James Ackerman Leonardo Da Vinci Art in Science Chapter 22

Abstract

Co-ordinate to the variety of fields of cognition that make up the scientific discipline of architecture, the affiliate investigates interrelations betwixt the technological literature on architecture and literature pertaining to humanistic scholarship as well every bit to mathematics and mechanics. (i) In the Renaissance, close interchanges developed between humanistic scholarship and architectural expertise, not but in relation to Vitruvius' famous De architectura libri decem simply likewise to archaeological questions concerning Roman antiquities. (2) Every bit regards the geometrical methods applied in the architectural design and structure 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. (three) Every bit regards structural design and scientific statics the chapter states that, co-ordinate to our present agreement, the master builders of the Gothic too the Renaissance historic period did not follow any principles of statics when designing structurally, but a number of geometrical procedures and rules instead. Accordingly, information technology was non until the 2nd 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.

Keywords

• Vitruvius
• Architectural drafting
• Perspective drawings
• Orthogonal plans
• Constructive geometry
• Structural blueprint
• Statics

Notes

1. 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. one.) English translation by Joseph Gwilt: The Compages of Thou. Vitruvius Pollio in X Books (London: Priestley and Weale, 1826, p. 3). This definition was restated by many authors up to the seventeenth century, due east.m. 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. ii.

   See Lefèvre (2017), department I.

3. iii.

   Vitruvius' volume was non 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, run across Schuler (1999). In the course of the Renaissance, the book gained the status of the canonical text in discourses on architecture. Later on the advent of press, 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 on editions and translations, see Olschki (1965) II 203 and 205, Kruft (1985) 72ff., Long (2011) 80ff.

4. iv.

   Alberti's De re aedificatoria of c. 1443 was initially disseminated equally a manuscript; the start 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. 5.

   De architectura, volume I chap. 1.

6. six.

   See, for example, Roth (1993).

7. 7.

   Since Vitruvius wrote his treatise in the get-go century BCE, it contained no information nigh building techniques of the Imperial Era, i.e., goose egg nearly developed edifice techniques with concrete or Roman vaulting techniques. For these techniques, come across Lancaster (2005).

8. 8.

   The images bear witness to archeological investigations.

9. 9.

   In volume 8 of his L'idea della architettura universale (Venice 1615), Vincenzo Scamozzi (1548–1616) touched upon gimmicky techniques although non in much particular. The Venetian architect Antonio Rusconi (c. 1500–1578) left backside a considerable number of engravings that depict several gimmicky structure techniques in item and certainly establish a valuable codification of these techniques. (Rusconi created these engravings for a planned Vitruvius translation which appeared posthumously in 1590.)

10. 10.

    Philibert De L'Orme: Nouvelles Inventions pour bien bastir et à petits Fraiz. Paris: F. Morel, 1561. For details, come across Campa (2006).

11. 11.

    In the mid-seventeenth century, Cosimo Noferi (?-c. 1663) compiled Travagliata Architettura, an illustrated manuscript on static problems of wood constructions – see Schlimme (2006). For roof constructions of churches in seventeenth-century Rome, meet Valeriani (2006).

12. 12.

    Niccola Zabaglia: Castelli e ponti con alcune ingegnose practiche. Rome: Due north. and M. Pagliarini, 1743.

13. xiii.

    For case, in the Italian Accademia della Vacchia. See Schlimme (2006) and Schlimme et al. (2014) department 2.12.three.

14. 14.

    Meet DMD – IDs LdVCA34, LdVCA35, gm94a, gm95a, sa1449, sa1450.

15. 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 endless pulleys and other machine parts.

16. sixteen.

