Reflections on the Scientific Conceptual Streams in Leonardo da Vinci and His Relationship with Luca Pacioli

Abstract

Leonardo da Vinci (1452-1519) is perhaps overrated for his contributions to physical science, since his technical approach. Nevertheless important components concerning practical problems of mechanics with great technical ability were abounded. He brought alive again the Nemorarius’ (fl. 12th - 13th century) tradition and his speculations on mechanics, if immature made known how difficult and elusive were the conceptual streams of the foundations of science for practitioners-artisans. Leonardo also had an interesting and intense relationship with mathematics but merely unhappy insights in his time. The meeting with Luca Bartolomeo de Pacioli (1445-1517) was very important for da Vinci since proposing stimulating speculations were implemented, but they were not definitive theoretical results. In this paper historical reflections notes on mechanics and mathematics in da Vinci and his relationships with Pacioli are presented.

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Pisano, R. (2013). Reflections on the Scientific Conceptual Streams in Leonardo da Vinci and His Relationship with Luca Pacioli. Advances in Historical Studies, 2, 32-45. doi: 10.4236/ahs.2013.22007.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Abattouy, M. (2006). The Arabic transformation of mechanics: The birth of science of weights. Foundation for Science Technology and Civilisation, 615, 1-25
[2] Abattouy, M., Jurgen, R., & Weinig, P. (2001) Transmission as transformation: The translation movements in the Medieval East and West in a comparative perspective. Science in Context, 14, 1-12. doi:10.1017/S0269889701000011
[3] Archimedes (1558). Archimedis opera non nulla a Federico Commandino Urbinate nuper in latinum conversa et commentariis illustrata. Apud Paulum Manutium, Aldi F. Venetiis
[4] Archimedes (2002). On the equilibrium of planes. In T. L. Heath (Ed.), The works of Archimedes (pp 189-220). New York: Dover.
[5] Aristotle (1853). On the definition and division of principles. In: O. F. P. Owen (Ed.), The organon, Or logical treatises, of Aristotle (pp. 263-266). London: Bohn H G.
[6] Aristotle (1949). Aristotle’s prior and posterior analytics. A revised text with introduction and commentary. Oxford: The Oxford University Press.
[7] Aristotle (1955a). De caelo. The Tech Classics Archive of M.I.T
[8] Aristotle (1955b). Mechanical problems. In: W. S. Hett (Ed.), Aristotle. Minor works. Cambridge: William Heinemann.
[9] Aristotle (1963). Minor works. Heinemann, Cambridge, London: The Harvard University Press.
[10] Aristotle (1984). The complete works of Aristotle. Princeton: The Princeton University Press.
[11] Aristotle (1996). The principles of nature-physics. Oxford: The Oxford University Press.
[12] Aristotle (1999). Physics. Oxford: The Oxford University Press.
[13] Bagni, G. T., & D’Amore, B. (2007). Leonardo e la matematica. In: I. Marazzani (Ed.), La matematica e la sua didattica (pp. 3-7). Bologna: Pitagora.
[14] Bellucci, G. B. (1598). Nuoua Inventione di fabricar Fortezze, di varie Forme in qualunque sito di piano, di monte, in acqua, con diuersi disegni, et un trattato del modo, che si ha da osseruare in esse, con le sue misure, et ordine di levar lepiante, tanto in fortezze reali, quanto non reali. Venezia: Roberto Meietti.
[15] Biagioli, M. (2003). Galileo e Derrida: Il libro della natura e la logica del supplemento. In Rinascimento ser (pp. 205-232). Firenze: Olschki.
[16] Brown, E. J. (1967-1968). The scientia de ponderibus in the later Middle Ages. Ph.D. Dissertation, Madison: University of Winscosin .
[17] Busard, H. L. L. (2005). Introduction to the text. Campanus of Novara and Euclid’s elements I. Stuttgart: Franz Steiner Verlag.
