Abstract
When Leonardo da Vinci claimed that mechanics is the paradise of the mathematical sciences, he was launching an approach to the design and improvement of machinery. His notebooks witness how far he himself had proceeded in the application of mathematical techniques to such tasks.
Only in the middle years of the sixteenth century, as artillery came to dominate the field of warfare did such ideas begin to take hold. Ancient works on mechanics were studied enthusiastically, like the Mechanical Problems, and Archimedes, who became a culture hero. Meanwhile Tartaglia, particularly in his Nova Scienza, suggested that similar methods could be used to describe bodies in motion. The development of artillery imposed a new style of fortification, which required a new military engineer, one whose skills were closer to those of the surveyor. Those who wished to hold command in war might need some help with problems of this kind, encouraging mathematicians to devise novel instruments, that would assist in carrying out observation and calculation.
The publications of Agricola and Biringuccio on mining and metallurgy also demonstrated how widely machinery was employed in these lucrative sectors of the economy. Bringing all this together, the first printed books of mechanical invention often illustrated mathematical instruments as well as their machines, while they insisted on the way their machines embodied simple mathematical concepts.
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Notes
- 1.
“la meccanica e il paradiso delle scientie matematiche perche con quella si viene al frutto matematico,” from ms E8b in J. P. Richter (ed. ), The Literary Works of Leonardo da Vinci (London: Phaidon, 1970), II: 241, 1155.
- 2.
Aristotle, Minor Works, ed. and trans. Walter Stanley Hett (Cambridge Mass.: Harvard University Press, 1936); Paul L. Rose and Stillman Drake, “The PseudoAristotelian Questions of Mechanics in Renaissance Culture,” Studies in the Renaissance 18 (1971): 65–104; Matteo Valleriani, “The Transformation of Aristotle’s Mechanical Questions: A Bridge Between the Italian Renaissance Architects and Galileo’s First New Science,” Annals of Science 66.2 (2009): 183–208.
- 3.
Plutarch, “Life of Marcellus,” xiv in Plutarch, Plutarch Lives: Agesilaus and Pompey, Pelopidas and Marcellus, trans. Bernadotte Perrin (Cambridge: Harvard University Press, 1917), 5: 470–77.
- 4.
See Katherine Hill, “‘Juglers or Schollers?’: Negotiating the Role of a Mathematical Practitioner,” British Journal for the History of Science 31 (1998): 253–74.
- 5.
For Brunelleschi see Frank D. Prager and Gustina Scaglia, Brunelleschi: Studies of his Technology and Inventions (Cambridge, Mass.: MIT Press, 1970).
- 6.
T. Schiøler, Roman and Islamic Waterwheels (Odense: Odense University Press, 1973).
- 7.
An overshot waterwheel for a mill is also described by Vitruvius , De Architectura X.5 (hereafter cited as ‘Vitruvius’). Terry S. Reynolds, Stronger than a Hundred Men, a History of the Vertical Waterwheel (Baltimore: Johns Hopkins University Press, 1983). Also Steven A. Walton, “reCOGnition: Medieval Gearing from Vitruvius to Print,” AVISTA Forum Journal 19.1/2 (2009): 28–41.
- 8.
Leon Battista Alberti, De Re Aedificatoria (1452; first printed Florence: Nicolai Laurentii, 1485), VI.6–8; translated as, On the Art of Building in Ten Books (Cambridge, Mass: MIT Press, 1988).
- 9.
For Taccola, see Frank D. Prager and Gustina Scaglia, Mariano Taccola and his Book de Ingeneis (Cambridge Mass.: MIT Press, 1972) and Mariano Taccola, De Rebus Militaribus (De machinis, 1449), ed. Eberhard Knobloch, Saecula Spiritalia Ingenieria e Arte Militare 11 (Baden-Baden: V. Koerner, 1984). For Francesco di Giorgio see C. Maltese (ed.), Francesco di Giorgio Martini, Trattati di Architettura, Ingenieria e Arte Militare, Trattati di architettura 3 (Milan: Il Polifilo 1967), and F.P. Fiore, Cittá e Macchine del ‘400 nei Disegni di Francesco di Giorgio Martini, Studi of the Accademia toscana di scienze e lettere La Colombaria 49 (Florence: L.S. Olschki, 1978). And for all these artist-engineers, see Pamela O. Long, Openness, Secrecy, Authorship: Technical Arts and the Culture of Knowledge from Antiquity to the Renaissance (Baltimore: Johns Hopkins University Press, 2001), esp. ch 4ƒƒ.
- 10.