    Cesariano, Cesare: Di Lucio Vitruvio Pollione de architectura libri decem. Como See SeeFilarete : Gotardus de Ponte, 1521. Daniele Barabaro: I dieci libri dell' architettura di Thousand. Vitruvio. Venice: Franceschi and Chrieger, 1556. Antonio Averlino: Trattato di architettura, c. 1462 (original not extant; manuscript copies, e.m. Biblioteca Nazionale, Florence: Codex Magliabechianus II, I, 140). – Buonaiuto Lorini: Delle fortificationi libri cinque. Venice: One thousand.A. Rampazetto, 1597. Francesco di Giorgio Martini's Trattati di architettura ingegneria due east arte militare, c. 1490, was disseminated past manuscript copies, e.thou. Codice South (Siena, Bibl. comunale, cod. S.Iv.iv) and codice M (Firenze, Bibl. nazionale, Magliabechiano II.I.141, parte 1). Mod edition: Francesco di Giorgio Martini: Trattati di architettura ingegneria e arte militare. Corrado Maltese (ed.), 2 vols., Milan: Edizioni di Polifilo 1967.

17. 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, South.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. 18.

    The fact that Vitruvius' De architectura were transmitted to the Westward without any of its accompanying drawings caused serious bug 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 non only on philological scholarship merely also on serious archeological investigations. To overcome the problems humanists besides 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 principal builder at the court of Urbino. The results of this commission were, however, rather disappointing. Meet Olschki (1965), vol. I 129.

19. 19.

    Giacomo Barozzi da Vignola: Regola delle cinque ordini d'architettura. Rome: unknown publisher, 1562.

20. 20.

    In the seventeenth century lavishly illustrated books on gimmicky 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. 21.

    See Gerbino and Johnston (2009).

22. 22.

    See Scotti (1983).

23. 23.

    Meet Duffy (1979/1985), Arnold (2002), and Bürger (2013). Come across as well Kruft (1985) section 9.

24. 24.

    The case of ballistics will be discussed in the affiliate on Gunnery in the present volume.

25. 25.

    See Marten et al. (2012).

26. 26.

    Even so, calculations of measures had to be done in units of length that differed from one country or metropolis land to another and demanded conversions that were far from fiddling. See, for case, Schlimme et al. (2014) section 2.vi.1.

27. 27.

    Three of them appeared in print: Matthäus Roritzer : Büchlein von der Fialen Gerechtigkeit (Regensburg, past the author) 1486; idem: Geometria Deutsch (Regensburg, past 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: north.t. (Wiener Werkmeisterbuch ) (Albertina Wien Cim Half-dozen 55) after 1500; Anonymous: Von des Chores Maß und Gerechtigkeit (original no longer extant) later 1500; Lorenz Lechler: north.t. (Unterweisungen) (original no longer extant) 1516. A diplomatic transcription of all of these books is provided by Coenen (1990).

28. 28.

    The booklets by Roritzer and Schmuttermayer.

29. 29.
30. 30.

    It is non clear whether or not another Geometria Deutsch written by a certain Hans Hoesch preceded Roritzer's booklet. In that location is a parallel to these Werkmeisterbücher, that is, to texts written past practitioners for fellow practitioners, namely German language gunners' manuscripts (Büchsenmeisterbücher) of the belatedly Middle Ages; see the chapter on Gunnery, Sect. 3.2.

31. 31.

    Hans Schmuttermayer was a goldsmith and engraver.

32. 32.

    The ii anonymous manuscripts and Lechler'southward booklet . For Lechler'south Unterweisungen, encounter Shelby and Mark (1979).

33. 33.

    For this comparison of Werkmeisterbüchern and Renaissance treatises on architecture, run into likewise 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. 34.

    As is well known, "disegno" was a key concept of art theories of the Italian Renaissance. For the philosophical background of this concept, see, for instance, Panofsky (1924) 29ff., Wolfgang Kemp (1974), and Barzman (2000) 145ff.

35. 35.

    For the following, encounter Lefèvre (forthcoming).

36. 36.

    For the pictorial language of tardily medieval and early modern car drawings, encounter McGee (2004); for the pictorial styles used in early modern literature on mining, come across Lefèvre (2010).

37. 37.

    Meet, for example, Booz (1956).

38. 38.

    For Ritzzeichnungen, meet, for instance, Schoeller (1989) or Pacey (2007) chap. 2; for Planrisse, see, for instance, Böker (2005), Köpf (1977), Recht (1989).

39. 39.

    Leon Battista Alberti'due south 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. 40.
41. 41.

    For this demarcation, see also Thoenes (1993).

42. 42.

