115. Here, he uses a strategy of combining tie beam and the vertical post of the existing ever, that the new beams, which replace the forms of construction) to mean a halved joint existing solutions and adapting them to the new truss and to stabilize the remaining structural struts, exert a great deal of horizontal thrust on between two beams, evidently because it re- situation: in this case, the common roof truss system by introducing new elements. We have the walls. Omitting the lower part of the new minded him of a pair of scissors. He regards the and the capra. Since Noferi reinforces the low- no description of the problem, but the basic idea beams, as he proposes in his third solution, does main problem of a roof truss without tie beams er parts of the rafters, he may well have under- emerges clearly from Giuseppe Balatri’s116 and not seem a proper answer, however. The long – namely, the spreading of the rafters – as more stood that these members would be subject to Cosimo Noferi’s117 comments. rafters are still supported in the middle, but the or less resolved by the second solution, and he deformation. He seems not to have been aware, In describing his solution (fig. 17), Noferi de- horizontal thrust that the rafters exert on the goes on to propose alternatives to the use of the though, of the fact that the free ends of the clares that the problem of the ends of the top of the wall is greater than ever120. collar beam, which he suggests can be replaced rafters would act as levers (cf. BALDI 1621, rafters pushing outwards would be increased as In Filippo Morosi’s solution (fig. 18), iron with vertical iron straps (fig. 14, 1.°) or timber above). Even by doubling the rafters, this effect a result of the struts: “But first of all, it seems straps are also used to tie the rafters to the ma- members (fig. 14, 2.°) that would stop the cannot be prevented. to me that apart from the other causes, one of sonry of the upper part of the wall, which is rafters sliding outwards114. The mass of the top Foggini’s solution (fig. 15) seems indebted to the major reasons why the rafters push out at again used as a counterweight to resist the out- of the wall to which the rafter is now tied pre- Serlio’s illustrations of various forms of roof the flanks is that the roof load bears on the ar- ward thrust of the rafters. Morosi, however, is vents it moving. In problem 33, too, Noferi pro- construction (fig. 13 “A” and lower “B”, to be cati [rafters are probably meant here]. These not aware of the function of the struts that have poses using the mass of masonry as a counter- read as “D”). This would explain why Foggini’s are supported in the roof trusses by struts that to support the rafters, and he provides no alter- weight (see manuscript edition in the second roof proposal is steeper than the usual Floren- press against the vertical post, which for com- native. In the solution proposed by Giuseppe part of this volume). tine roof. He was aware of the play of forces in pensating all these defects… [the sentence is in- Balatri (fig. 19), an element is introduced that Noferi’s preferred solution, however, is to make the system he suggested, yet he had no clear complete]”118. replaces the struts and supports the rafters in

82 83 22. San Giovannino, general view than the main rafters, intersecting each other 24. Building survey of carried out by Boccia in 1989 (fig. 24), for exam- of roof (photograph Hermann below the ridge, where they are fixed to what San Giovannino in Florence, ple. Nevertheless, they have not been described Schlimme / Jens Niebaum). cross-section showing roof trusses remains of the vertical post. From there, the (from BOCCIA 1989). or analysed to date. 23. San Giovannino, detail of roof (photograph Hermann Schlimme / secondary rafters continue until they intersect A single roof truss (figs. 22, 23) has a span of Jens Niebaum). with the main rafters on the opposite side of the roughly 12.80 metres and consists of four wood- roof. At the three points of intersection, the en beams approximately 27 cm wide and 36 cm members are fixed to each other with a large deep. Two of these beams are the actual rafters. number of nails to create a torsionally rigid Springing from the tops of the walls, where they joint. The load-bearing principle is that horizon- are seated on timber consoles, they meet at the tal thrust from the framed construction is ab- ridge. The roof has a pitch of 18–19°, which cor- sorbed within the truss, with the ridge detail de- responds to the 1:3 gradient recommended by signed as a rigid angle: the two main rafters are Noferi in his Travagliata121. The other two, subject to compression, the lower pair to ten- slightly longer beams rest on the same consoles sion stresses. In addition, at the points of inter- in the wall, but are not inclined so steeply. They section, all elements are subject to bending mo- intersect each other below the ridge line and ments in view of the torsionally rigid fixings. continue on to connect up with the rafters as In the other solutions shown in figure 20, the well. These four intersections are in the form of lower pair of rafters is either replaced altogeth- halved joints [giunzione a mezzo legno], mark- er by long iron straps (middle), or by shorter that Fontani’s concept was adopted, but not ing an improvement on Fontani’s nailed solu- iron straps just at the connection points (top). used, as intended, for altering the existing tion. At these points, the individual beams are The straps can resist only tension loading and structure but for an entire rebuilding of the reduced in thickness to 20 cm. Since one explic- the middle. In Balatri’s solution, however, the are not fixed to the main rafters in a torsionally roof. Nor was it a coincidence that the rafters as it purpose of this form of construction was to fixing of the different elements is weak. What is rigid form. In this way, the load-bearing effect executed in the roof of San Giovannino have ex- prevent the roof trusses exerting outward more, he connects the vaulting to the roof truss- of the structure is reduced to compression ceptionally large dimensions. Whether this was thrust on the tops of the walls, the beams inter- es, which would mean that any small degree of forces on the rafters, and tension forces on the seen as an all-embracing measure to cover the sect in this form to achieve a maximum contact deformation in the roof would automatically be iron straps. The rafters are still subject to bend- general risks of an unfamiliar structure (as inti- surface. In this way, it was possible to absorb transmitted to the vaulting, subjecting it to po- ing stresses, but the lack of torsionally rigid mated above), or whether it was a specific reac- the horizontal forces. The whole structure is tentially destructive forces. connections at the points of intersection, mean tion to the considerable bending moments in- tied together with iron straps and bolts (fig. that not all elements are subject to bending volved remains open to conjecture. 23). The roof consists of a total of eight trusses, Domenico Fontani’s solution to problem 37 stresses. As a result, the trusses are less rigid which are coordinated with the rhythmic struc- While all the solutions to date seek to save an than the one constructed entirely of timber (fig. The roof trusses as executed in ture of Ammannati’s architecture over the en- obviously compromised roof truss by introduc- 20, bottom). San Giovannino, Florence tire length of the church. The wooden vaulting ing secondary elements, Domenico Fontani pro- Despite the functional quality of this solution, Although in problem 37 some thought was giv- is not fixed to the roof construction. Unfortu- posed a new, cohesive and very effective truss Fontani did not introduce elements that would en to a simple modification of the existing roof nately, in 1993-1994 restoration engineers de- based on a completely different load-bearing replace the missing struts and support the long structure in the church of San Giovannino in cided to support the roof with an unnecessary principle (fig. 20; rudimentary sketch fig. 21). main rafters in the middle. On the contrary, the Florence, in the end it was completely rebuilt. steel skeleton structure (fig. 22). It remains to Although this is conversion work, it does not main rafters are subject to additional loading: Unfortunately, there are no extant sources de- be hoped that this will not damage the roof tim- seem to be so. Fontani draws three different the pairs of tension-stressed secondary rafters scribing the decision-making process behind bers, which have shown remarkable resilience: versions of his idea. The first one, at the bottom below the main rafters increase the bending this. It would seem that Domenico Fontani’s so- in more than three centuries, there has not been of the sheet (fig. 20), shows two main rafters, loading on the latter, as if more weight were be- lution to problem 37 was so interesting, despite any visible deflection. which determine the line of the roof. These are ing imposed. It is doubtful whether the main the weaknesses described above, that the new Over and above the unique quality of this roof supported by a second pair of rafters in the rafters of the original roof trusses could have roof structure was developed along these lines. truss in Italy (an aspect that will be discussed form of two parallel boards. This second pair of withstood this additional loading, however. To The roof trusses actually installed in San Gio- below), a number of paradigm shifts can also be rafters is fixed to the feet of the main rafters. what extent the academicians were also aware vannino have not gone entirely unnoticed, of observed. Simple lapped and halved connec- From here they rise at a slightly smaller angle of this is not known. It is significant, however, course: they formed part of the building survey tions were used instead of the art of classical

84 85 25. Problem 17: location of roof 26. Johann WILHELM, 28. Roof of St Matthias, Poplar 29. Designs for roof trusses with trusses; solution by Cosimo Architectura Civilis, Nürnberg High Street, London, 1636-1654 raised tie beams. Note the line Noferi; files of the Accademia 1668, 2nd part, fig. 13. (from YEOMANS 1992, p. 129). of the vaulting, which extends up della Vachia (BNCF, Ms., Fondo into the roof space (Francis 27. Church roof in Lyenhoe in Nazionale, II_46, f. 60r; coloured PRICE, The British Carpenter, Norfolk (from OSTENDORF 1908, reproduction in the manuscript London 1733, plate K). fig. 177). edition contained in this book: plate 6).