Niccolo Tartaglia, Quesiti e Inventioni diverse (Venice: Lulio, 1546). The seventh book is devoted to a discussion of the “questioni mechanice, which he avers is “benissimo et certamente le sono cose suttilissime et di profonda dottrine.” See also Matteo Valleriani, Lindy Divarci, and Anna Siebold, Metallurgy, Ballistics, and Epistemic Instruments: the Nova scientia of Nicolò Tartaglia (Berlin: Edition Open Access, 2013) and Raffaele Pisano and Danilo Capecchi, Tartaglia ’s Science of Weights and Mechanics in the Sixteenth Century, History of Mechanism and Machine Science 28 (Dordrecht: Springer, 2015).
- 11.
The manuscript was written at Trento in 1545 or 1546, but not printed. It was published by R. Foulché-Delbosch, “Mechanica de Aristoteles,” Revue Hispanique 5 (1898): 365–405.
- 12.
Alessandro Piccolomini, In Mechanicas Quaestiones Aristotelis Paraphrasis (Rome: A. Bladum, 1547).
- 13.
Guido Ubaldo del Monte, Mechanicorum Liber (Pesaro: Hieronymum Concordiam, 1577). For his fundamental concepts, see M. van Dyck, “Gravitating toward Stability: Guidobaldo’s Aristotelian-Archimedean Synthesis,” History of Science 44 (2006): 373–407. The best introduction to this theme is still Stillman Drake and I.E. Drabkin, Mechanics in Sixteenth Century Italy (selections from Tartaglia, Benedetti Guido Ubaldo and Galileo) (Madison: University of Wisconsin Press, 1969).
- 14.
E.g., Oreste Vannocci Biringucci, Parafrasi di monsignor Alessandro Piccolomini sopra le Mecaniche d’Aristotile (Rome: F. Zanetti, 1582) and Filippo Pigafetta, Le mechaniche: nelle quali si contiene la vera dottrina di tutti gli istrumenti principali da mover pesi grandissimi con picciola forza (Venice: Francesco di Franceschi, 1581).
- 15.
Petrus Apianus, Instrument Buch (Ingolstadt: P. Apianus , 1533).
- 16.
Gemma Frisius’ Libellus de Locorum describendorum ratione is attached to Apianus’ Cosmographicum liber (Antwerp: Arnoldum Birckman, 1533).
- 17.
Georgius Agricola, De Re Metallica (Basel: H. Frobenium et N. Episcopium, 1556), translated as Herbert and Lou Henry Hoover (ed. and trans.), De Re Metallica (New York: Dover Publications, 1950).
- 18.
Jacques Besson, Le Cosmolabe ou Instrument universel concernant toutes observations qui se peuvent faire par les sciences mathématiques, tant au ciel, en la terre (Paris: Ph. G. Deroville, 1567). In the same year he published his inventions book, he also published a more ‘traditional’ text on waterworks : L’Art et science de trouver les eaux et fontaines cachées soubs terre, autrement que par les moyens vulgaires des agriculteurs & architects (Orleans: E. Gibier, 1569). His first work was on the medicinal extracts of the olive tree: De absoluta ratione extrahendi olea & aquas e medicamentis simplicibus (Tiguri [Zurich]: Andream Gesnerum Jr., 1559).
- 19.
Jacques Besson, Instrumentorum et Machinarum. Liber Primus (Orleans or Lyons?, 1569). Only later editions are entitled Theatrum instrumentorum et machinarum (e.g., Leiden: B. Vincentium, 1578).
- 20.
Christopher Duffy, Siege Warfare; the Fortress in the Early Modern World (London: Routledge & Kegan Paul, 1979). Horst de La Croix, “The Literature on Fortification in Renaissance Italy,” Technology and Culture 4 (1963): 30–50 lists well over a hundred treatises specifically on fortification. He adds some books of general advice to army officers, including material on this theme, which has been the basis for continued study.
- 21.
For Ramelli, Le Diverse et Artificiose Machine (Paris: casa del Autore, 1588), see Eugene S. Ferguson (ed.) and Martha T. Gnudi (trans.), The Various and Ingenious Machines of Agostino Ramelli (1588) (Baltimore: John Hopkins University Press, 1976) and cf. Alex G. Keller, review of this edition as “Renaissance Theaters of Machines,” Technology and Culture 19 (1978): 495–508. For Jean Errard, Le Premier Livre des Instruments Mathématiques et Mécaniques (Nancy: Jan-Janson, 1584) see Albert France-Lanord (ed.), Le Premier livre des instruments mathématiques méchaniques (Paris: Berger-Levrault, 1979). Both Ramelli and Errard had sons who followed them into the new profession, which suggests its attraction as a career at the time.
- 22.