    Run across, for case, the notebooks and portfolios mentioned in a higher place (note 17); see too Huppert (2015).

43. 43.

    Run into Lepik (1994); encounter also Alberti De re aedeficatoria book Two, chap. 1.

44. 44.

    See Lefèvre (2004).

45. 45.

    Run into Camerota (2004).

46. 46.

    Ibid. Every bit 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 but instructions on how to derive plans from plans in his writings , particularly in the Underweysung der Messung of 1525 simply also in his Vier Bücher von menschlicher Proportion of 1528.

47. 47.

    For the following, run into Lefèvre (2017) section 3.

48. 48.

    This may have been an important task when prefab natural stones were ordered from distant quarries, a logistical practice that became more and more customary from the thirteenth century on. See Kimpel (1983), Werner Müller (1990) 126ff., Hurx (2018) chap. iii–7.

49. 49.

    Shelby (1972). Come across also Bork (2011) and Lefèvre (2017) section 3.

50. 50.

    See folios 39 to 41 of this thirteenth-century logbook. Mod editions: Hahnloser (1972) or Barnes (2007).

51. 51.

    Run across Hahnloser (1972), "Abbildungen" 91 and 99, and Shelby and Mark (1979); for Werkmeisterbücher , see note 27 above.

52. 52.

    See fig. 33 in Albrecht Dürer'south Underweysung der Messung (book I).

53. 53.

    See Haselberger (1999).

54. 54.

    See Becchi (2014a).

55. 55.

    The similarity of this method to the combined views method discussed in a higher place can hardly be overlooked. For Bogenaustragung, see Müller (1990) chap. five.four.ane and five.4.2.

56. 56.

    For the principal difference betwixt the Gothic and Renaissance mode of using natural stones, which I cannot explore hither, come across Rabasa-Díaz and Calvo-López (2009), particularly department iii.

57. 57.

    The project techniques adult in this context of advanced stereotomy are far too complicated to exist explained here. For the art of stereotomy in the long sixteenth century come across Sakarovitch (1998), chap. i and two; Rabasa-Díaz (2000), chap. ii and iii; Camerota (2004), department 5.

58. 58.

    Le premier tome de l'architecture de Philibert de l'Orme. Paris: Federic Morel1567 . There is no known show that de 50'Orme had any formal mathematical didactics (see Blunt (1958), chap. 1; see also Potié (1996)). Equally the son of a main builder who became a master builder himself, he stood out for his uncommon familiarity with classical architecture caused through journeys and commerce with humanists. He may likewise have acquired his mathematical knowledge through such commerce.

59. 59.

    "As proven by the names [east.g. trompe de Montpellier, trompe quarrée etc.] yet used to define some of these vaults, they are architectural types derived from the Romanesque and Gothic tradition of Southern French republic." Camerota (2004), 203.

60. sixty.

    Mathurin Jousse: Le hole-and-corner 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'Compages de voûtes ou l'Art des traits et coupe des voûtes. Paris: chez Sebastian Cramoisy, 1643.

61. 61.

    Gérard Desargues: Brouillon project d'exemple d'une manière universelle du S.G.D.50. touchant la practique du trait à preuves pour la coupe des pierres en l'compages. Paris: published by the author 1640.

62. 62.

    In the 1995 article on Desargues mentioned above (note forty), she refers to projective geometry. Just she could have said the aforementioned about descriptive geometry, since the stories of these two disciplines are strikingly parallel. "While stereotomy, together with carpentry, provides ane of the richest examples of the uses of applied geometry, information technology is too at the root of a branch of erudite geometry, namely descriptive geometry. To sum upwards the state of affairs, ane 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 hitting. Both practices adult during the Gothic menses – whether on rock cutting work sites or in painters' workshops. The first treatises were edited during the Renaissance and the mathematicians of the 'Monge Schoolhouse' explicitly theorized stereotomy and perspective at the stop of the 18th and get-go of the nineteenth century" (Sakarovitch (2003) 72). It remains to add that stereotomic techniques did not originate with Gothic architecture just can be traced dorsum to times before Classical Antiquity; see, for instance, Semper (1863), 10. Hauptstück.

