Abstract
“An arch is nothing but a strength caused by two weaknesses; that is why an arch in buildings is composed of two quarter-circles; these quarter-circles, each very weak in itself, wish to fall, and opposing each other’s ruin, convert weakness into a single strength.”1
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References
R. Marcolongo, Studi vinciani,Vol. 7 (Naples, 1937) (hereafter Marcolongo, Studi vinciani),p. 237.
Leonardo’s intuition has ancient roots. See for example Seneca’s “Epistola 95,” quoted in G.W. Krafft, “Resolutiones problematum spectantium ad architecturam civilem,” Commentarii Novae Academiae Scientiarum Imperialis Petropolitanae,Vol. 4 (1752–1753), pp. 200–234. According to Seneca, “Society is similar to the stones of an arch; they would fall, if they did not hinder each other, and thus they hold themselves up.”
Leonardo da Vinci, Forster Codex II, fol. 82v.
Marcolongo, Studi vinciani,p. 239.
L.B. Alberti, De re aedificatoria (L’architettura). Ed. G. Orlandi (Milan, 1966), Book 3, ch. 13, pp. 235–237.
G. Guarini, Architettura civile (Turin, 1787); F. Blondel, “Résolution des quatre principaux problmes d’architecture,” Mémoires de l’Académie Royale des Sciences depuis 1666 jusqu’à 1699, Vol. 5 (1729), pp. 355–530; B. Vit-tone, Istruzioni elementari per l’indirizzo dei giovani allo studio dell’ architettura (Lugano, 1760), pp. 509–514.
V. Viviani, Formazione e misura di tutti i cieli (Florence, 1692), in G. Grandi, Geometrica demonstratio viveanorum problematum (Florence, 1703 ) pp. 23–26.
Ibid.,p. 143.
V Scamozzi, Dell’ idea dell’ architettura universale (Venice, 1615), part 2, book 8, ch. 14, p. 320.
Galilei, Opere,Vol. 8, pp. 604–605.
Ibid.,pp. 143–144.
S. Di. Pasquale, “Una ipotesi sulla struttura della cupola di S. Maria del Fiore,” Restauro, Vol. 28 (1976).
F. Derand, L’architecture des voûtes, ou l’art des traits, et coupes des voûtes, new ed. (Paris, 1743 ).
Ibid.,part 1, ch. 6, p. 10.
J. Rondelet, Traité théorique et pratique de l’art de bâtir (Paris, 1802 ).
E. Viollet le Duc, Dictionnaire raisonné de l’architecture française du XI° au XVI° siècle (Paris, 1854–1868). In his degree dissertation, an Iranian student of mine, Mr. A. Naderi, has shown that the medieval Arabian builders used a slight variant of Derand’s rule. They determined points B and C by intersecting the intrados with a circle centered in D and tangent to the axis of the arch.
C, Wolff, Elementa matheseos universae (Magdeburg, 1717), Vol. 2, Elementa architecturae civilis,ch. 5, problem 18, p. 994; B.A. Vittone, op. cit.; B. Forest de Belidor, La science des ingénieurs dans la conduite des travaux de fortification et d’architecture civile (Paris, 1729), ch. 8; G.B. Borra, Trattato della cognizione pratica delle resistenze geometricamente dimostrato .. (Turin, 1748), pp. 109–122; F. Milizia, Principj di architectura civile 2d ed. (Bassano, 1804)
All quotations from Fabri are taken from Fabri, Physica, Tractatus 2, book 5, pp. 622–627.
This odd “explanation” of the thrust induced by an arch on its abutments can be found also in one of Leonardo’s sketches.
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Benvenuto, E. (1991). Knowledge and Prejudice before the Eighteenth Century. In: An Introduction to the History of Structural Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2994-0_1
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