Thomas Smith, Art of Gunnery (London: n.p. for William Ponsonby, 1600), 74. Gabriello Busca, Della Architettura Militare. Primo libro (Milan: Bordone and Locarno 1601), proposed in a ‘book III’ to deal with machines, explaining how necessary it was for a “military architect” to know how to make them. Diego Ufano, Tratado de la Artilleria (Brussels: Juan Momarte, 1612), 142 and 223–53, also insists on knowledge of machines for the gunnery officer. Pigafetta , in the dedication to the military engineer and general d’altegliaria of the Republic of Venice, Count Giulio Savorgnan , of his translation of Guid’Ubaldo’s work (n.14, above), stresses this point. See also, A.G. Keller, “Mathematicians Mechanics and Experimental Machines in Northern Italy in the Sixteenth Century,” in Maurice P. Crosland (ed.), The Emergence of Science in Western Europe (London: Science History Publications, 1975), 15–34.
- 23.
Jacks, spanners and wrenches appear in Ramelli, pl. 155–59 and the use of a jack for undermining a wall in Errard, Le Premier Livre (n.21, above), pl. 4.
- 24.
Ramelli, Le Diverse et Artificiose Machine, pl. 189.
- 25.
Vittorio Zonca, Novo Teatro di Machine et Edificii (Padua: Pietro Bertelli, 1607), btw. 88–89.
- 26.
Agostino Ramelli, La Fabrica et l uso del triangolo del Capitan Agostino Ramelli dal Ponte della Tresia ingegniero del Christianissimo Re di Francia, noted as being “on vellum with beautiful drawings”; Catalogue of the Library at Chatsworth (London: Chiswick Press, 1879), 4: 347. [The manuscript apparently has a printed title page, so it is possible that Ramelli tried to get the manuscript into print; Martha Teach Gnudi Research and Publication Papers 1540–1977, Louise M. Darling Biomedical Library History, History and Special Collections Division, University of California–Los Angeles, ms Coll. no. 307, box 2, folder 3.—ed.]
- 27.
Jean Errard, La geometrie et practique generalle d’icelle (Paris: D. Le Clerc, 1594).
- 28.
E.g., Petrus Ramus, Proœmium Mathematicum (Paris: Wechelus, 1567), 291–93. And in general, see Walter J. Ong, Ramus, Method, and the Decay of Dialogue: From the Art of Discourse to the Art of Reason (Chicago: University of Chicago Press, 2004) and Steven J. Reid and Emma Annette Wilson (eds.), Ramus, Pedagogy, and the Liberal Arts: Ramism in Britain and the Wider World (Farnham: Ashgate, 2011).
- 29.
Robert Recorde, The Grounde of Artes, Teachyng the Worke and Practice of Arithmetike (London: Reginalde Wolfe, 1551) and The Pathway to Knowledge, Containing the First Principles of Geometrie (London: Wolfe 1551). John Dee, preface to Euclid, The Elements of Geometrie, trans. Henry Billingsley (London: Iohn Daye, 1570), for which see, The mathematicall praeface to the Elements of geometrie of Euclid of Megara (1570), intro. Allen G. Debus (New York: Science History Publications, 1975).
- 30.
Henry Heller, Anti-Italianism in Sixteenth Century France (Toronto: University of Toronto Press, 2003).
- 31.
See A.G. Keller, “Aconcio, Jacopo (c.1520–1566/7?),” in Oxford Dictionary of National Biography, eds. H. C. G. Matthew and Brian Harrison (Oxford: OUP, 2004); online ed., ed. Lawrence Goldman, January 2014, and Lynn White, Jr., “Jacopo Acontio as an Engineer,” American Historical Review 72.2 (1967): 425–444. Although Genebelli appears in nearly all accounts of the siege of Antwerp, and after his move to England in various official records, there does not seem to be any survey of his curious career. For some notice of his activities, see Steven A. Walton, “State Building through Building for the State: Domestic and Foreign Expertise in Tudor Fortifications,” in Eric Ash (ed.), Expertise and the Early Modern State, Osiris 25 (2010): 66–84.
- 32.
Biringucci, Parafrasi … Piccolomini (n.14, above), 6.
- 33.
A.G. Keller, “The Missing Years of Jacques Besson, Inventor of Machines, Teacher of Mathematics, Distiller of Oils and Huguenot Pastor,” Technology and Culture 14 (1973): 28–39.
Primary Sources
Smith, Thomas. 1600. The Arte of gunnerie: Wherein is set foorth a number of seruiceable secrets, and practical conclusions, belonging to the art of gunnerie, by Arithmeticke Skill to be Accomplished. London: [Richard Field] for William Ponsonby.
Tartaglia, Niccolò. 1537. Nova Scientia. Venice: S. da Sabio.
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Keller, A.G. (2017). Machines as Mathematical Instruments. In: Cormack, L., Walton, S., Schuster, J. (eds) Mathematical Practitioners and the Transformation of Natural Knowledge in Early Modern Europe. Studies in History and Philosophy of Science, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-49430-2_6
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