63. 63.

    However, at the request of Desargues the engraver Abraham Bosse (1604–1670) published a book on stereotomy idea to exist more than 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. 64.

    Monge [1798/99]. See also Dhombres (1992).

65. 65.

    Run into Schlimme et al. (2014) 295ff.

66. 66.

    For these conjectures and speculations, meet, for example, Konrad Hecht (1997), W. Müller (1990) 229ff.; see as well Long (2001) 213ff. and Sakarovitch (2003) 71.

67. 67.

    Some of these rules have been reconstructed from Renaissance and Baroque treatises, run into Huerta (2002).

68. 68.

    For the following, see Ackerman (1991).

69. 69.

    Ibid. 246. Ackerman'southward article is the archetype study on the Milan consultation. See besides Hecht (1997) 113–170. For the geometric grids, see Velte (1951) and Lyman (1987).

70. lxx.

    (one) Paris A f. 51a; (two) Madrid I f. 142v-143r. For Leonardo's studies on arches and vaults, see, for instance, Chastel (1987) or Kurrer (2002) 214 and 386ff.

71. 71.

    For the rules presented in Gil de Hontanón's manuscript, encounter Kubler (1944) and Müller (1990) 235ff.

72. 72.

    Straub (1992) 107. Most of the famous architects of the Roman Bizarre – such as Carlo Maderno , Gian Lorenzo Bernini, Francesco Borromini, and Pietro da Cortona – did not compile treatises on architecture. Guarino Guarini'south Architettura Civile (drawn upwardly c. 1670, published posthumously in Torino in 1737) is an exception.

73. 73.

    Archimedes 1543 (Tartaglia) and 1558 (Commandino), Hero 1575, 1589 (Aleotti), 1616 (Baldi) etc. Since Hero's Mechanica, preserved just in Arabic, was non yet published at the time, his and Archimedes' discussion of the support of a beam or architrave by pillars remained unknown to them. Come across Drachmann (1963) 91–146.

74. 74.

    For this group, see, for example, Drake and Drabkin (1969) 10–16 and 41–52; meet also Nobis (2009).

75. 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 case, Kurrer (2002) chap. 6.iii.

76. 76.

    For the post-obit, see Becchi (2014b).

77. 77.

    De verborum Vitruvianorum significatione (Augsburg 1612).

78. 78.

    In mechanica Aristotelis problemata excertitationes (Mainz 1621). His conceptions on the forcefulness of materials are developed in his commentaries on Ps-Aristotle'southward problems fourteen and 16.

79. 79.

    In the 5th book of his treatise on fortification (see note xvi in a higher place), 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. 80.

    An exception is Cosimo Noferi'south Travagliata Architettura, mentioned above (note 11).

81. 81.

    This holds too for François Derand'southward very sophisticated treatise on vaults mentioned above (note sixty) 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 simply the geometric profile of a cupola but also a consummate set of rules for constructing cupolas. See, for case, Schlimme et al. (2014) section 2.9.5. and Schlimme (2015) 72ff.

82. 82.

    Fusco and Villani (2003) 579.

83. 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 connexion with statics of structure were also discussed by prominent scientists of the time, e.g. past Christiaan Huygens (1629–1695), Leibniz, Musschenbroek (1692–1761), and others; moreover, experiments apropos the strength of materials were carried out, e.m. past 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. 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. 85.

    "No quantitative awarding of statical theory is recorded before the time of Wren." – Mainstone (1968) 306.

86. 86.

    Jacob Bernoulli: "Curvatura Laminae Elastica …" Acta Eruditorum 1694 (pp. 262–276); Bernard Forest de Bélidor: La scientific discipline des ingénieurs dans la conduite des travaux de fortification et d'architecture civile (Paris: Jombert 1729); Charles-Augustin Coulomb'due south Memoir on statics (Memoir read to the French Academy 1773); Jean-Baptiste Rondelet'southward Traité théorique et pratique de 50'art de bâtir (Paris: published past the author, 1802–17).