The intended publication of the roof truss bines his capra-based concept with Fontani’s the structure in Florence, which has a span of in Noferi’s Travagliata Architettura second pair of rafters, which he cuts off at the 12.80 metres (fig. 26). The examples presented In the first part of his Travagliata, Noferi de- intersection with the raised tie beam. The sec- by Wilhelm also involved the insertion of arched scribes the roof-truss tests in the following ond pair of rafters supports the tie beam and at vaulting in a roof space. The roof structure in words: “I go on to the presentation of different the same time restrains the lower ends of the San Giovannino differs from the ones in Ger- roof trusses – and there are more of them that main rafters, so that they can no longer act as many, however. It was designed in a simpler, could be invented. Since everyone is allowed to levers. While this version has halved joints that more basic constructional form, and the pitch is speak about things that are seen in public and to are resistant to tension, roof truss C (fig. 9) has much flatter. express his own opinions about them, I should a very short vertical post, which defines the From the 13th century onwards in England, it like to interest people in roof trusses, or rather joint between the second pair of rafters and the was common to omit the horizontal tie beam, es- scissor-like constructions [forbicioni], which we collar beam. Although Noferi was perfectly pecially where the roof construction was to re- want to implement in the church of S. Giovanni- aware that the second pair of rafters was sub- main exposed. Examples of this include Stuton no. I should like to speak about this invention as ject to tension, he introduced a vertical post that in Suffolk and Lyenhoe in Norfolk (fig. 27) as a public and widely known thing, and I should separates the elements, and had to bridge this well as Ely Cathedral132. In the opinion of Yeo- like to see whether the roof trusses are well de- connection with an iron plate. The reason for mans, roofs with a raised tie beam and with cru- signed and built according to the criteria I give, this complication is not clear. Noferi neverthe- ciform secondary beams that may bear a resem- and whether they will serve the intended pur- less described the detail – similar to modern blance to the solution used in San Giovannino pose without those inconveniences which some- nailed plate construction – at great length127. did not serve to neutralize horizontal forces. times occur. Furthermore, I show the designs Although Noferi’s Travagliata was certainly in- They were meant above all to strengthen the for roof trusses that were not used in the above- tended for publication, it appeared in print for long rafters. This functions well in the case of mentioned building”125. the first time only recently128. As a result, the steeply pitched roofs (approximately 60°), In other words, Noferi wished to make things roof trusses used in San Giovannino did not re- where the horizontal thrust of the rafters public (“come cosa pubblica”), and the passage ceive a wider degree of exposure and were not scarcely poses a problem. According to Yeo- carpentry joints such as the mortise and tenon. quoted above is a kind of illustrated (fig. 9) re- used elsewhere to any extent. The author is not mans, roof trusses based on the Italian model This necessitated the use of iron elements to search report that invites everyone to discuss aware of any examples of this type of construc- were introduced in England in the 17th centu- hold the wooden beams together (fig. 23). the approach to the problem and the outcome. tion in Italy in the period immediately following ry133. This type of construction means that the Roof trusses were usually raised to the tops of Though the public discussion of building issues the rebuilding of the roof; nor do there appear horizontal forces are concentrated at a few the walls as a series of separate components is nothing new, one can see a paradigm shift in to be any antecedents for this type of construc- points at the crown of the wall. Roofs of flatter and then assembled in situ. Trimming marks the case of San Giovannino. In Noferi’s words, tion. To determine whether Fontani’s idea was pitch also became more popular. If vaulting was were therefore required to indicate the posi- the goal of the Accademia della Vachia is once really unique, it is worth looking further afield, to be extended into the roof space under these tions of the joints. No such marks can be found more made explicit: namely, the wish actively to to England and Germany. In the 17th century, circumstances, appropriate measures had to be on the roof trusses in San Giovannino. All the create an open republic of knowledge (as advo- Italy was mostly an exporter of constructional taken to resist the horizontal forces. As in evidence suggests that they were assembled cated by Bacon) in the building sector. know-how129. It seems unlikely, therefore, that it France and Italy (capra), the obvious solution in on the ground and hoisted as entire units to the Commenting on roof truss A (fig. 9), Noferi would be the recipient of information from Eng- England was to raise the tie beam to a higher roof122. Indeed, among the problems consid- says that it is not enough just to fix the halved land or Germany. Nevertheless, a look at paral- level. This form of construction can be found ered by the Accademici della Vachia, one finds and lapped joints with a nail. One has to prevent lel developments in those countries may be in- from the 17th century onwards, establishing it- an illustrated description by Cosimo Noferi of the joint from failing and thus avoid outward structive. self on a broader basis in the early 18th century. the act of lifting preassembled trusses (in this thrust from the trusses on the tops of the walls. To avoid deflection in the unrestrained ends of case of classical construction) to a rooftop (fig. This can be achieved by reinforcing the roof A comparison with Germany and England the rafters, braces were introduced. The church 25), using a pole crane123. The drawing even truss at joints 1, 2 and 3 with angles (fig. 9 In Germany, the horizontal tie beam was omit- of St Matthias in Poplar High Street in London, shows a narrow street like the Via de’ Gori, “B”), which should be held in position by iron ted from roof trusses only in exceptional cas- built by the East India Company in the years which runs along the northern side of San Gio- straps126. This was not done in the roof of the es130. In his Architectura Civilis (first published 1636-1654, is an early example of this develop- vannino124, so one may suppose that the crane church, however (fig. 22). 1649), Johann Wilhelm depicts three such forms ment. There, too, the arched vaulting extends was conceived specifically for the church build- Noferi adds two further versions of a roof truss of construction131. With spans of 9, 10 and 11.5 into the roof space. The braces are so long that ing site. (fig. 9, lower left, and “C”). In these, he com- metres respectively, they can be compared with they are actually in contact with each other, and

86 87 further timber elements extend them to the nand II and his brother Leopoldo established cases, they probably visited the locations in as Sur la construction des vôutes dans les edi- rafters on the opposite side (fig. 28)134. The re- the Accademia del Cimento (1657-1667), which question. Proof of this certainly exists for the fices (1712) as part of the proceedings of the sulting roof truss was capable of absorbing the took Galileo as its guiding light. In reality, bridge in Pisa138. Académie des Sciences. At the same time, he horizontal forces, and it is based on the same though, the academy was interested in only one lectured on these subjects in the Académie structural concept as that used in San Giovanni- particular aspect of Galileo’s work, namely his Institutionalization of the discussion between d’Architecture141. This reciprocal relationship no in Florence. If one compares the illustrations experimental method. In view of its mixed natural philosophers and building craftsmen between the worlds of building construction and from England (figs. 27, 28), it seems feasible membership, which consisted of avowed follow- During the period when Galileo, Torricelli and natural science had its origin in the interest that a familiar constructional form dating from ers of Galileo like Giovanni Alfonso Borelli Castelli were active, the link between (building) philosophers showed for technology, and it the 13th century was adapted to meet new (1608-1679), moderate adherents like Viviani technology and natural science was mostly in formed the basis of discussion between the var- structural needs. and others who tended towards an Aristotelian one direction: the philosophers were interested ious disciplines. As such, it was a driving force It would be interesting to pursue the theme and philosophy, the academy was unable to make up in the knowledge of technicians and made this in building development. Slowly, this interaction see how this structural form was disseminated its mind to follow an offensive line in interpret- the basis of their deliberations. The Accademia between the two realms became institutional- by means of construction manuals in the course ing experiments in the spirit of Galileo. For ex- della Vachia, on the other hand, stood for the de- ized and a force in its own right which manifest- of the 18th and especially the 19th century; but ample, the academicians could not agree that velopment of reciprocal contacts and a discus- ed itself in the disciplines of the polytechnic that would exceed the scope of this chapter. As Torricelli’s experiment, using a tube filled with sion between the two sides. The Grand Duchy of schools. The firs of these was the École des one example, reference may be made to Price mercury, demonstrated that nature can also Tuscany was thus on the cutting edge of a devel- Ponts et Chaussées founded in Paris in 1748142. (1733)135, whose roof truss (fig. 29) was closely create a vacuum136. Not only Galileo’s interpre- opment that was taking place at the same time This development shifted from Italy to England related to that depicted in Noferi’s Travagliata. tative approach was excluded; the Accademia in England and France. Decisive roles were and above all to France. The Accademia della It was also designed for the same purpose, del Cimento also failed to involve itself explicit- played in this process by the Royal Society in Vachia, on the other hand, came to an abrupt namely to accommodate vaulting below. It ly with findings from the world of technology. London, founded in 1660, and the Académie end, probably with the death of Noferi (around would be worthwhile investigating whether the