[18] Capecchi, D. (2011). Weight as active or passive principle in the Latin and Arabic scientia de ponderibus. Organon, 43, 29-58
[19] Capecchi, D. (2012). The history of virtual work laws. Basel: Springer. doi:10.1007/978-88-470-2056-6
[20] Capecchi, D, & Pisano, R. (2007). Torricelli e la teoria dei baricentri come fondamento della statica. Physis, XLIV, 1-29
[21] Capecchi, D., & Pisano, R. (2008). La meccanica in Italia nei primi anni del Cinquecento. Il contributo di Niccolò Tartaglia. In Proceedings of XXV SISFA Congress (pp. C17.1-C17.6). Milano: University of Milano.
[22] Capecchi, D., & Pisano, R. (2010a). Scienza e tecnica nell’architettura del Rinascimento. Roma: CISU.
[23] Capecchi, D., & Pisano, R. (2010b). Reflections on Torricelli’s principle in mechanics. Organon, 42, 81-98.
[24] Capecchi, D., & Pisano, R. (2013). Tartaglia’s science of weights. The Mechanics in XVI century. Dordrecht: Springer
[25] Cartelon, H. (1975). Does Aristotle have a mechanics? In Barnes et al. (Eds.), Articles on Aristotle. Vol. I: Science. London: Duckworth.
[26] Clagett, M. (1959). The science of mechanics in the Middle Ages. Madison: The University of Wisconsin Press.
[27] Clagett, M. (1964-1984). Archimedes in the Middle Ages, Madison-Philadelphia, memoirs of the American Philosophical Society. Oxford: The Clarendon University Press.
[28] Clagett, M., & Moody, E. (1960). The medieval science of weights. Scentia de ponderibus. Madison: The University of Wisconsin Press.
[29] Comandino, F. (1565). Federici commandini vrbinatis liber de centro gravitatis solidorum. Bononiae: Ex Officina Alexandri Benacii.
[30] Comandino, F. (1575). De gli elementi di Euclide libri quindici. Con gli scholii antichi. Tradotti prima in lingua latina da m. Federico Commandino da Vrbino, & con commentarij illustrati, et hora di ordine delli istesso trasportati nella nostra vulgare, et da lui riueduti in Vrbino: appresso Domenico Frisolino In Vrbino: in casa di Federico Commandino.
[31] da Vinci, L. (1940). I libri di meccanica nella ricostruzione ordinata di Arturo Uccelli preceduti da una introduzione critica e da un esame delle fonti. Milano: Hoepli.
[32] dal Monte, G. (1581). Le Meccaniche dell’Illustrissimo Sig. Guido Ubaldo dè Marchesi del Monte, tradotto in volgare dal Sig. Filippo Pigafetta. Venezia: Evangelista Deuchino.
[33] dal Monte, G. (1588). In duos Archimedis aequeponderantium libros paraphrasis. Pisauri: Hieronymum Concordiam.
[34] de Ridder-Symoens, H. (1992). A history of the university in Europe. Vol. I. Universities in the Middle Ages. Cambridge: The Cambridge University Press.
[35] Dijksterhuis, E. J. (1957). Archimedes. New York: The Humanities Press.
[36] Dijksterhuis, E. J. (1955). The principal works of Simon Stevin, vol. I. Amsterdam: C. V. Swets & Seitlinger.
[37] Drachmann, A. G. (1967-1968). Archimedes and the science of physics. Centaurus, 12, 1-11. doi:10.1111/j.1600-0498.1968.tb00074.x
[38] Duhem, P. M. (1905-1906). Les origines de la statique 2 vol. Paris: Hermann.
[39] Duhem, P. M. (1906-1913). Etudes sur Léonard de Vinci. Paris: Hermann.
[40] Euclid (1945) The optics of euclid. Trans. by Burton, H. E. Journal of the optical society, 35, 357-372.
[41] Galileo, G. (1890-1909). Le opere di Galileo Galileo: Edizione nazionale sotto gli auspici di sua maestà il re d’Italia. Firenze: Barbera.
[42] Galluzzi, P. (1988). Leonardo da Vinci: Engineer and Architect. Montreal: Montreal Museum of Fine Arts.
[43] Galluzzi, P., & Torrini, M. (1975-1984). The works of Galileo Galilei’s disciples 2 Vols. Correspondence. Firenze: Gunti-Barbera (In Italian).
[44] Gille, B. (1966). Engineers of the renaissance. Cambridge, MA: MIT Press.
