Abstract
According to the variety of fields of knowledge that make up the science of architecture, the chapter investigates interrelations between the technological literature on architecture and literature pertaining to humanistic scholarship as well as to mathematics and mechanics. (1) In the Renaissance, close interchanges developed between humanistic scholarship and architectural expertise, not only in relation to Vitruvius’ famous De architectura libri decem but also to archaeological questions concerning Roman antiquities. (2) As regards the geometrical methods applied in the architectural design and construction processes, the chapter shows that all of the remarkable methods cannot be taken as applications of erudite (Euclidean) geometry but rather as instances of a “constructive geometry” that developed alongside it. (3) As regards structural design and scientific statics the chapter states that, according to our present understanding, the master builders of the Gothic as well the Renaissance age did not follow any principles of statics when designing structurally, but a number of geometrical procedures and rules instead. Accordingly, it was not until the second half of the seventeenth century that some architects began to resort routinely to early modern scientific statics when designing structures, and that a technological literature on structural design emerged.
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Notes
- 1.
“Architectura eſt ſcientia pluribus diſciplinis, & uarijs eruditionibus ornata: cuius iuditio probantur omnia, quæab cæteris artibus perficiuntur opera.” (Vitruvius: De architectura libri decem , book I chap. 1.) English translation by Joseph Gwilt: The Architecture of M. Vitruvius Pollio in Ten Books (London: Priestley and Weale, 1826, p. 3). This definition was restated by many authors up to the seventeenth century, e.g. by Giovanni Branca in 1629: “L’architettura … è una scienza di più dottrine insieme congiunte; dalla quale si approvano tutte le opera …” (Manuale d’architettura , book I chap. 1).
- 2.
See Lefèvre (2017), section I.
- 3.
Vitruvius’ book was not forgotten during late Antiquity and the Middle Ages. About 80 medieval manuscripts of Vitruvius’ De architectura are known. For the medieval tradition and reception of De architectura, see Schuler (1999). In the course of the Renaissance, the book gained the status of the canonical text in discourses on architecture. After the advent of printing, it was published in several editions and languages: First print edition in Latin by Giovanni Sulpicio (Rome c. 1486); several Italian editions in Latin and Italian, e.g. by Fra Giocondo (Venice 1511), Cesariano (Como 1521), Barbaro (Venice 1556 and 1567) etc.; other translations into vernaculars: into French by Jean Martin (Paris 1547), German by Walther Ryff (Nuremberg 1548), English by Henry Wotton (London 1624) etc. For these early editions and translations, see Olschki (1965) II 203 and 205, Kruft (1985) 72ff., Long (2011) 80ff.
- 4.
Alberti’s De re aedificatoria of c. 1443 was initially disseminated as a manuscript; the first print edition appeared in 1485: De re aedificatoria opus elegantissimum et quam maxime utile. Florence: Laurentius; Sebastiano Serlio: Sette libri d’architettura, Venice and other places, 1537–1575; Andrea Palladio: I quattro libri dell’architettura. Venice 1570; Giovanni Branca Manuale d’architettura. Rome 1629; Georg Andreas Böckler: Compendium architecturae civils. Frankfurt 1648.
- 5.
De architectura, book I chap. 1.
- 6.
See, for instance, Roth (1993).
- 7.
Since Vitruvius wrote his treatise in the first century BCE, it contained no information about building techniques of the Imperial Era, i.e., nothing about developed building techniques with concrete or Roman vaulting techniques. For these techniques, see Lancaster (2005).
- 8.
The images testify to archeological investigations.
- 9.
In book 8 of his L’idea della architettura universale (Venice 1615), Vincenzo Scamozzi (1548–1616) touched upon contemporary techniques although not in much detail. The Venetian architect Antonio Rusconi (c. 1500–1578) left behind a considerable number of engravings that depict several contemporary construction techniques in detail and certainly constitute a valuable codification of these techniques. (Rusconi created these engravings for a planned Vitruvius translation which appeared posthumously in 1590.)
- 10.
Philibert De L’Orme: Nouvelles Inventions pour bien bastir et à petits Fraiz. Paris: F. Morel, 1561. For details, see Campa (2006).
- 11.
- 12.
Niccola Zabaglia: Castelli e ponti con alcune ingegnose practiche. Rome: N. and M. Pagliarini, 1743.
- 13.
- 14.
See DMD – IDs LdVCA34, LdVCA35, gm94a, gm95a, sa1449, sa1450.
- 15.
Della transportatione dell’obelisco vaticano et delle fabriche di nostro signore Papa Sisto V, fatte dal cavalliere Domenico Fontana, architetto di Sua Santita. Roma: Domenico Basa, 1590. Fontana devised and coordinated the concerted effort of 900 men, 75 horses, and countless pulleys and other machine parts.