The exchange of ideas with technicians and Royale des Sciences in Paris, founded six years 1663), and there was no institutional successor. development in England described above craftsmen, on the other hand, was one of the ba- later, as well as by the discussions that took In Florence, the Accademia del Cimento as well formed the basis of Price’s drawings, or sic tenets of Galileo’s scientific work, and his at- place there between persons of different back- as the Accademia della Vachia explored many whether there was possibly a link with Flo- tentive followers must have felt the need to ad- ground and education. The rebuilding of St aspects of the natural sciences in the spirit of rence. To what extent Fontani was acquainted dress technology and to analyse technical Paul’s Cathedral in London by mathematician Galileo in a preinstitutionalized form and with with the English and German examples, on the knowledge. In view of this and the fact that the and architect Sir Christopher Wren (1632-1723) great success in part. Nevertheless, in Flo- other hand, is something that can scarcely be support of science remained an important goal was a subject of debate in the Royal Academy. rence, these activities did not lead to the cre- determined. At all events, the construction tri- in Tuscany, it is not surprising that the Accade- Wren used a catenary curve for the cross-sec- ation of an enduring scientific academy devoted als that were carried out in connection with the mia della Vachia existed in Florence. An acade- tional form of the new cathedral dome. His col- to technical progress as they did in London and new roof in Florence were certainly an excep- my of this kind could be of enormous benefit to league Robert Hooke (1635-1703) had formulat- Paris. Support for the sciences declined in the tional episode, regardless whether the roof as a territorial state organized along modern lines ed the theory that since a chain suspended from Tuscan city. Leopoldo de’ Medici, who had head- executed was designed by Domenico Fontani or with a centralized administration and an inter- two points can withstand only tensile forces, it is ed the Accademia del Cimento, was made a car- was possibly a transfer of knowledge adapted to est in the advance of knowledge. Architectural- the form it assumes that allows it to do so, dinal in 1667. Borelli had returned to Messina in the pitch of the Italian roof. ly, 17th-century Tuscany was not so much dis- namely a catenary curve. Turned upside down, 1666, and his pupils no longer enjoyed the sup- tinguished by great aesthetic achievements, but the catenary would therefore be the ideal form port of the Medicis in their dispute with the The Accademia della Vachia and science by the centralized organization of building ac- for vaulting139. In Paris, one can observe an in- Aristotelians143. The protagonists were not in- in the Grand Duchy of Tuscany in tivity in which rationalization could help to save tense cooperation between the Académie terested, as they had possibly once been, in es- the 17th century funds137. It is not surprising, therefore, that the Royale des Sciences and the Académie d’Archi- tablishing an institution in the form of a scientif- Galileo Galilei’s condemnation by the Inquisi- Accademia della Vachia made topical issues a tecture (founded in 1671). This collaboration ic academy. Exchanges between the natural sci- tion in 1633 did not put an end to support of the central theme of its work, issues such as the was personified in particular by Philippe de La ences and the practical world of building contin- natural sciences in the Grand Duchy of Tuscany, bridge in Pisa, the roof trusses over San Gio- Hire (1640-1718). The treatise on mechanics140 ued on a broad scale, of course, also in Italy. An but it did mark a shift of these measures to vannino, surveying existing fortifications and that La Hire drew up was set against a back- example of this were the Rigoristi in Venice, pupils of Galileo, such as Evangelista Torricelli building new ones, the water supply to build- ground of technical construction issues that who carried out scientific experiments with ma- and Vincenzo Viviani (1622-1703). Fifteen years ings, and the draining of lakes. The academi- were a matter of everyday interest for him, and terials under standardized conditions and who after Galileo’s death in 1642, Grand Duke Ferdi- cians did not withdraw to their studies; in many he published texts on construction topics such counted Carlo Lodoli (1690-1761) among their

88 89 members144. Inevitably, Lodoli’s architectural Galilean natural science and building technolo- Medici coat of arms, but without the passage says: “Il Manoscritto porta il 22 Bruno Casini and Roberto Ciabani marchese Clemente Vitelli fatta da cardinal’s insignia. The sheets contain- seguente titolo ‘La risoluzione di più give no information about the family Francesco Barzini fiorentino professo- theory was no longer based on Vitruvius, but gy. Nelli, who was aware of the unique nature of ing Noferi’s solutions to problems 35 (f. Problemi stati proposti nell’Accademia della Vacchia. Bruno CASINI, I libri re d’astronomia, sopra l’apparizione took as its points of reference Galileo and, sig- this collection, made it available to prospective 119) and 46 (f. 143) bear the Medici coat del Sig. Abate della Vacchia [sic] l’anno d’oro della nobiltà fiorentina e fieso- del nuouo fenemone, o macchia del cie- nificantly enough, the Académie des Sciences in architects and engineers as educational materi- of arms in a neutral escutcheon with a 1661 con i nomi di chi propose, e di chi lana, Firenze 1993; Roberto CIABANI, lo, doue si riconoscono le cagioni del 145 cartouche. Giuliano Ciaccheri, who later ha risoluto’ [italics in the original]”, Le famiglie di Firenze, Firenze 1992. suo nascimento, Firenze 1680. Paris. One line of continuation of the Accademia al . If Nelli’s offer is modest in comparison became a building engineer, also had di- ibid., p. 779. It is worth mentioning that 23 At the end of the document, the fol- 30 In Angelo FABRONI, Historia Acade- del Cimento and above all of the Accademia del- with institutions like the French Academy and rect contacts with Cardinal Giovanni Nelli corrected the name of the acade- lowing certifications are made in an an- miae Pisanae, Pisa 1791-1795, vol. 3, p. Carlo de’ Medici, since his father was my in the title of the manuscript and nual sequence: 399, Albizzini is called “Florentinus”. la Vachia in Florence may be seen in the collec- the École des Ponts et Chaussées, they all re- bottigliere (cellarman) to the cardinal. wrote “Vacchia”. “Vinc E. Peronus IVD ac Cane E qualis Lectureship and professorship are tion of treatises, drawings and manuscripts veal a similar motivation, which at the time of Information from Luigi Zangheri’s arti- 9 Giuseppe MAZZATINTI, Inventari dei Archi Flor. Vidit die 31 May 1666 —- recorded in Storia dell’Università di compiled by Giovanni Battista Clemente Nelli the Accademia della Vachia seems to have been cle on Ciaccheri in DBI, vol. 25 (1981), manoscritti delle biblioteche d’Italia, 13 Vinc E. Peronus IVD ac Cane E qualis Pisa, Commissione rettorale per la sto- pp. 78 et seq. vols., Forlì 1892-1906, vol. VII, 1897, p. Archi Flor. Vidit die 27 May 1667 —- ria dell’Università di Pisa, ed., Pisa (1725-1793), which covered the area between just as strong in Florence as it was in Paris. 6 BNCF, Ms., Fondo Nazionale, II_46: 215. Vinc E. Peronus IVD ac Cane E qualis 1993, vol. 1, t. 2, p. 505. Albizzini is dates of the meetings between f. 71 10 Giovanni GIOVANNOZZI, “Un asserito Archi Flor. Vidit die 28 May 1668 —- recorded as a student in the Registro and f. 155; the manuscript says 4 discepolo di Galileo, Cosimo Noferi”, Vinc E. Peronus IVD ac Cane E qualis sez. D I, 19, preserved in the Archivio di March 1661, but as New Year’s Day in Memorie della Pontificia Accademia Archi Flor. Vidit die 23 May 1669 —-”, Stato di Pisa, Fondo del Rettorato, c. Florence fell on 25 March, we have to Romana dei Nuovi Lincei, ser. 2, 5 ASF, Notarile Moderno, Protocolli, E- 262v, [date 11.4.1658], cited in Mar- read 1661 as 1662; the exact weekday (1919), pp. 109-120, pp. 117-119. stremi: 18959-18960, Patriarchi, Fran- gherita GIUNTA, Libri matricolari was checked at: http://www.adoption.de/ 11 Michele MAYLENDER, Storia delle Ac- cesco 1663-1672, f. 3r-4r. Studii Pisani, 1609-1737, Pisa 1983. The illustrations from the manuscript nelleschi”, Annali dell’Istituto e Museo spelling “Vachia” is used. “Vacchia” is init_kalender.htm. Of 18 dates, 13 are on cademie d’Italia, 5 vols., Bologna 1926- 24 Through his brother Lorenzo, Ottavio Thanks are due to Daniele Ronco from BNCF, Ms., Fondo Nazionale II_46, in di Storia della Scienza di Firenze, A. 2, reserved for the person. Sundays, one on a further holiday, one 1930. della Vacchia granted a pension to his the Archivio dell’Università di Pisa for 12 the present contribution have been pub- fasc. 1 (1977), pp. 71-111, esp. pp. 94-97; 4 Antonino PELLICANÒ, Da Galileo on a Monday, two on Tuesdays and one Michelangelo MURARO, “Cosimo De’ sister Margherita, who was a nun in the this information. 31 lished with the permission of the Minis- Antonio BECCHI, “Chambre H. Per una Galilei a Cosimo Noferi: verso una on a Saturday. Noferi ignoto fiorentino”, Rivista d’arte convent of Santa Chiara. Ottavio also “Renaldinio amisso, quantum detri- tero per i Beni e le Attività Culturali / storia del costruire”, in Degli archi e nuova scienza: un inedito trattato di 7 Elisabeth Kieven has analysed the col- 35 (1960), pp. 71-97, pp. 86-89. left his brother Francesco della Vacchia, menti Academia acceperit, neminem Biblioteca Nazionale Centrale di Firen- delle volte. Arte del costruire tra mecca- architettura nella Firenze del 1650, lections of the two Nellis in connection 13 Luigi ZANGHERI, ed., Avvertimenti e rector of the Church of Sant’Andrea di sane praeteriit. Ipsius in philosophiam ze. Reproduction or duplication by any nica e stereotomia, A. Becchi and F. Firenze 2005. This work was published with the creation of the collection of ar- discorsi di Bartolomeo Vanni, Inge- Rispoli in the diocese of Pisa, legacies merita plures exacuerunt, ut vigilanter technique whatsoever is not permitted. Foce, eds., Venezia 2002, pp. 17-127, p. when the present book was already go- chitectural drawings in the Uffizi. Elisa- gnere Mediceo (1662-1732), Firenze that he himself had inherited. Della Vac- nervoseque adversus Peripateticos sta- The same applies to illustration 3 from 30. Becchi – based on the example of lat- ing to print, so that it was no longer pos- beth KIEVEN, “Notizen zur Geschichte 1977, note 80, p. 28. chia stipulated that he should be buried rent. Ex his in primis commemorandi the manuscript BNCF, Ms. Galileiani er 17th-century France – studies the re- sible to take account of it here. der Sammlungen von Architekturzeich- 14 Original quotation: “Formatosi alla in the family grave in Santa Chiara in mihi videntur Jo. Andreas Albizzinius 147, and the illustrations 9 and 11 from lationship between architecture and ap- 5 The paper used in the manuscript re- nungen. Die Sammlung Nelli in den Uf- scuola degli epigoni di Galileo Galilei”, Florence, a church that was demolished Florentinus, qui in instituendis disci- the manuscript BNCF, Ms. Galileiani plied science; Hermann SCHLIMME, veals a number of striking watermarks, fizien”, in Opere e giorni: Studi su mille DBI, vol. 25 (1981), pp. 78 et seq. in the 19th century to make way for the pulis suis ne latum quidem unguem ab 122. “Construction Knowledge in Compari- especially one of the Medici coat of arms anni di arte europea dedicati a Max 15 Original text: “Lernte in der von den central market in Florence. A will iis, quae proposuerat Galilejus, sibi son: Architects, Mathematicians and with a cardinal’s hat. At the time, this Seidel, K. Bergdolt and G. Bonsanti, Schülern Galileis geführten Schule Ar- drawn up in 1695 by a further member discedendum putabat (1), […]”. The 1 Over the past ten years, various focus- Natural Philosophers Discuss the Dam- was the prerogative solely of Grand eds., Venezia 2001, pp. 667-672. chit. und Ing.