[45] Grendler, P. F. (2002). The universities of the Italian renaissance. Baltimora: The Johns Hopkins University Press.
[46] Hall, B. S. (1997). Weapons & warfare in renaissance Europe. Baltimore: The John’s Hopkins University Press.
[47] Harrison, P. (2006). The book of nature and early modern science. In: K. van Berkel, & A. Vanderjagt (Eds.), Book of nature in early modern and modern history (pp. 1-26). Leuven: Peeters.
[48] Heath, T. L. (2002). The works of Archimedes. New York: Dover Publications Inc.
[49] Hero, A. (1575). Heronis alexandrini spiritalium liber. A federico commandino urbinate, ex graeco, nuper in latinum conversus. Urbini: Frisolino Domenico.
[50] Hero, A. (1893). Les mécaniques ou l’élévateur de Héron d’Alexandrie Arabic text and French translation by Carrà de Vaux. Journal Asiatique, 9, 386-472.
[51] Heron, A. (1900). Herons von Alexandria Mechanik und Katoptrik. In L. Nix, & W. Schmidt (Eds.), Heronis Alexandrini opera quae supersunt omnia. Leipzig: Teubner.
[52] Heron, A. (1999). Heron alexandrinus mechanica. English translation by Jutta Miller. http://archimedes.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.cgi
[53] Jesseph, D. M. (2004). Galileo, Hobbes and the book of nature. Perspectives on science, 12, 191-211. doi:10.1162/106361404323119871
[54] Knorr, W. R. (1978-1979). Archimedes and the “elements”: Proposal for a revised chronological ordering of the Archimedean corpus. Archive for History of Exact Science, 19, 211-290.
[55] Knorr, W. R. (1985). Archimedes and the pseudo-Euclidean ‘catoptrics’: Early stages in the ancient geometric theory of mirrors. International Archive on the History Science, 35, 114-115; [1986] 28-105.
[56] Kusukawa, S. (2012). Picturing the book of nature: Image, text and argument in sixteenth-century human anatomy and medical botany. Chicago, IL: The Chicago University Press. doi:10.7208/chicago/9780226465289.001.0001
[57] Locqueneux, R. (2009). Une histoire des idées en physique. Vol. 57. Cahiers d'histoire et de philosophie des sciences. Paris: Vuibert.
[58] Maitte, B. (2003). La géométrie dans les arts décoratifs islamiques. Le Caire: CFCC.
[59] Marcacci, F. (2009). Galileo Galilei, sidereus nuncius. Traduzione e commento di giustini PA. Roma: The Lateran University Press.
[60] Marcolongo, R. (1932). La meccanica di Leonardo da Vinci. Napoli: Stabilimento Industrie Editoriali Mendionali. [Id. 1937 (1937). Studi vinciani. Memorie sulla geometria e la meccanica di Leonardo da Vinci. Napoli: Stabilimento Industrie Editoriali Meridionali.
[61] Numbers, R. L. (2006). Reading the book of nature through American lenses. In K. van Berkel, & A. A. Vanderjagt (Eds.), Book of nature in early modern and modern history (pp. 261-274). Leuven: Peeters.
[62] Van Ophuijsen, J. M. (2005). The two fold action of mind in Aristotle’s proto-book of nature. In K, van Berkel, & A. Vanderjagt (Eds.), Book of nature in antiquity and the Middle Ages (pp. 1-12). Leuven: Peeters.
[63] Othman, A. (1949.) Farabi: La statistique des sciences. (2 ed.). Cairo: Dar al-fikr al-’arabi.
[64] Pacioli, L. (1494). Summa de arithmetica, geometria, proportioni et proporzionalità. Venezia: Paganino de’ Paganini.
[65] Pacioli, L. (1496-1508). De viribus quantitatis. Bibliotheca: University of Bologna.
[66] Pacioli, L. (1509). De divina proportione opera a tutti gli’ingegni perspicaci e curiosi necessaria […]. Venezia: Paganino de’ Paganini.
[67] Pacioli, L. (1509). Euclidis megarensis, philosophi acutissimi mathematicorumque omnium sine controversia principis, opera a Campano interprete fidissimo tra[s]lata.. […]. Venezia: Paganino de’ Paganini.