- 16.
Cesariano, Cesare: Di Lucio Vitruvio Pollione de architectura libri decem. Como : Gotardus de Ponte, 1521. Daniele Barabaro: I dieci libri dell’ architettura di M. Vitruvio. Venice: Franceschi and Chrieger, 1556. Antonio Averlino: Trattato di architettura, c. 1462 (original not extant; manuscript copies, e.g. Biblioteca Nazionale, Florence: Codex Magliabechianus II, I, 140). – Buonaiuto Lorini: Delle fortificationi libri cinque. Venice: G.A. Rampazetto, 1597. Francesco di Giorgio Martini’s Trattati di architettura ingegneria e arte militare, c. 1490, was disseminated by manuscript copies, e.g. Codice S (Siena, Bibl. comunale, cod. S.IV.4) and codice M (Firenze, Bibl. nazionale, Magliabechiano II.I.141, parte 1). Modern edition: Francesco di Giorgio Martini: Trattati di architettura ingegneria e arte militare. Corrado Maltese (ed.), 2 vols., Milan: Edizioni di Polifilo 1967.
- 17.
The earliest known notebook is the logbook of Villard de Honnecourt , an architect active in the thirteenth century. Famous Italian notebooks of the time around 1500 and collections of such drawings are Giuliano da Sangallo’s Taccuino Senese (Biblioteca Communale, Siena, S.IV.8), the Codex Mellon (Pierpont Morgan Library, New York, 1978.44.88) or the Codex Coner (Sir John Soane’s Museum, London). See Merrill (2017) and Brothers (2017).
- 18.
The fact that Vitruvius’ De architectura were transmitted to the West without any of its accompanying drawings caused serious problems as to how the text should be understood. All drawings and diagrams in Vitruvius editions of the sixteenth century must, therefore, be taken as interpretations – interpretations of the text based not only on philological scholarship but also on serious archeological investigations. To overcome the problems humanists as well as architects experienced with the Vitruvian text, a special team of linguistic experts was convened when the Sienese engineer and architect Francesco di Giorgio Martini served as chief architect at the court of Urbino. The results of this commission were, however, rather disappointing. See Olschki (1965), vol. I 129.
- 19.
Giacomo Barozzi da Vignola: Regola delle cinque ordini d’architettura. Rome: unknown publisher, 1562.
- 20.
In the seventeenth century lavishly illustrated books on contemporary exemplary buildings of Baroque Rome, e.g. by Valerien Regnart, Giovanni Giacomo Rossi, Domenico De Rossi, and Guarino Guarini can be regarded as counterparts to books on exemplary buildings of ancient Rome published in the sixteenth century.
- 21.
See Gerbino and Johnston (2009).
- 22.
See Scotti (1983).
- 23.
- 24.
The case of ballistics will be discussed in the chapter on Gunnery in the present volume.
- 25.
See Marten et al. (2012).
- 26.
However, calculations of measures had to be done in units of length that differed from one country or city state to another and demanded conversions that were far from trivial. See, for instance, Schlimme et al. (2014) section 2.6.1.
- 27.
Three of them appeared in print: Matthäus Roritzer : Büchlein von der Fialen Gerechtigkeit (Regensburg, by the author) 1486; idem: Geometria Deutsch (Regensburg, by the author) 1487/88; Hans Schmuttermayer: Fialenbüchlein (Nuremberg: Georg Stuchs) 1489. Of the other three booklets, only manuscript copies or copies of copies are known: Anonymous: n.t. (Wiener Werkmeisterbuch ) (Albertina Wien Cim VI 55) after 1500; Anonymous: Von des Chores Maß und Gerechtigkeit (original no longer extant) after 1500; Lorenz Lechler: n.t. (Unterweisungen) (original no longer extant) 1516. A diplomatic transcription of all of these books is provided by Coenen (1990).
- 28.
The booklets by Roritzer and Schmuttermayer.
- 29.
For a thorough analysis of these Werkmeisterbücher , see Coenen (1990). For further literature, see https://de.wikipedia.org/wiki/Werkmeisterb%C3%BCcherr
- 30.
It is not clear whether or not another Geometria Deutsch written by a certain Hans Hoesch preceded Roritzer’s booklet. There is a parallel to these Werkmeisterbücher, that is, to texts written by practitioners for fellow practitioners, namely German gunners’ manuscripts (Büchsenmeisterbücher) of the late Middle Ages; see the chapter on Gunnery, Sect. 3.2.
- 31.
Hans Schmuttermayer was a goldsmith and engraver.
- 32.