-Wesen”, AKL (XLI, 2004, of the family, Giuseppe della Vacchia, al- note says: “Huic rei argumento esse es of activity can be mentioned, like the age to St. Peter’s Dome in 1743”, in Pro- Duke Ferdinando II’s brother, Cardinal 8 “Cosimo Noferi Pittore, ed Architetto, 491). so exists; ASF, Notarile Moderno, Te- possunt: Philosophica asserta ex Lu- book series Between Mechanics and ceedings of the 2nd International Con- Giovanni Carlo de’ Medici (1611–1663). del quale abbiamo alla luce un Opuscolo 16 Original text: “ [...] war der Accad. stamenti Coram Parocho, Pezzo: 5, no. cubrationibus praestantissimi viri Gali- Architecture, Basel 1995- (initiated by gress on Construction History, M. Paper with this watermark was, howev- Mattematico, e che lasciò alla sua morte Geometrica des Abtes Della Vecchia 19, f. 2r-2v. lei depromta, publice discutienda pro- Patricia Radelet de Grave and Edoardo Dunkeld, J. Campbell, H. Louw, M. er, also used by Leopoldo de’ Medici, inedite molte Opere manoscritte trat- [sic] verbunden, in der die Mitgl. 25 Information from: Klaus LANKHEIT, ponit Jo. Cosmus Villifranchi Volater- Benvenuto) and Studies in the History Tutton, B. Addis, C. Powell, R. Thorne, who was made a cardinal in 1667. To tanti di Geometria ed Architettura Civi- geometr., archit. und mathemat. Prob- Florentinische Barockplastik. Die ranus, patrocinante Excellentis. Domi- of Civil Engineering, Aldershot 1997– eds., Cambridge 2006, pp. 2853-2867. confirm this, the author looked through le, e Militare, fu discepolo del nostro Fi- leme erörterten”, AKL (XLI, 2004, 491). Kunst am Hofe der letzten Medici. no Jo. Andrea Albizzini Florentino in 2001 (Joyce Brown general editor). Ref- For the context of shipbuilding, cf. Jür- the whole stock of letters that Mattia losofo [Galileo]. Interveniva ad un’Acca- 17 Cf. note 1. 1670-1743, München 1962, p. 47. Pisana Academia Extraordinariam phi- 18 erence should also be made to the activ- gen RENN and Matteo VALLERIANI, de’ Medici received from his brother demia Geometrica composta di vari in- Antonio BECCHI, Q. XVI. Leonardo, 26 ZANGHERI 2000, p. 132: “Foggini Jaco- losophiam publice profitente, Serenissi- ities and publications of the Associa- “Galileo and the Challenge of the Arse- Leopoldo. Leopoldo uses a series of wa- dividui della sua patria, e quest’Adunan- Galileo e il caso Baldi: Magonza, 26 po Maria, scultore, tasse 1643-47; (…); mo Ferdinando II. M.E.D. dicata Pisis zione Edoardo Benvenuto, the Archive nal”, Nuncius, A. 16, 2 (2001), pp. 481- termarks, among them the Medici coat za si faceva in casa del Sig. Abate della Marzo 1621, Venezia 2004, pp. 17 et eletto Accademico 13.12.1648; (…); eletto 1662 [italics in the text].” Thanks are of the Art and Science of Construction 503. of arms with a cardinal’s hat: ASF, Vacchia Gentiluomo Fiorentino nell’an- seqq., cites as an example the corre- Conservatore 26.8.1657; eletto Festaiolo due to Daniele Ronco of the Archivio (Genoa), the Construction History Soci- 3 BNCF, Ms., Fondo Nazionale, II_46. Archivio Mediceo del Principato, No. no 1660. I Soci erano lo stesso Noferi, spondence between Frézier and Ber- 8.9.1658; eletto Consigliere 8.12.1658; dell’Università di Pisa for pointing out ety, the Istituto e Museo di Storia della English translation of the title: “The so- 5393, ff. 108, 125, 133, 139, 159, 605, 607, Giuseppe Balatri, Iacopo Foggini, Ora- noulli in 1717. eletto Conservatore 14.9.1659; eletto this text. Scienza (Florence), the Sociedad Espa- lution of several problems presented 616, 687, 689, 702 (letters dating from zio Vanni, Domenico Masini, Domenico 19 RENN/VALLERIANI 2001. Conservatore 16.1.1660; Consigliere English translation: “What a loss it was ñola de Historia de la Construcción and, within the academy of Abbot Ottavio 1643 to 1659). Fontana, Gio. Battista e Paolo Antonio 20 BECCHI 2004. 30.4.1670; sqittinato 22.5.1670; eletto Fe- for the academy when Rinaldini left. finally, the International Seminar Teo- della Vachia in the year 1662, with the No fewer than six sheets with drawings Magnali, Domenico [sic] Barzini, Iacopo 21 Searches were made for all members staiolo 21.8.1679; eletto Consigliere There was nobody to take it over. His ria e pratica del costruire: saperi, stru- names of those who proposed them and by Cosimo Noferi in the Vachia manu- Ramponi, Filippo Morosi, Dottor Gio- of the academy in the following places: 1.5.1680; eletto Console risulta defunto.” services to philosophy spurred several menti, modelli (Ravenna 2005) and the those who solved them”. script bear this coat of arms: his solu- vanni Andrea Albizzini, e l’esperto Inge- SBN-OPAC; OPAC of the Bibliotheca 27 Information from: AKL (XLI, 2004, people to take a firmer, more vigilant International Congresses on Construc- In the present context and in the man- tions to problems 3 (f. 8), 16 (f. 56), 17 gnere Giuliano Ciaccheri. In essa propo- Hertziana; AKL; ThB; Google; Luigi 491, article by Susanna Partsch). stand against the peripatetics. The most tion History (Madrid 2003, Cambridge uscript edition in the second part of the (ff. 59, 60), 19 (f. 63) as well as a further nevansi a risolvere diversi Problemi ZANGHERI, ed., Gli accademici del di- 28 Information from: LANKHEIT 1962, p. memorable among these, it seems to 2006) with their respective proceedings. present volume, the spelling “Vachia” sheet with notes by Noferi (f. 65). Geometrici, Architettonici, i quali erano segno. Elenco alfabetico, Firenze 2000; 47; AKL (XLI, 2004, 491, article by Su- me, was Giovanni Andrea Albizzini from Cf. contribution of Antonio Becchi in the was chosen, because that is quite clear- Noferi was evidently in close contact sciolti da uno degli Accademici. Gli atti ASF, Notarile Moderno, Testamenti; sanna Partsch); for Santi Michele e Gae- Florence, who, in teaching his pupils, present volume. ly the form used in the manuscript ti- with the Medici and probably kept them originali esistono nella mia Libreria”, Filippo BROCCHI, Collezione alfabetica tano, cf. Ezio CHINI, La chiesa e il con- believed he should not deviate by a 2 Paolo GALLUZZI, “Le colonne fesse tle. The person who gave his family informed of the activities of the Accade- Giovanni Battista Clemente NELLI, Vi- di uomini e donne illustri della vento dei Santi Michele e Gaetano a hair’s breadth [literally, “by the breadth degli Uffizi e gli screpoli della cupola: il name to the academy, however, was Ot- mia della Vachia. Sheet 23, on which ta e Commercio Letterario di Galileo Toscana, Firenze 1852; DBI. Where the Firenze, Firenze 1984. of a fingernail”] from the things Galileo contributo di Vincenzo Viviani al dibatti- tavio della Vacchia. Wherever refer- Giovanni Battista Magnali formulated Galilei, 2 vols., Lausanne 1793, pp. 778 search revealed no information, these 29 Including Francesco BARZINI, Rispo- had pronounced (1) [...].” The note says: to sulla stabilità della cupola del Bru- ence is made to the academy, the his solution to problem 8, bears the et seq. The note at the end of the quoted sources are not cited. sta ad vna domanda dell’illustriss. sig. “Openly to discuss philosophical evi-

90 91 dence drawn from the nocturnal labours Noferi a follower of Galileo, an “ottimo fior. [crossing out by Coso Ferimoni] le proportioni, i tempi, e quello che gli chanical, except they be such as may be 65 BACON 1992, pp. 42 et seq. nebleau to Giovanni Faber in Rome in 76 “Ora io dico che oviandosi presto al of that outstanding man Galileo, as sug- professore in pratica di geometria” (ex- Appendice Al Compasso Geometrico, e suggerirà l’intelletto da specolare sopra thought secrets, rarities, and special 66 For the concept of progress in Bacon, August 1625: “[…] M’è ben venuto un li- disordine ogni minima forza basterà per gested by Giovanni Cosimo Villifranco cellent professor of practical geometry) Militare di Galileo Galilei 1662 e 63, di tale accidente, e questa sarà quella subtleties”, Francis BACON, The Profi- see Corinna MIETH, “‘Multi pertransi- bro d’un Autore che, se non stesse in In- fermarla, e che lasciando far l’apertura from Volterra, under the patronage of and gave the dates of his life incorrectly BNCF, Palatina. The manuscript proves strada, che l’incamminerà ad una tal cience and Advancement of Learning, bunt et augebitur scientia’: Die Insze- ghilterra, vorrei facessimo ogn’opera grande, una volta ci vorrà una forza the admirable Giovanni Andrea Albizzi- as ca. 1602-1660. Targioni Tozzetti cites that Noferi considered himself to be a perfetione, che potrà ben altri haver London 1605, II, 5. nierung der Grenzüberschreitung als d’averlo dalla nostra: questo è quello eguale al peso e può anche essere che ni from Florence, who teaches Extraor- a manuscript by Giovanni Cinelli, who follower of Galileo. Cosimo Noferi him- maggior chiacchiera, et eloquenza, o 58 Francis BACON, Francisci de Veru- Begründung der Fortschrittsgeschich- stesso che mandò in stampa i Saggi mo- una volta vi si ricerchi forza mille volte dinary Philosophy publicly at the Pisan lived from 1624 to 1705 (Firenze, Bi- self evidently replaced his name with memoria, ma egli saggio, e prudente con lamio Summi Angliae Cancellaris In- te in Francis Bacons Instauratio Ma- rali e De sapientia veterum, Francesco maggiore del peso.” Evangelista TORRI- academy, dedicated to the most illustri- blioteca Nazionale, Ms., Fondo Maglia- “Coso Ferimoni”, since the handwrit- brevi e poche parole saprà quietare ogni stauratio Magna, London 1620 / idem, gna”, in Grenzen und Grenzüberschrei- Bacone, il quale più fa, ha messo fuori CELLI, Opere di Evangelista Torricelli, ous Ferdinand II de’ Medici, Pisa, bechiano, cl. IX, cod. 66, p. 309), in ing is the same. Coso Ferimoni is evi- peripatetica alterezza [...]” BNCF, Ms., Francesco Bacone. Novum Organum, tungen, Conference proceedings, W. un’opera De dignitate et augmentis edite in occasione del III centenario 1622.” Quotations from: FABRONI 1791- which Cinelli referred to Noferi as dently an anagram of Cosimo Noferi, Galileiani 122, Discorso primo, parte se- E. de Mas, ed., Roma/Bari 1992. The In- Hogrebe, ed., Bonn 2002. scientiarum, opera gentilissima, e di della nascita col concorso del Comune 1795, vol. 3, pp. 398 et seq. (Translation “Mattematico eccellentissimo”; Giovan- as GIOVANNOZZI 1919, p. 117, note 1, conda, f. 15r. stauratio Magna contains the Novum 67 But Bacon’s doubts on this score are farsene molto profitto per l’avanzamen- di Faenza, G. Loria and G. Vassura, by Jens Niebaum and Peter Green). ni TARGIONI TOZZETTI, Notizie degli ag- suspected. 