References

• Ackerman, James S. 1991. "Ars Sine Scientia Nihil Est". Gothic Theory of Architecture at the Cathedral of Milan [1949]. In Distance Points: Essays in Theory and Renaissance Art and Compages, ed. James S. Ackerman, 211–268. Cambridge, MA: The MIT Press.

  Google Scholar

• Andersen, Kirsti. 2007. The Geometry of an Art – The History of the Mathematical Theory of Perspective from Alberti to Monge. New York: Springer.

  Google Scholar

• Arnold, Thomas. 2002. The Renaissance at State of war. London: Cassell.

  Google Scholar

• Barnes, Carl F. 2007. The Portfolio of Villard de Honnecourt. A New Disquisitional Edition and Color Facsimile. Burlington: Ashgate.

  Google Scholar

• Barzman, Karen-Edis. 2000. The Florentine Academy and the Early Country. The Subject area of Disegno. Cambridge: Cambridge Academy Printing.

  Google Scholar

• Becchi, Antonio. 2014a. Die Gestalt der Säule. In Wissensgeschichte der Architektur, ed. Jürgen Renn, Wilhelm Osthues, and Hermann Schlimme, 369–396. Berlin: Edition Open Admission.

  Google Scholar

• ———. 2014b. Architektur und Mechanik. In Wissensgeschichte der Architektur, ed. Jürgen Renn, Wilhelm Osthues, and Hermann Schlimme, 397–428. Berlin: Edition Open Access.

  Google Scholar

• Blunt, A. 1958. Philibert de 50'Orme. London: Zwemmer.

  Google Scholar

• Böker, Johann Joseph. 2005. Architektur der Gotik – Bestandskatalog der weltgrößten Sammlung an gotischen Baurissen der Akademie der Künste Wien. Salzburg: Pustet.

  Google Scholar

• Booz, Paul. 1956. Der Baumeister der Gotik. München: Deutscher Kunstverlag.

  Google Scholar

• Bork, Robert. 2011. The Geometry of Cosmos. Architectural Drawing and the Dynamics of Gothic Design. Farnham: Ashgate.

  Google Scholar

• Brothers, Cammy. 2017. What Drawings did in Renaissance Italia. In The Companion to Early on Modern Architecture, ed. Alina Payne, vol. I. Hoboken: Blackwell Printing.

  Google Scholar

• Büchi, Tobias. 2012. "Mathematische Demonstration« und »mechanische Operation": Buonaiuto Lorini, Galileo Galilei und die Analogie von Festung und Maschine. Scholion, Bulletin 7: 41–57.

  Google Scholar

• Bürger, Stefan. 2013. Architectura Militaris – Festungsbautraktate des 17. Jahrhunderts von Specklin bis Sturm. Berlin: Deutscher Kunstverlag.

  Google Scholar

• Camerota, Filippo. 2004. Renaissance Descriptive Geometry. In Picturing Machines 1400–1700, ed. Wolfgang Lefèvre, 175–208. Cambridge, MA: The MIT Press.

  Google Scholar

• Campa, Maria Rita. 2006. "Les Nouvelles Inventions cascade Bien Batir et a Petits Fraiz" by Philibert de l'Orme: A New Way to Conceive Woods Roof Roofing. In Proceedings of the 2nd International Congress on Structure History, ed. Construction History Society, 525–541. Newcastle: University of Newcastle upon Tyne.

  Google Scholar

• Cesariano, Cesare, ed. 1969. Di Lucio Vitruvio Pollione de architectura libri dece (1521). Reprint München: Fink.

  Google Scholar

• Chastel, André. 1987. The Problem of Leonardo's Compages in the Context of his Scientific Theories. In Leonardo da Vinci – Engineer and Architect, ed. Paolo Galluzzi, 193–206. Montreal: Montreal Museum of Fine Arts.

  Google Scholar

• Coenen, Ulrich. 1990. Dice spätgotischen Werkmeisterbücher in Germany. Untersuchung und Edition der Lehrschriften für Entwurf und Ausführung von Sakralbauten. München: Scaneg.

  Google Scholar

• Dhombres, Jean, ed. 1992. 50'École normale de fifty'an III. Leçons de mathematiques. Laplace, Lagrange, Monge. Paris: Dunod.