The two anonymous manuscripts and Lechler’s booklet . For Lechler’s Unterweisungen, see Shelby and Mark (1979).
- 33.
For this comparison of Werkmeisterbüchern and Renaissance treatises on architecture, see also Werner Müller (1990) 291. Below, in the context of graphical design techniques, we will return to the geometry taught in the booklets by Roritzer and Schmuttermayer.
- 34.
- 35.
For the following, see Lefèvre (forthcoming).
- 36.
- 37.
See, for example, Booz (1956).
- 38.
- 39.
Leon Battista Alberti’s Della pittura and Piero della Francesca’s De prospectiva pingendi were disseminated only in manuscripts form in the fifteenth and early sixteenth centuries. Albrecht Dürer: Vnderweysung der Messung mit dem Zirckel vnd Richtscheyt. Nuremberg: Hieronymus Andreae 1525. For perspective rendering in the Renaissance, see Panofsky (1997), Martin Kemp (1992) part I, and Andersen (2007).
- 40.
See Andersen (2007); see also Judith Field in an article on Desargues published in 1995 on a website of the University of St. Andrews School of Mathematics (http://www-history.mcs.st-and.ac.uk/Biographies/Desargues.html)
- 41.
For this demarcation, see also Thoenes (1993).
- 42.
See, for instance, the notebooks and portfolios mentioned above (note 17); see also Huppert (2015).
- 43.
See Lepik (1994); see also Alberti De re aedeficatoria book II, chap. 1.
- 44.
See Lefèvre (2004).
- 45.
See Camerota (2004).
- 46.
Ibid. As for Sangallo, who published no treatises, his handmade architectural drawings show that he had full command of the combined views technique. Dürer did not present any geometrical discussions but just instructions on how to derive plans from plans in his writings , particularly in the Underweysung der Messung of 1525 but also in his Vier Bücher von menschlicher Proportion of 1528.
- 47.
For the following, see Lefèvre (2017) section 3.
- 48.
- 49.
- 50.
- 51.
- 52.
See fig. 33 in Albrecht Dürer‘s Underweysung der Messung (book I).
- 53.
See Haselberger (1999).
- 54.
See Becchi (2014a).
- 55.
The similarity of this method to the combined views method discussed above can hardly be overlooked. For Bogenaustragung, see Müller (1990) chap. 5.4.1 and 5.4.2.
- 56.
For the principal difference between the Gothic and Renaissance mode of using natural stones, which I cannot explore here, see Rabasa-Díaz and Calvo-López (2009), particularly section 3.
- 57.
- 58.
Le premier tome de l’architecture de Philibert de l’Orme. Paris: Federic Morel1567 . There is no known evidence that de l’Orme had any formal mathematical education (see Blunt (1958), chap. 1; see also Potié (1996)). As the son of a master builder who became a master builder himself, he stood out for his uncommon familiarity with classical architecture acquired through journeys and commerce with humanists. He may also have acquired his mathematical knowledge through such commerce.
- 59.
“As proven by the names [e.g. trompe de Montpellier, trompe quarrée etc.] still used to define some of these vaults, they are architectural types derived from the Romanesque and Gothic tradition of Southern France.” Camerota (2004), 203.
- 60.
Mathurin Jousse: Le secret d’architecture découvrant fidèlement les traits géométriques, coupes, et dérobemens nécessaires dans les bastiments: enrichi d’un grand nombre de figures, adioustées sur châque disours pour l’explication d’iceux. La Flèche: Georges Griveau , 1642. François Derand: L’Architecture de voûtes ou l’Art des traits et coupe des voûtes. Paris: chez Sebastian Cramoisy, 1643.
- 61.
Gérard Desargues: Brouillon project d’exemple d’une manière universelle du S.G.D.L. touchant la practique du trait à preuves pour la coupe des pierres en l’architecture. Paris: published by the author 1640.
- 62.
In the 1995 article on Desargues mentioned above (note 40), she refers to projective geometry. But she could have said the same about descriptive geometry, since the stories of these two disciplines are strikingly parallel. “While stereotomy, together with carpentry, provides one of the richest examples of the uses of applied geometry, it is also at the root of a branch of erudite geometry, namely descriptive geometry. To sum up the situation, one might say that stereotomy is to descriptive geometry what perspective is to projective geometry. The parallel between the evolution of stereotomy and perspective is indeed striking. Both practices developed during the Gothic period – whether on stone cutting work sites or in painters’ workshops. The first treatises were edited during the Renaissance and the mathematicians of the ‘Monge School’ explicitly theorized stereotomy and perspective at the end of the 18th and beginning of the nineteenth century” (Sakarovitch (2003) 72). It remains to add that stereotomic techniques did not originate with Gothic architecture but can be traced back to times before Classical Antiquity; see, for instance, Semper (1863), 10. Hauptstück.