48 BECCHI 2004, pp. 67-71. Organum, which is intended as secunda contradicted by Domenico Fontana’s ac- to delle speculazioni in tutte le scienze, eds., Faenza 1919-1944, vol. II, p. 246, Galluzzi describes Carlo Rinaldini – also grandimenti delle scienze fisiche ac- 41 Cosimo NOFERI, Opusculum Geome- 49 Trivium: grammar, rhethoric, logic. pars instaurationis. The full title is complished integration of various fields perché sveglia bellissimi punti. Vedrò di transcription from the manuscript an Accademico del Disegno – as such a caduti in Toscana nel corso degli anni tricum in quo proportionis parabo- Quadrivium: arithmetic, music, astrono- Novum Organum sive indicia vera de of theoretical knowledge into his me- provvedere queste ed altre opere sue BNCF, Ms., Galileiani 147. careful and rigorous thinker that he 60 del secolo 17, Firenze 1780, p. 315. larum cum diversis superficiebus enu- my, geometry. interpretazione naturae. chanical enterprise – for example, he curiose, per servitio costì e di lei e d’al- 77 BNCF, Ms., Galileiani 147; the manu- even furthered the cause of Aristotelian Caverni declares that Noferi was a slav- cleatur doctrina [...], Firenze 1660, dis- 50 On Cusanus’s Idiota Dialogues, cf. 59 In the editio princeps of 1620 (BACON calculated the dead weight of the tri amici. […]”. script contains a description of the thought. Paolo GALLUZZI, ed., Scien- ish follower of Galileo, but that he was cusses parabolas. Jan-Hendryck DE BOER, “Plädoyer für 1620/BACON 1992), the Novum Or- obelisk by defining the specific weight “[...] I welcomed a book by an author for problem by Torricelli himself (auto- ziati a corte: l’arte della sperimen- not very polite towards Benedetto 42 Ten manuscripts by Noferi are con- den Idioten. Bild und Gegenbild des ganum is followed by a Descriptio his- of the stone from which it is made. whom, if he did not stay in England, we graph, f. 78r-79r), a copy by Verenai (f. tazione nell’Accademia Galileiana del Castelli (cf. problem 28 in the manu- served in the Biblioteca Nazionale in Gelehrten in den Idiota-Dialogen des toriae naturalis, et experimentalis, a 68 BACON 1992, 1st part, aphorism 95, p. should do anything to have him here: it 87r-87v) and a copy by Vincenzo Viviani Cimento [1657-1667], Exh. cat. Firenze, script edition in the present volume); Florence, Galileiani 116-125. Gal. 116- Nikolaus von Kues”, Concilium medii text titled Aphorismi de conficienda 106. is the same author who published the (f. 103r-f. 108r). Galleria degli Uffizi, Livorno 2001. Raffaello CAVERNI, Storia del metodo 121 deal mostly with geometry. Gal. 122- aevi 6 (2003), pp. 195-237. historia prima and a Catalogus histori- 69 Ibid., aphorism 73, p. 83. Saggi morali and De sapientia veterum, The full text by Torricelli reads: “Pri- 32 ASF, Archivio Mediceo del Principato, sperimentale in Italia, Firenze 1891- 125 constitute the Travagliata Architet- 51 DE BOER 2003, p. 214. arum particularium. 70 The reception of Bacon’s ideas in the Francis Bacon, who, several years ago, mieramente si cerca perché causa un pezzo 5545, ff. 10-15. 1900 (reprint Bologna 1970), vol. 1, pp. tura. Gal. 123 deals with bridges, 124 52 The Quadrivium, which includes 60 The building crafts in question are: Netherlands in the first half of the 17th published De dignitate et augmentis sci- piccol cerchio di ferro che fascia una co- 33 Domenico Masini posed two geomet- 166 et seq. with building on water, 125 with the con- mathematics, played a subordinate role Nos. “100. Historia Ferri-Fabrilis. 101. century is analysed by Paul DIBON, “Sur entiarum, a most noble work, of which lonna fessa (come nel cortile del Palazzo ric tasks (7 and 8). GIOVANNOZZI 1919 collected the cited struction of mills and fountains. The in the universities until well into the Historia Latomiae sive Lapicidarum. la réception de l’œuvre de F. Bacon en one should make best use in order to ad- De Medici e sotto le logge delli Orefici) 34 Orazio Vanni proposed solutions to statements and recalled the testimony first part of the Travagliata (Gal. 122) is 15th century; cf. DE BOER 2003, pp. 219 102. Historia Lateraria, & Tegularia. Hollande dans la première moitié du vance speculation in all sciences, be- sia bastante a tener quella colonna che three problems, in particular those that of Antonio Magliabechi (1633-1714, un- of greater interest in this case, since it et seq. and 229. 103. Historia Figularis. 104. Historia XVIIe siècle”, in Francis Bacon. Ter- cause it raises beautiful points. I will try non s’apra e per conseguenza a regger involved the determination of specific fortunately without any reference), who deals with vaults, roofs and foundations. 53 Nicolaus CUSANUS, Idiota de staticis Caementaria, & Crustaria. 105. Histo- minologia e fortuna nel XVII secolo, M. to get these and other interesting books quella macchina acciò non rovini. gravity. had declared that Noferi was “di profes- In addition, there is the above-men- experimentis, L. Baur, ed., in Nicolai de ria Ligni-fabrilis. 106. Historia Plum- Fattori, ed., Roma 1984, pp. 91-115. The by him in order to assist you and other Sia la colonna fessa AB, quale si consi- 35 Jacopo Ramponi, in a document in sione Pittore” (a painter by profession) tioned treatise on ballistics. The manu- Cusa Opera Omnia. Iussu et auctori- baria. 107. Historia Vitri & omnium Vi- Novum Organum was reviewed in 1623 friends […]”. The letter is in the Archi- deri in quattro parti divisa. Certo è che which his son is designated an Accade- and died young. Giovannozzi also listed script: Cosimo Noferi, Ricreazion Mat- tate academiae litterarum Heidelber- treorum, & Vitriaria. 108. Historia Ar- by Isaac Beeckman de Middelburg vio Storico Linceo, Rome, Ms. XII, ff. prendendo il peso della fabbrica sovra- mico del Disegno, is referred to as an Noferi’s writings and noted Noferi’s tematica, cioè più Problemi, et espe- gensis ad codicum fidem edita, vol. 5, chitecturae in genere. […] 125. Historia (1588-1637). Dibon describes how 300-301. It is published in: Giuseppe posta in AC, la colonna procurerà di sla- “Ingegnere della parte”: “Felice Inno- membership of the Accademia del Sig. rienze, che hà scelti dall’opere di Ga- Leipzig 1937, pp. 121-125. Miscellanea diversarum Materiarum Descartes was greatly influenced by GABRIELI, ed., Il carteggio linceo della garsi in EF, non potendo AC discendere cenzo di Jacopo Ramponi, ingegnere Abate Ottavio della Vachia (pp. 117 et lileo Galilei, formerly in the Biblioteca 54 Nicolaus CUSANUS, Idiota de sapien- Artificialium; ut Esmaltae, Porcellanae, Bacon. In the Disputatio prima de vecchia Accademia di Federico Cesi se nelle parti di mezzo la fessura della della Parte, tassa 1680; sottoposto 1684; seqq.). Nelli, is now lost; mentioned by GIO- tia. Der Laie über die Weisheit, transl. complurium Caementorum, &c. […] natura et constitutione Physicae pub- (1603-1630), 3 vols., Roma 1941-1942, colonna non si slarga. […] eletto Accademico 26.2.1727”; “Fe- Procissi found sources that testify to the VANNOZZI 1919, p. 116. PROCISSI 1985, and ed. by Renate Steiger, in Die 127. Historia Miscellanea diversarum lished in 1635, Henricus Renerius, pro- vol. II, p. 1059. I wish to thank Alessan- Ora io dico che ovviandosi presto al di- lice Innocenzo of Jacopo Ramponi, engi- fact that Noferi taught mathematics. In p. 47, mentions another manuscript by Schriften des Nikolaus von Kues in Machinarum, & Motuum. 128. Historia fessor at the universities in Deventer dro Borgo-Marinei for kindly sharing sordine ogni minima forza basterà per neer of the Parte Guelfa, taxed 1680, a letter written by Antonio Magliabechi Noferi: Disceptatio pro Euclide et Tor- deutscher Übersetzung, E. Hoffmann, P. Miscellanea Experimentorum Vulga- and Utrecht, advocated the use of opti- this information with me. fermarla, e che lasciando far l’apertura subordinate 1684; [...] elected academi- to Geminiano Montanari (1632-1687), ricellio adversus Pestitutum Eucli- Wilpert and K. Bormann, eds., Ham- rium, quae non coaluerunt in Artem.” cal instruments to strengthen the per- 73 A letter dated 29 December 1634, grande, una volta ci vorrà una forza cian 26.2.1727”, from ZANGHERI 2000, p. the former says about Noferi: “à Noferi dem a Johanne Alphonso Borellio in burg 1988, I, 27, 2 et seq.; cf. DE BOER BACON 1620, appendix, pp. 25-36. ception of the eye and pleaded for the written by Nicolas Claude Fabri de eguale al peso e può anche essere che 268. de qui j’ai appris le peu que je sais de Pisana Academia Matheseos Profes- 2003, p. 228. 