  Google Scholar

• Drachmann, A.G. 1963. Fragments from Archimedes in Heron's Mechanics. Centaurus 8: 91–146.

  CrossRef  Google Scholar

• Drake, Stillman, and I.E. Drabkin. 1969. Mechanics in Sixteenth-Century Italian republic. Selections from Tartaglia, Benedetti, Guido Ubaldo & Galileo. Madison: Academy of Wisconsin Press.

  Google Scholar

• Duffy, Christopher. 1979/1985. Siege War – The fortress in the Early on Modern World. 2 vols. London: Routledge.

  Google Scholar

• Dürer, Albrecht. 1969. Hierinn sind begriffen vier Bücher von menschlicher Proportion (1528). Reprint Nördlingen: Uhl.

  Google Scholar

• Fusco, Annarosa Cerutti, and Marcello Villani. 2003. Pietro da Cortona'southward Domes between New Experimentations and Construction Cognition. First International Conference on Construction History, Madrid.

  Google Scholar

• Gerbino, Anthony, and Stephen Johnston. 2009. Compass and Rule – Architecture every bit Mathematical Practice in England. New Oasis: Yale Academy Press.

  Google Scholar

• Hahnloser, Hans R., ed. 1972. Villard de Honnecourt: Kritische Gesamtausgabe des Bauhüttenbuches ms. Fr. 19093 der Pariser Nationalbibliothek. 2nd ed. Graz: Akademische Druck- u. Verlagsanstalt.

  Google Scholar

• Haselberger, Lothar. 1999. Essence and Appearance. Refinements in Classical Architecture. Philadelphia: University of Pennsylvania Museum Publications.

  Google Scholar

• Hecht, Konrad. 1997. Maß und Zahl in der gotischen Baukunst. Hildesheim: Olms.

  Google Scholar

• Huerta, Santiago. 2002. The Mediaeval 'Scientia' of Structures: The Rules of Rodrigo Gil de Montanós. In Towards a History of Construction, ed. Antonio Becchi, Massimo Corradi, Federico Foce, and Orietta Pedemonte, 567–585. Basel: Birkhäuser.

  Google Scholar

• Huppert, Ann C. 2015. Condign an Builder in Renaissance Italia: Art, Science and the Career of Baldassarre Peruzzi. New Oasis: Yale University Printing.

  Google Scholar

• Hurx, Merlijn. 2018. Architecture equally Profession. The Origins of Architectural Exercise in the Low Countries in the Fifteenth Century. Turnhout: Brepols Publishers.

  CrossRef  Google Scholar

• Kemp, Wolfgang. 1974. Disegno. Beiträge zur Geschichte des Begriffs zwischen 1547 und 1607. Marburger Jahrbuch für Kunstgeschichte 19: 219–240.

  CrossRef  Google Scholar

• Kemp, Martin. 1992. The Scientific discipline of Art: Optical Themes in Western Art from Brunellesci to Seurat. New Haven: Yale University Printing.

  Google Scholar

• Kimpel, Dieter. 1983. Dice Entfaltung der gotischen Baubetriebe – Ihre sozio-ökonomischen Grundlagen und ihre ästhetisch-künstlerischen Auswirkungen. In Architektur des Mittelalters - Funktion und Gestalt, ed. F. Möbius and East. Schubert, 246–272. Weimar: Böhlaus Nachfolger.

  Google Scholar

• Köpf, Hans. 1977. Dice gotischen Planrisse der Ulmer Sammlungen. Stuttgart: Kohlhammer.

  Google Scholar

• Kruft, Hanno-Walter. 1985. Geschichte der Architekturtheorie. München: C.H. Beck.

  Google Scholar

• Kubler, George. 1944. A Late Gothic Computation of Rib Vault Thrusts. Gazette des Beau-Arts 25: 135–148.

  Google Scholar

• Kurrer, Karl-Eugen. 2002. Geschichte der Baustatik. Berlin: Ernst.

  Google Scholar

• Lancaster, Lynne C. 2005. Physical Vaulted Construction in Imperial Rome. Cambridge: Cambridge Academy Press.