- 63.
However, at the request of Desargues the engraver Abraham Bosse (1604–1670) published a book on stereotomy thought to be more comprehensible to stone masons: La pratique du trait à preuves de M. des Argues Lyonnois pour la coupe des pierres en Architecture. Paris: Claude Jombert, 1643.
- 64.
Monge [1798/99]. See also Dhombres (1992).
- 65.
See Schlimme et al. (2014) 295ff.
- 66.
- 67.
Some of these rules have been reconstructed from Renaissance and Baroque treatises, see Huerta (2002).
- 68.
For the following, see Ackerman (1991).
- 69.
- 70.
- 71.
- 72.
Straub (1992) 107. Most of the famous architects of the Roman Baroque – such as Carlo Maderno , Gian Lorenzo Bernini, Francesco Borromini, and Pietro da Cortona – did not compile treatises on architecture. Guarino Guarini’s Architettura Civile (drawn up c. 1670, published posthumously in Torino in 1737) is an exception.
- 73.
Archimedes 1543 (Tartaglia) and 1558 (Commandino), Hero 1575, 1589 (Aleotti), 1616 (Baldi) etc. Since Hero’s Mechanica, preserved only in Arabic, was not yet published at the time, his and Archimedes’ discussion of the support of a beam or architrave by pillars remained unknown to them. See Drachmann (1963) 91–146.
- 74.
- 75.
Discorsi e dimonzationi mathematiche intorno a due nuove scienze … (Leiden: Elzevir, 1638), First day and Second day. For Galileo’s treatment of the subject, see, for example, Kurrer (2002) chap. 6.3.
- 76.
For the following, see Becchi (2014b).
- 77.
De verborum Vitruvianorum significatione (Augsburg 1612).
- 78.
In mechanica Aristotelis problemata excertitationes (Mainz 1621). His conceptions on the strength of materials are developed in his commentaries on Ps-Aristotle’s problems 14 and 16.
- 79.
In the fifth book of his treatise on fortification (see note 16 above), Buonaiuto Lorini discussed the stability of small machine models in comparison to full-scale machines, a discussion Galileo might have known about. See Büchi (2012).
- 80.
An exception is Cosimo Noferi’s Travagliata Architettura, mentioned above (note 11).
- 81.
This holds also for François Derand’s very sophisticated treatise on vaults mentioned above (note 60) that still treated structural questions geometrically since its focus was on stereometrical issues in the tradition of De l’Orme. Carlo Fontana (1638–1714), in his Il tempio Vaticano of 1694, provided not only the geometric profile of a cupola but also a complete set of rules for constructing cupolas. See, for instance, Schlimme et al. (2014) section 2.9.5. and Schlimme (2015) 72ff.
- 82.
Fusco and Villani (2003) 579.
- 83.
De La Hire also presented his theories in a treatise : Traité de mecanique (Paris 1695). See Kurrer (2002) chap. 6.4 and Becchi (2014b) 418ff. Issues in connection with statics of construction were also discussed by prominent scientists of the time, e.g. by Christiaan Huygens (1629–1695), Leibniz, Musschenbroek (1692–1761), and others; moreover, experiments concerning the strength of materials were carried out, e.g. by the architect Pierre Bullet (1639–1716), and a table with the values resulting from such experiments by the mathematician Antoine Parent (1666–1716) was published in 1718.
- 84.
Kurrer (2002) 215: “Die Gewölbetheorie La Hires war nicht eine rein akademische Übung der klassischen Mechanik, sondern speiste sich auch aus dem Bedürfnis nach wissenschaftlicher Legitimation des Gewölbeentwurfs – mithin der Begründung der règles de l’art durch die klassische Mechanik.“
- 85.
“No quantitative application of statical theory is recorded before the time of Wren.” – Mainstone (1968) 306.
- 86.
Jacob Bernoulli: “Curvatura Laminae Elastica …” Acta Eruditorum 1694 (pp. 262–276); Bernard Forest de Bélidor: La science des ingénieurs dans la conduite des travaux de fortification et d’architecture civile (Paris: Jombert 1729); Charles-Augustin Coulomb’s Memoir on statics (Memoir read to the French Academy 1773); Jean-Baptiste Rondelet’s Traité théorique et pratique de l’art de bâtir (Paris: published by the author, 1802–17).
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Lefèvre, W. (2021). Architecture. In: Minerva Meets Vulcan: Scientific and Technological Literature – 1450–1750. Archimedes, vol 60. Springer, Cham. https://doi.org/10.1007/978-3-030-73085-7_2
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