61 BACON 1605, The Second Book, Histo- study of nature as developed by man Peiresc to Cassiano dal Pozzo, an- una volta vi si ricerchi forza mille volte 36 So written by ThB. Mathématiques” (from Noferi I learnt sore, now in the Biblioteca di Urbania, 55 Paolo Rossi’s 1962 overview of early ria Mechanica. See also BACON 1992, pp. (the arts), in order to understand nature nounces the sending of the works of maggiore del peso. 37 NELLI 1793, p. 779. the few things I know about mathemat- Ms. 44. modern scientific interest in everyday 31 et seq.; Bacon declares that only very better (thesis XV). After 1650, Bacon Francis Bacon. The letter is published Sia la fessura ABCD, l’apertura o lar- 38 In 1677, Ciaccheri was checking the ics); Angiolo Procissi, La Collezione 43 BNCF, Ms., Galileiani 122. technology is still an important point of special phenomena seem to be worthy remained the “homme-symbole de la in: Cecilia RIZZA, Peiresc e l’Italia, Tori- ghezza della quale sia BD e linea per- contracts for and supervising the Galileiana della Biblioteca Nazionale 44 Although drawings by Cosimo Noferi reference, although he touches only tan- of study, and he pleads that study be fo- Liberta Philosophica”. Johannes Clau- no 1965. I again wish to thank Alessan- pendicolare sia AC. Se per le cose sup- restoration work to the Palazzo di Fra- di Firenze, vol. 2: Contemporanei e Di- dated 1651 exist, cf. MURARO 1960, p. 82, gentially on the building industry; Paolo cused in particular on the most common berg (1622-1665) referred to Bacon’s dro Borgo-Marinei for referring me to poste in principio, e da provarsi, ponendo ternità in Arezzo. In 1685, he designed scepoli (parte 1), Roma 1985. Procissi note 10, this does not contradict the fact ROSSI, I filosofi e le macchine: 1400- and everyday phenomena (BACON 1992, Novum Organum in the Prolegomena this letter. un peso in A ed una potenza eguale in D, and executed the decorations in the quoted from Brack 1808 (Lettres de that Noferi was born in 1635. There are 1700, Milano 1962 (3rd ed. 2002). Cf. al- 1st part, aphorism 119, p. 122), such as: to his Initiatio Philosophi sive Dubita- 74 The Barberini copy has the collocation il momento della potenza a quello del chapel of the Medici villa in Lappeggio plusieurs savans tirées de Manuscrits no known sources that mention Cosimo so R. HOOYKAAS, “The Rise of Modern What is paper? (BACON 1992, 2nd part, tion cartesiana, ad Metaphysicam Cer- “Barberini L VIII 1”. The copy with the peso sta come la AO alla OD. (together with Francesco Coralli). The Autographes et publiées à-present pour Noferi earlier than 1651. Science: When and Why?”, British aphorism 31, p. 205); cf. also Ursula titudinem viam aperiens. A. Reeland collocation “Racc. Gen. Filosofia III 52” Per far dunque che i momenti siano design for the Palazzo Monte di Pietà in la première fois, translated from Italian 45 “Non solo di quello che propongo di Journal for the History of Science: KLEIN, “Experiment, Spiritus und (1676-1708), in his Herderwijk inaugu- has been in the Biblioteca Vaticana since eguali porgasi una potenza che al peso Arezzo followed in 1701 and for the by C. Brack, Genova 1808, p. 48). fare do la sola regola, ma sopra vi faccio BJHS (1987), pp. 453-473. okkulte Qualitäten in der Philosophie ral lecture (1700) titled De incremento the late 19th century. The provenance of sia come DO ad OA. Così poi diremo in Ponte al Romito in 1703. Information MURARO 1960, who is interested in lezione, et discorso, e provo con ragioni 56 Gerhard HARIG, “Die beiden Aspekte Francis Bacons”, Philosophia Natu- quod philosophia coepit hoc seculo, the copy with the collocation “R. I. II questo modo, la potenza piccola alla from: ZANGHERI 1977, note 80; Noferi as an artist, mentions signed geometriche, o ragioni naturali, e così der wissenschaftlichen Revolution des ralis 2 (1996), pp. 289-315, p. 291. called Bacon the first of a whole series 155 copia 2”, bound together with other grande sta come DO ad OA, ma la gran- Zangheri’s article on Ciaccheri in DBI, drawings dated 1651 and 1652. For the tali discorsi non sono di semplice prati- 17. Jahrhunderts und die Gegenwart”, 62 BACON 1992, 1st part, aphorism 99, pp. of scientists: Gilbert, Kepler, Galileo, Bacon texts, is unclear. de al peso stava come AO ad OD, ergo vol. 25 (1981), pp. 78 et seq.; and AKL relationship between Noferi and Borel- co ma da speculativo filosofo, che tale, NTM 8 (1966), pp. 1-10. 108 et seq. Harvey, Torricelli, Digbé, Boyle, 75 Paolo GALLUZZI, “Le colonne fesse ex aequo la potenza piccola è eguale al (XIX, 1998, 124). In ZANGHERI 1977, li, cf. Enrico GIUSTI, Euclides reforma- come proverò deve essere il perito ar- 57 Cf. Francis Bacon’s critique of the de- 63 BACON 1992, p. 43. Huyggens, Descartes (DIBON 1984). degli Uffizi e gli screpoli della cupola: il peso. note 80, reference is also made to a tus, la teoria delle proporzioni nella chitetto” BNCF, Ms., Galileiani 122, liberate exclusion of the manual arts 64 Domenico FONTANA, Della Trasporta- 71 Francis BACON, Franc. Baconis de contributo di Vincenzo Viviani al dibat- Si cava dunque che per tenere unite le number of treatises by Ciaccheri on hy- scuola galileiana, Torino 1993. Proemio, f. 2r; see also Discorso quarto, from learning in his Advancement of tione dell’Obelisco Vaticano et delle fa- Verulamio Summi Angliae Cancellarij tito sulla stabilità della cupola del Bru- colonne che non si aprino maggior- draulic construction. 40 Noferi’s treatise about ballistics is f. 62v. Learning: “For it is esteemed a kind of briche di Nostro Signore Papa Sisto V Novum Organum Scientiarium, Lei- nelleschi”, Annali dell’Istituto e Museo mente, ci vuole una forza la quale al pe- 39 We know little about Cosimo Noferi. dated 1662/1663, La Nuova Prattica 46 RENN/VALLERIANI 2001. dishonour unto learning to descend to fatte dal Cavallier Domenico Fontana den 1650. di Storia della Scienza di Firenze, A. 2, so abbia la proporzione che ha il dia- NELLI 1793, pp. 778 et seq., called del Tiro del Cannone di Cosimo Noferi 47 “[…] considera le forze, i moti, i pesi, inquiry or meditation upon matters me- architetto di Sua Santità, Roma 1590. 72 Cassiano dal Pozzo wrote from Fontai- fasc. 1 (1977), pp. 71-111, pp. 94-97. metro della figura BD alla perpendico-

92 93 lare AC.” The transcription follows are the Venetian edition dating from 95 BNCF, Ms., Gal. 72. gnesi, ed., Roma 1989, vol. 1, pp. 95-104; ma e la chiesa di S. Alessandro in Mi- i.e. the French roofs constitute a trian- line] e che percio si domandava qual di figura simile alaguto, o chiodo. Il se- TORRICELLI 1919-1944, vol. II, p. 246. 1537 and the Bolognese edition dating 96 Leon Battista ALBERTI, Leonis Bap- Mario BENCIVENNI, L’architettura del- lano (1602), Conference proceedings, F. gular form. The length of the bottom sorte di Cavalletto si dovesse adoperare condo modo senza il palo di ferro e che 78 The reinstatement of the Acqua from 1566. There was renewed interest tistae Alberti Florentini viri clarissimi la Compagnia di Gesù in Toscana, Repishti and G. M. Cagni, eds., Roma line of the roof forms the base of an in tal caso. eletto di quercia, o di Castagno lo perno Vergine was completed in 1570 after a in the subject of conical sections at the de Re aedificatoria opus elegantissi- Firenze 1996 (each with bibliography). 2003, pp. 123-132. equilateral triangle, which is compart- Tre sorte ne propongo nella inclusa figu- PQ al quale fattogli il mezzo capo R construction period of more than 100 beginning of the 16th century. Innova- mum, et quam maxime utile, Firenze 100 As early as 17 April 1655, the Gener- 106 Bernardino BALDI, In mechanica mentalized and strengthened as ra, la cons.ra del p(rim)o è che i due q(ues)to [46v] li impernerà in modo che years; cf. Frank BECKER, “Intorno al- tive work did not manifest itself until 1485, book 2, chapter 1. Thoenes recon- al of the Jesuit Order sent his compli- Aristotelis problemata exercitationes. shown.” puntoni AB, BC per una parte puntino leghi il mensolone, il letto, et parte della l’acquedotto Vergine a Roma”, in Ar- the first half of the 17th century, howev- structs this development; Christof ments in a letter to the Grand Duke. Adiecta succinta narratione de autoris Italian original: “Le quattro figure qui al monaco BD et per l’altra alli due muraglia, ma adesso punti il puntone chitettura e tecnologia. Acque, tecniche er, with authors of note like Girard De- THOENES, “Vitruv, Alberti, Sangallo. BÖSEL 1985, p. 81 (Archivum Romanum vita et scriptis, Mainz 1621, pp. 102 et accanto son fatte, al meno due di esse al Mensoloni AF, intaccati non altrimenti spuntato come sta et si vede per PR nel- e cantieri nell’architettura rinascimen- sargues, Blaise Pascal, Claude Mydorge Zur Theorie der Architekturzeichnung Societatis Iesu ARSI, Roma, 31 II, f. seqq., discussed in BECCHI 2004, pp. 82 costume Francese puro, & massima- che s’intacchino l’asticciole, ma ancora i la figura.” tale e barocca, Conference proceedings, and Jan De Witt; cf. Julian Lowell in der Renaissance”, in Hülle und 421). Bösel says that the Grand Duke al- et seqq. Becchi mentions as further ex- mente la segnata A. & la segnata D. per- sud(dett)i mensoloni contrastino a 115 BNCF, Ms., Fondo Nazionale, II_46, C. Conforti and A. Hopkins, eds., Roma COOLIDGE, A history of the conic sec- Fülle. Festschrift für Tilmann Budden- lowed an addition of six braccia in amples the manuscripts of Giovanni cioche per l’ordinamento le coperture sud(dett)i puntoni, mediante l’intaccatu- f. 46v. English translation: “In order to 2002, pp. 159-177. tions and quadric surfaces, New York sieg, A. Beyer, V. Lampugnani and G. height. This is never stated explicitly in Battista da Sangallo and Guidobaldo del alla Francese son fatte di forma triango- rae G, H fate ne puntoni medesimi, con eliminate the thrust, if the convenience 79 The Acqua Felice had been taken into 1968, 1Oxford 1945, pp. 26-33. Schweikhart, eds., Alfter 1993, pp. 565- the sources, but the new roof truss does Monte. Sangallo’s sketches of roof lare, cioè quanto sarà larga la copertu- i quali si colleghino i mensoloni medi- allows it, it would be good to make the service again under Sixtus V. Francesco 88 NOFERI 1660. 584; also in: Christof Thoenes, Opus in- effectively have roughly this height. trusses are contained in a copy of the ra, per linea piana, si farà di essa linea ante li loro staffoni, come sta nel dise- roof trusses more steep, like the third Fontana describes the history of this 89 Cf. Deichsel on this whole subject, certum. Italienische Studien aus drei BENCIVENNI 1996 briefly mentions the first edition of Vitruvius’ treatise (VI- un triangolo di tre lati eguali, comparti- gno. La figura dei quali staffoni sia roof truss. The upper part of this is waterway; Francesco FONTANA, Re- especially the chapter “Die Uhr als wis- Jahrzehnten, München/Berlin 2002, pp. raising of the roof, while BOCCIA 1989 TRUVIUS, De architectura libri decem, to, & armato poi nel modo che si vede.” come l’I, con gli ochi sopra, et sotto, et nothing other than an ordinary roof lazione dello stato vecchio, e nuovo del- senschaftliches Instrument” (The clock 317-341. cites BÖSEL 1985 and concentrates on G. Sulpizio, ed., Roma 1486), available 112 BNCF, Ms., Fondo Nazionale, II_46, con i paletti più sopra et sotto.” truss, which through the rafters ST is l’Acqua Felice [...], Roma 1696. as a scientific instrument); Eckehard Lefèvre distinguishes the orthographic the original Ammannati designs. as a reprint (Ingrid D. ROWLAND, ed., f. 46r; English translation: “Because 113 BNCF, Ms., Fondo Nazionale, II_46, doubled with smaller beams. At the oth- 80 Raffaele MARCHETTI, Sulle Acque di DEICHSEL, “Die Uhr als Bedeutungs- projection of the Renaissance from its 101 From 1656 to 1659, Luigi Lamberti Vitruvius. Ten Books on Architecture. the height of a roof to be erected on a f. 46r; Italian original: “Il secondo Ca- er end, these press against the supports Roma antiche e moderne, Roma 1886, träger”, “Vom Zeitgeber zum Zeitmes- alleged forerunners in the Middle Ages; was the Superior in Florence. He The Corsini Incunabulum. With the