  CrossRef  Google Scholar

• Lefèvre, Wolfgang. 2004. The Emergence of Combined Orthographic Projections. In Picturing Machines – 1400–1700, ed. Wolfgang Lefèvre, 209–244. Cambridge, MA: The MIT Press.

  CrossRef  Google Scholar

• ———. 2010. Picturing the Globe of Mining in the Renaissance – The Schwazer Bergbuch (1556). Berlin: MPI for the History of Science.

  Google Scholar

• ———. 2017. Architectural Noesis. In The Structures of Practical Knowledge, ed. Matteo Valleriani, 247–269. Cham: Springer.

  CrossRef  Google Scholar

• ———. forthcoming. Compages on Paper: The Development and Functions of Architectural Drawings in the Renaissance. In Creating Place in Early on Modern European Architecture, ed. Elizabeth One thousand. Merrill. Amsterdam: Amsterdam University Press.

  Google Scholar

• Lepik, Andres. 1994. Das Architekturmodell in Italien 1353–1500. Worms: Wernersche Verlagsgesellschaft.

  Google Scholar

• Long, Pamela O. 2001. Openness, Secrecy, Authorship: Technical Arts and the Culture of Cognition from Antiquity to the Renaissance. Baltimore: John Hopkins University Printing.

  Google Scholar

• ———. 2011. Artisan/Practitioners and the Ascension of the New Sciences, 1400–1600. Corvallis: Oregon Country University Press.

  Google Scholar

• Lyman, Thomas W. 1987. "Opus ad triangulum" vs. "opus advertizing quadratum" in Mediaeval Five-aisled Churches. In Artistes, artisans et production artistique au Moyen Âge, Colloque international. Centre National de la Recherche Scientifique, Université de Rennes Two, vol.two, 203–219. Paris: Baral Altet.

  Google Scholar

• Mainstone, R.J. 1968. Structural Theory and Design before 1742. Architectural Review 143: 303–310.

  Google Scholar

• Marten, Bettina, Ulrich Reinisch, and Michael Korey, eds. 2012. Festungsbau: Geometrie, Technologie, Sublimierung. Berlin: Lukas Verlag.

  Google Scholar

• McGee, David. 2004. The Origins of Early Modern Machine Pattern. In Picturing Machines: 1400–1700, ed. Wolfgang Lefèvre, 53–84. Cambridge, MA: The MIT Press.

  Google Scholar

• Merrill, Elizabeth M. 2017. Pocket-Size Architectural Notebooks and the Codification of Practical Knowledge. In The Structure of Applied Knowledge, ed. Matteo Valleriani, 21–54. Cham: Springer.

  CrossRef  Google Scholar

• Müller, Werner. 1990. Grundlagen gotischer Bautechnik. München: Deutscher Kunstverlag.

  Google Scholar

• Nobis, Heribert K. 2009. Naturgesetz und Weltmaschine: die Bedeutung der peripatetischen Quaestiones mechanicae und ihrer frühneuzeitlichen Kommentare für dice Grundlegung der exakten Wissenschaften. Augsburg: Rauner.

  Google Scholar

• Olschki, Leonardo. 1965. Geschichte der neusprachlichen wissenschaftlichen Literatur. Reprint ed., 3 vols. Vaduz: Kraus.

  Google Scholar

• Pacey, Arnold. 2007. Medieval Architectural Drawing – English Craftsmen'southward Methods and their Later Persistence (c.1200–1700). Stroud: Tempus.

  Google Scholar

• Panofsky, Erwin. 1924. "Idea" – Ein Beitrag zur Begriffsgeschichte der älteren Kunsttheorie. Leipzig: Teubner.

  Google Scholar

• ———. 1997. Perspective as Symbolic Form (Die Perspektive als symbolische Form, 1927). New York: Zone Books.

  Google Scholar

• Potié, Philippe. 1996. Philibert de l'Orme. Figures de la pensée constructive. Marseille: Parenthèses.

  Google Scholar

• Rabasa-Díaz, Enrique. 2000. Forma y Construccíon en piedra. De la cantería medievale a la estereotomía del sieglo XIX. Madrid: Ediciones Akal.

  Google Scholar

• Rabasa-Díaz, Enrique, and José Calvo-López. 2009. Gothic and Renaissance Design Strategies in Stonecutting. In Creating Shapes in Ceremonious and Naval Architecture. A Cross-Disciplinary Comparison, ed. Horst Nowacki and Wolfgang Lefèvre, 167–192. Leiden: Brill.

  Google Scholar

• Recht, Roland. 1989. Les Bâtisseurs des cathedrales gothiques – Catalogue d'exposition. Strasbourg: Musées de la ville de Strasbourg.

  Google Scholar

• Roth, Leland M. 1993. Understanding Architecture: Its Elements, History and Meaning. Boulder: Westview Press.

  Google Scholar

• Sakarovitch, Joel. 1998. Épure d'architecture. De la Coupe des pierres à la géométrie descriptive – XVIe–XIXe siècles. Basel: Birkhäuser.

  Google Scholar

• ———. 2003. Stereotomy, a Multifacetd Technique. In Proceedings of the First International Congress of Construction History, ed. Santiago Huerta, 69–79. Madrid: Instituto Juan de Herrera.

  Google Scholar

• Schlimme, Hermann. 2006. Between Compages, Scientific discipline and Technology: The Accademia della Vacchia in Florence, 1661–1662. In Practice and Science in Early Mod Italian Building, ed. Hermann Schlimme, 61–96. Milan: Electa.

  Google Scholar

• ———. 2015. Kontexte der Lehrbuchproduktion im Italien der frühen Neuzeit. In Der Lehrbuchdiskurs über das Bauen, ed. Uta Hassler, 66–77. Zurich: vdf Hochschulverlag.

  Google Scholar

• Schlimme, Hermann, Dagmar Holste, and Jens Niebaum. 2014. Bauwissen im Italien der frühen Neuzeit. In Wissensgeschichte der Architektur, ed. Jürgen Renn, Wilhelm Osthues, and Hermann Schlimme. Berlin: Edition Open Admission.

  Google Scholar

• Schoeller, Wolfgang. 1989. Ritzzeichnungen – Ein Beitrag zur Geschichte der Architekturzeichnung im Mittelalter. Architectura XIX: 36–61.

  Google Scholar

• Schuler, Stefan. 1999. Dice Rezeption von "De architectura" von der Antike bis in die frühe Neuzeit. Cologne/Weimar/Vienna: Böhlau.

  Google Scholar

• Scotti, Auror. 1983. Il collegio degli architetti, ingegneri due east agrimensori tra il Sixteen e il XVIII secolo. In Construire in Lombardia – Aspetti e problemi di storia edilizia, ed. Aldo Castellano and Ornella Selvafolta, 92–108. Milan: Electa.

  Google Scholar

• Semper, Gottfried. 1863. Keramik, Tektonik, Stereotomie, Metallotechnik. Munich: Friedrich Bruckmann.

  Google Scholar

• Shelby, Lon R. 1972. The Geometrical Noesis of Mediaeval Master Masons. Speculum 4: 395–421.

  CrossRef  Google Scholar

• Shelby, Lon R., and Robert Mark. 1979. Late Gothic Structural Design in the 'Instructions' of Lorenz Lechler. Architectura 9 (2): 113–131.

  Google Scholar

• Straub, Hans. 1992. Geschichte der Bauingenieurkunst. Basel: Birkhäuser.

  Google Scholar

• Thoenes, Christof. 1993. Vitruv, Alberti, Sangallo. Zur Theorie der Architekturzeichnung in der Renaissance. In Hülle und Fülle – Festschrift für Tilmann Buddensieg, ed. Andreas Beyer, 379–391. Weimar: VDG.

  Google Scholar

• Valeriani, Simona. 2006. Kirchendächer in Rom. Petersberg: Imhof.

  Google Scholar

• Velte, Maria. 1951. Die Anwendung der Quadratur und Triangulatur bei der Grund- und Aufrissgestaltung der gotischen Kirchen. Basel: Birkhäuser.

  Google Scholar

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   Wolfgang Lefèvre

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Lefèvre, Westward. (2021). Compages. 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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