building is limited, and since the form of valletto è fatto per mezzo d’intaccature, as described above, and are clamped p. 258; Italian original: “L’esatta livel- ser”, in Uhrzeiten. Die Geschichte der Wolfgang LEFÈVRE, “Emergence of planned to erect a dome over the trib- annotations and autograph drawings the vault to be erected below the roof is come si formano i forbicioni i puntoni and fixed together as above; and this is lazione delle acque, affinchè da tutti Uhr und ihres Gebrauches, Exh. cat. Combined Orthographic Projections”, une of the church (cf. BÖSEL 1985). On of Giovanni Battista da Sangallo, Ro- given, it is impossible to use the roof del quale [last four words added above what I thought I could say about the venga goduta quella giusta quantità che Frankfurt/Main, Historisches Museum, in Pictorial means in Early Modern 15 June 1658, the General of the Jesuits ma 2003); in the reprint, the sketches trusses with the usual tie beam, and [al- the line] non solo sono collegati con l’in- proposed problem.” gli è stata concessa.” I. A. Jenzen, ed., Marburg 1989, pp. 95- Engineering, 1400-1650, W. Lefèvre, ordered Lamberti to stop these plans are to be found on pages 89 and 271. Del so] not so many scissor-like forms of taccatura K, ma anco con le due ML del Italian original: “Et per ovviare anco al- 81 Sesto Giulio FRONTINO, Gli acquedot- 120, pp. 99-102. ed., Max-Planck-Institut für Wis- (ARSI, Roma, 32 I, f. 92). After this, Monte, Meditatiunculae Guidi Ubaldi construction. As far as the inclination of traversone ML et come nel altro Caval- lo spingere se la comodità lo permette ti di Roma, Italian-Latin. Introduction, 90 DEICHSEL 1989, p. 112. senschaftsgeschichte, Preprint 193, Lamberti did not dare to undertake any […], Bibliothèque Nationale de France, the roof is concerned, which has been letto vadino i puntoni a puntare nelli sarebbe bene il fare li cavalletti più ripi- translation and notes by Francesco Gal- 91 Ibid. Berlin 2002, pp. 81-113. building activity. On 4 January 1660, his Paris, M Lat. 10246. For the develop- positioned as far as possible from the mensoloni proposti quali doveranno es- di, come è il terzo cavalletto, del quale li, Lecce 1997, pp. 100 et seqq. 92 Giuseppe BRUSA, “Origine e 97 Wolfgang LEFÈVRE, “The limits of successor, Lidano Colonelli is first men- ment of roof trusses in Rome, cf. Si- built vault, or from the vault to be built, sere, o di Castagno, o di quercia, et la p(art)e superiore non è altro che un 82 Ibid., p. 102: “Circa conlocandos definizione dell’orologio meccanico”, in pictures. Cognitive Functions of Im- tioned (ARSI, Roma, 32, I). We have no mona VALERIANI, “Historic carpentry in the question was: which type of roof staffati come sopra, et che riposino so- ordinario Cavalletto, che mediante li quoque calices observari oportet ut ad Museo di Storia della scienza: catalogo, ages in Practical Mechanics – 1400 to further written evidence for the build- Rome”, in Proceedings of the First In- truss should be used in this case? pra del suo letto di lastroni di pietra, puntoni ST raddoppiati di travette vie- lineam ordinentur nec alterius inferior M. Miniati, ed., Firenze 1991, pp. 188- 1600”, in The Power of images in Early ing of the roof; unfortunately. There are ternational Congress on Construction In the enclosed figure, I propose three come sta nel disegno.” ne retto et li quali puntono [sic!] punta- calix, alterius superior ponatur. Inferior 221, pp. 190 et seq. Modern Science, W. Lefèvre, J. Renn no sources in the ASF. In the ASF History, S. Huerta, ed., Madrid 2003, types. In the first one, the two rafters 114 BNCF, Ms., Fondo Nazionale, II_46, no per l’altra parte nelli mensoloni co- plus trahit; superior, quia cursus acquae 93 APOLLONIUS PERGAEUS, Apolloni Per- and U. Schöpflin, eds., Basel 2003, pp. “Compagnie religiose soppresse da pp. 2023-2034 and Simona VALERIANI, AB, BC at the one end press against the f. 46r/46v. English translation: “The me si è d(ett)o di sopra, et come sopra ab inferiore rapitur, minus ducit”. gami Conicorum libri quattuor, 4 vols., 69-88 and Wolfgang LEFÈVRE, ed., Pic- Pietro Leopoldo”, Patrimonio Ex Ge- “S. Cecilia in Trastevere und die Ge- vertical post BD, and at the other end problem is the thrust which they exert staffati et collegati, et q(ues)to è quanto 83 Edict, ASR, Collezione dei bandi, n. Bologna 1566; EUCLID, Elementorum turing Machines. 1400-1700, Cam- suitico, pezzi 1064 and 1065, there are schichte der römischen Dachwerke”, they press against the two supports AF, at their flanks, especially the first roof mi pareva di poter dire in tal proposto 445, c. 240; detail of archive shelf mark geometricorum libri XV, Basel 1558. bridge, Mass. /London 2004. only records of the construction of the Architectura 35, no. 1 (2005), pp. 32-46. to which they should be connected in no truss. The second one does not exert so problema &.” in Simonetta PASCUCCI and Rosella 94 Domenico Fontani quotes GALILEI 98 In a rudimentary form, the following convent in the 17th century. The church For when the roof truss was “imported” other way than shown. Although [usual- much thrust because of the collar beam 116 BNCF, Ms., Fondo Nazionale (ex TANI, “Le ‘Acque Correnti’: L’Acque- 1638 (Galileo GALILEI, Discorsi e di- analysis formed the subject of a lecture was reconsecrated on 28 October 1665; from Italy into Britain by Inigo Jones ly] one would have to insert tie beams, LM, which we can, however, substitute Nelli), II_46, f. 122r. English transla- dotto Vergine”, in L’Angelo e la Città, 2 mostrazioni matematiche, intorno a the author gave in 2004 at a meeting of BÖSEL 1985, p. 81. (1573-1652), Sir Christopher Wren the aforementioned supports [which are in two ways. The first one is with iron tion: “The present drawing presents a vols., Exh. cat. Roma, Castel Sant’An- due nuoue scienze attenenti alla meca- the Koldewey Society in Dresden. A 102 Filippo Morosi, who proposed the (1632-1723) and others, see David T. seen here as the rest of the tie beam] stakes N, O [see fig. 14, 1.°], which fix roof truss, below which one wishes to gelo, Roma 1987, vol. 2: La città nel Set- nica & i mouimenti locali, Leiden summary of that lecture has since ap- task again as problem 37 in January YEOMANS, The Trussed Roof: its history will form a counterweight to the afore- the rafters to the supports and the bed- erect a vault made of rush mats. In or- tecento, G. Curcio, ed., pp. 46-55, p. 48, 1638) in problem 10; Cosimo Noferi peared in the documentation of that 1662 (in Florence 1661), probably and development, Brookfield, Vt. 1992, mentioned rafters. They are fitted to- ding, and also penetrate part of the ma- der to make it spacious, it was decided note 9. Quoted in full in MARCHETTI does so in problem 22. Francesco Barzi- event. In the meantime, the author has played a decisive role in this context. To p. 30. gether thanks to the oblique cuts G and sonry. These stakes should have a form to cut the tie beam of the aforemen- 1886, pp. 260 et seq. ni refers to the pendulum in problem 25, had the opportunity to present and dis- this day, however, his identity remains a 107 BNCF, Ms., Galileiani 122, Discorso H, which are made in the rafters them- similar to the alaguto [word unclear] or tioned roof truss, and to strengthen it as 84 A drawing is preserved in the Nation- but he does not mention the name of cuss these issues in lectures at the Bib- mystery. quarto, f. 65r. selves and with which they are connect- to the nail. The second way is without shown, leaving the roof shell unaltered. al Library in Naples (Sez. manoscritti e Galileo. Fontani expressly cites Galileo’s liotheca Hertziana, Max Planck Insti- 103 “Data la centinatura ADB d’una vol- 108 Cf. Massimo MUSSINI, “La trattatisti- ed to the supports, using the iron straps iron stakes, but with stakes PQ made of What is shown here for one [roof truss] rari, ms. XII, D.1, f. 8), showing the Discorsi su corpi galleggianti (1612) in tute for Art History in Rome, and at the ta da farsi, et il pendio del tetto FE di- ca di Francesco di Giorgio. Un problema [staffoni] as shown in the drawing. The oak or chestnut [fig. 14, 2.°]. These has to be done to more of them, secur- palace under construction. relation to problem 32. In the context of Max Planck Institute for the History of stante in CD un b(racci)o si deve fare il critico aperto”, in Francesco di Giorgio iron straps should be made as shown in have a half-heading R, through which ing them with this [shown] reinforce- 85 Cf. Paolo GALLUZZI and Maurizio TOR- problem 28, Cosimo Noferi quotes Science in Berlin. cavalletto in modo che non impedisca la architetto, F. P. Fiore and M. Tafuri, the drawing I, with lugs at the upper they are hooked in, in a way that fixes ment before cutting the aforementioned RINI, eds., Le opere dei discepoli di Evangelista Torricelli with the title De 99 In 1773, the Jesuits were expelled fabbricazione della sud(dett)a volta”, eds., Milano 1994, pp. 378-399, pp. 382- and lower ends and wedges rather at together support, bedding and a part of tie beam.” Galileo Galilei, Carteggio 1642-1648, motu acquarum. What is meant is the from Florence, and the church and con- BNCF, Ms., Fondo Nazionale (ex Nelli), 385. the upper than at the lower end.” the wall. But now the blunt rafter Italian original: “Si dice nel presente Firenze 1975, vol. 1, p. 86. De motu gravium naturaliter descen- vent were given to the Piarists II_46, f. 45v. 109 BALDI 1621, p. 104, discussed in BEC- Italian original: “Essendo stata limitata presses through PR as is shown in the Disegno di un Cavalletto, volere sotto 86 Evangelista TORRICELLI, De motu ac- dentium, et projectorum (1644). In con- (Scolopi). For more information about 104 Adriano PERONI, “Einige Überlegun- CHI 2004, pp. 84 et seq.; cf. ibid., glos- l’altezza d’una tettoia da farsi ad una image.” fare una volta di Stuoia, e per farla sfo- quarum, published as appendix to junction with problem 28, Cosimo the church, see: Richard BÖSEL, Jesui- gen zum gebundenen System, zu Ein- sary, p. 129. fabrica, et data la centinatura d’una vol- Italian original: “La difficoltà è dello gata tagliare l’asticciola del d(ett)o ca- Evangelista Torricelli, De motu gravi- Noferi cites Bernardo Castelli’s Della tenarchitektur in Italien 1540-1773. wölbungen und zu Körper- und 110 ASF, Archivio Mediceo del Principa- ta da farsi sotto della sud(dett)e tettoia, spingere che fanno ai fianchi, particolar- valletto, e non toccare la tettoia arman- um naturaliter descendentium, et pro- misura dell’acque correnti (1628). Die Baudenkmäler der römischen und Wandgliederungen der romanischen to, pezzo 5545, ff. 10-15. ne segua [corrected from “seguiva”] mente il primo Cavalletto, il che non fa dolo come si dimostra; quello che si di- jectorum, Firenze 1644. This also plays Domenico Fontani refers to Vignola’s neapolitanischen Ordensprovinz, Wien Architektur in der Lombardei”, in Ro- 111 SERLIO 1575, book 7, p. 198; English non potersi adattare i Cavalletti con tanto il secondo mediante lo traversone mostra d’uno farlo in molti, assicuran- a role in problem 10. Due Regole della Prospettiva in prob- 1985; Vieri Franco BOCCIA, “L’attività manik in Nieder-Sachsen, H. Thies, translation: “At least two of the four im- l’asticciula conforme al solito, ne tam LM, che però potremo supplire in due dolo con questa armadura avanti si tagli 87 In the early modern age, the standard lem 27; Jacopo Barozzi da VIGNOLA, Le conclusiva di Bartolomeo Ammannati: ed., Braunschweig 1997, pp. 205-220. ages shown besides [in the present pa- poco i forbicioni. In riguardo del pendio modi il primo è con li pali di ferro N, O la d(ett)a asticciola.” work on the geometry of conic sections due regole della prospettiva pratica con la chiesa di San Giovanni a Firenze”, in 105 Christof THOENES, “San Pietro: La per fig. 13] are made in accordance with del tetto quale si poneva distante al piu che inchiodino insieme i puntoni con li 117 BNCF, Ms., Fondo Nazionale (ex was the treatise by Apollonius, an au- i commentarij del R.P.M. Danti, Roma Architettura a Roma e in Italia, 1580- fortuna di un modello nel Cinquecento”, the pure French mode, especially the dalla cons(trui)ta volta, o da construissi mensoloni, et il letto, trapassando anco Nelli), II_46, f. 118r. English transla- thor in late antiquity. Of special interest 1583. 1621, Conference proceedings, G. Spa- in La pianta centrale nella Controrifor- figure called ‘A’ and the figure called ‘D’; (que)sta [last word added above the in parte della muraglia quali pali sieno tion: “Three problems were posed in

94 95 the last session, the first of which was figura & et questo è il primo modo. Il se- shown in N, they are of ample width and del Granducato Mediceo”, in Storia del- to erect a vault inside a large hall, condo modo assicura con le sud(dett)e with a double row of nails, one row of l’architettura italiana. Il Seicento, A. which was necessary in order to en- Catene BC, et con lo Tri HJK, come sta which is fixed to the collar beam and the Scotti Tosini, ed., Milano 2003, pp. 322- hance its effect and its required mag- l’altra parte della figura.” other to the rafters and the vertical 335. nificence; or [as a solution it would have 120 Ibid., English translation: “But as post. The plates N have two projections, 138 Noferi describes the cradling to the been conceivable] to raise the roof, the rafter [in the sense of a beam] GL, in a way that the inner part between single-arch bridge in Pisa in his which would have caused an exaggerat- like IK, seems to push too much on the them is linked very close to the wood. In Travagliata Architettura, vol. 2, BNCF, ed cost, so that for the aforementioned flanks of the walls, it would be better to the projections, the two iron straps are Ms., Galileiani 122, Discorso quarto, f. enhancement it was proposed to just leave out GL and to link instead the placed; the two others in the positions P 64v. Noferi must have seen the cradling, cut away the tie beam and the vertical rafter EF with the other pieces, using P. The effect of the iron straps is to pre- therefore. post of the aforementioned roof truss- the double iron straps LM, which would vent the rafters drifting apart.” 139 For a description of Hooke’s idea and es. For this reason, one asked how the have the same effect. This is the third Italian original: “[…] discorro sopra its application in St Paul’s Cathedral, roof trusses could be stabilized, so that mode. Thus far the first problem.” dello C, et E, e dello C gl’è lo F un mo- see Jacques HEYMAN, “Hooke’s Cubico- the thrust they exerted would not crack Italian original: “Et perchè, et perchè naco piccolo connesso, e conficcato alla Paraboical Conoid”, Notes and records the walls. In the three modes presented [sic!] tanto lo puntone GL, come lo IK, trauersa, al quale uanno puntati i due of the Royal Society of London 52, 1 in the sketch enclosed and for the form, pare che spinghino troppo le fiancate puntoni, e fermati insieme con lo mona- (1998), pp. 39-50. Hooke is not the first I say that it is possible to achieve a sim- della muraglia, perció sará meglio inve- co, e trauersa, mediante due piane di to think about the catenary in the con- ilar effect.” ce di esso GL legare lo puntone EF et le ferro confitte una dauanti, e l’altra die- text of vaulted forms, however. For the Italian original: “Tre problemi furono altre parti con lo doppio staffone LM tro, fabbricate come è la N in commoda history of this idea, see the chapter by proposti nella passata sessione, il quale fará l’effetto medesimo, che è il larghezza con doppie conficcature, sì Antonio Becchi in the present volume. p(rim)o de i quali era che volendosi fa- terzo modo, et questo quanto al p(rim)o che una parte di essa uenga confitta su 140 Philippe de LA HIRE, Traite de bricare una volta dentro d’uno stanzone problema.” la trauersa e l’altra parte ne puntoni, e mecanique, ou l’on explique tout ce qui era necessario ci per dargli sfogo, come 121 BNCF, Ms., Galileiani 122, Discorso monaco, et alle medesime piane N si est necessaire dans la pratique des arts, anco il suo competente rigoglio, o d’inal- quarto. fanno li due risalti, si che la parte inter- & les proprietes des corps pesants zare [later addition: di] essa la tettoia, 122 Thanks are due to Frank Becker for na fra essi uenga commessa nel legno lesquelles ont un plus grand usage che riusciva spesa troppo eccedente, si- drawing my attention to this question. rasente li quali risalti uenghino le due dans la physique, Paris 1695. ché per lo sfogo pred(ett)o era solamen- 123 For the pole crane [antenna], cf. arti- staffe e l’altre due nelle parti P P, l’effet- 141 BECCHI 2002, p. 31. Becchi is inter- te proposto il segare la Asticciola, et cle by Nicoletta Marconi in this volume. to delle quali staffe op[er]eranno che i ested in the wider relationship between monaco delli cavalletti sud(dett)i. Perlo- 124 BNCF, Ms., Fondo Nazionale (ex puntoni non si slarghino.” architecture and mechanics and analy- che si domandava il modo di assicurargli Nelli), II_46, f. 59r. The problem is 128 PELLICANÒ 2005. ses to what extent lithotomy (the surgi- in modo che con il loro spingere non posed and solved by Cosimo Noferi. 129 Wotton compiled a body of construc- cal removal of stones from the body) sforzassero la muraglia, perloche. [sen- Complete quotation in the source edi- tional knowledge for English readers, contributed to the development of a the- tence incomplete] In tre modi nello tion of the present volume. taking special account of Italian au- ory of vaulting. For a list of La Hire’s schizzo incluso, et per la figura Dico po- 125 “[…] vengo alla esposizione di diversi thors; Henry WOTTON, Elements of ar- lecturing activities at the Académie tersi conseguire un simigliante effetto.” cavalletti, et altri quali possonsi inventa- chitecture. Collected by Henry Wotton d’Architecture, cf. BECCHI 2002, p. 34. 118 BNCF, Ms., Fondo Nazionale (ex re, e p[er]che sopra delle cose esposte al Knight, from the best Authors and Ex- See also Wolfgang SCHÖLLER, Die Nelli), II_46, f. 118r. Italian original: pubblico, e p[er]messo a ciascheduno il amples, London 1624. In addition, there “Académie Royale d’Architecture”, “Ma p(rim)a mi pare che oltre l’altre sia discorrere, e dirvi sopra il suo parere, are numerous translations of Italian 1671-1793. Anatomie einer Institution, una delle cause principali per le quali li p[er]ciò mosso a curiosità cavalletti, o treatises. Köln/Weimar/Wien 1993, p. 164, for a puntoni spingono a i fianchi, il carico più tosto forbicioni, che dir vogliamo po- 130 Friedrich OSTENDORF, Die Geschich- list of La Hire’s lectures. della tettoia si posato sopra degli arcati, sti in op[er]a alla Chiesa di S. Giovanni- te des Dachwerks, Leipzig 1908, pp. 152 142 Cf. André GUILLERME, “La formation quali nelli cavalletti vengono sorretti no voglio sopra tale inventione discorre- et seq., 155. des nouveaux édiles: Ingénieurs des dalle razze puntanti nel monaco che pe- re, come cosa pubblica, e nota, e vedere, 131 In the second edition: Johann WIL- ponts et chaussées et architectes (1804- rò per assicurare tutte queste mancanze se dalle r[ag]ioni che addurò tali caval- HELM, Architectura Civilis, Nürnberg 1815)”, in Villes et territoire pendant la [sentence incomplete].” letti sieno ben considerati, e fabbricati, 1668, first part, sheet 4 and second part, période napoléonienne, Conference 119 Ibid., English translation: “Any roof e che sieno p[er] havere q[ue]i fini che si sheets 12, 13. proceedings, Roma 1987, pp. 35-57. truss will be chosen that has the double pretende, senza gl’inconvenienti, che 132 OSTENDORF 1908 shows two exam- 143 For a description of the decline of sci- tie BC, which is to be linked to the mid- potrebbero succedere, ed in più dimo- ples and refers to further cases in the ence in the Grand Duchy of Tuscany, see point of the rafters. The rafters GL, EF strerò il modo di far q[ue]llo che non è text, pp. 97 et seq.; YEOMANS 1992, p. 14. GALLUZZI 2001, pp. 24 et seq. are linked to the [remaining] length DE stato fatto in tal fabbrica”, BNCF, Ms., 133 The roof truss was “imported” by Ini- 144 Roberto GARGIANI, “Vers une con- [collo DE] of the [former] tie beam, as Galileiani 122, Discorso quarto, f. 73r. go Jones (1573-1652), Sir Christopher struction parfaite. Machines et calcul de one can see in figure E; and this is the 126 BNCF, Ms., Galileiani 122, Discorso Wren (1632-1723) and others; cf. YEO- résistance des matériaux”, Matières 6 first mode. The second mode assures quarto, f. 73r. MANS 1992, p. 30. (2003), pp. 99-115, p. 107. [stability] through the ties BC and with 127 Ibid., English translation: “I talk 134 YEOMANS 1992, chapter “Raised ties 145 KIEVEN 2001, cf. NELLI 1793. the tri[angles] HJK, as is shown in the about the C and E, and within the C and scissors”, pp. 128-135. other part of the figure.” there is a small vertical post F, which is 135 Francis PRICE, The British Carpen- Italian original: “Si farà elezione per connected and nailed to the collar beam ter, London 1733. ciaschedun Cavalletto delle della [sic!] on which the [second pair of] rafters are 136 See GALLUZZI 2001 for information doppia catena BC da legare insieme li pressing. They are fixed together with on the Accademia del Disegno and on puntoni nella loro metà et lasciato lo the vertical post and the collar beam by science in the Grand Duchy of Tuscany Collo DE del asticciola ad esso si adatta- means of two iron plates, one of them at in the second half of the 17th century. ranno li puntoni GL, EF come sta nella the front the other one at the back. As 137 Cf. Luigi ZANGHERI, “L’architettura

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