[68] Pappus, A. (1588). Mathematica collectiones a Federico Commandino urbinate in latinum conversae. Pisauri: Hieronimum concordiam.
[69] Pappus, A. (1970). The Arabic version of the mathematical collection of Pappus Alexandrinus Book VIII. Ph.D. Dissertation. Cambridge: The University of Cambridge Press.
[70] Pedersen, O. (1992). The book of nature. Città del Vaticano: The Vatican Observatory Publications.
[71] Pedretti, C. (1978). Leonardo architetto. Milano: Electa. [Id., 1999 Leonardo. Le macchine, Giunti Editore, Firenze 1999; et refs. on Codex]
[72] Pedretti, C. (1998). Leonardo da Vinci, Il codice arundel 263 nella British library. 2 vols. Firenze: Giunti.
[73] Pisano, R. (2013b). Historical and epistemological reflections on the principle of virtual laws. Submitted to Archive Internationales d’Histoire des Science.
[74] Pisano, R., & Capecchi, D. (2013b-forthcoming). Conceptual and mathematical structures of mechanical science between 18th and 19th centuries. Almagest, in Press.
[75] Pisano, R. (2007). Brief history of centre of gravity theory. Epistemological notes. In M. Kokowski (Ed.), Proceedings of the 2nd ESHS Congress (pp. 934-941). Krakow.
[76] Pisano, R. (2009a). Continuity and discontinuity. On method in Leonardo da Vinci’ mechanics. Organon, 41, 165-182.
[77] Pisano, R. (2009b). Il ruolo della scienza archimedea nei lavori di meccanica di Galilei e di Torricelli. In E. Giannetto, G. Giannini, D. Capecchi, & R. Pisano (Eds.), Proceedings of XXVI SISFA Congress (pp. 65-74). Rimini: Guaraldi Editore.
[78] Pisano, R. (2009c). On method in Galileo Galilei’ mechanics. In H. Hunger (Ed.), Proceedings of ESHS 3rd Conférence (pp. 147-186). Vienna: Austrian Academy of Science.
[79] Pisano, R. (2009d). Galileo Galileo. Riflessioni epistemologiche sulla resistenza dei corpi. In E. Giannetto, G. Giannini, & M. Toscano (Eds.), Relatività, Quanti Chaos e altre Rivoluzioni della Fisica (61-72). Rimini: Guaraldi Editore.
[80] Pisano, R. (2011). Physics-mathematics relationship. Historical and epistemological notes. In E. Barbin, M. Kronfellner, & C. Tzanakis (Eds.), European Summer University history and epistemology in mathematics (pp. 457-472). Vienna: Verlag Holzhausen GmbH-Holzhausen Publishing Ltd.
[81] Pisano, R., & Bussotti, P. (2012). Galileo and Kepler. On theoremata circa centrum gravitates solidorum and mysterium cosmographicum. History Research, 2, 110-145.
[82] Pisano, R., & Capecchi, D. (2009). Il ruolo della meccanica ne le fortificationi di Buonaiuto Lorini (pp 797-808). Napoli: Cuzzolin Editore.
[83] Pisano, R., & Capecchi, D. (2010a) Galileo Galilei: Notes on trattato di fortificazione. In A. Altamore, & G. Antonini (Eds.), Galileo and the Renaissance Scientific Discourse (pp. 28-41). Roma: Edizioni Nuova Cultura.
[84] Pisano, R., & Capecchi, D. (2010b) On Archimedean roots in Torricelli’s mechanics. In S. A. Paipetis, & M. Ceccarelli (Eds.), The genius of Archimedes. Proceeding of an internal conference (pp. 17-28). Syracuse.
[85] Pisano,R., & Capecchi, D. (2008). La meccanica in Italia nei primi anni del Cinquecento. Il contributo di Niccolò Tartaglia. In P. Tucci (Ed.), Proceedings of XXV SISFA Congress (pp. C171-C176). Milano. http://www.brera.unimi.it/sisfa/atti/index.html
[86] Pisano, R., & Capecchi, D. (2009). Il ruolo della meccanica ne Le fortificationi di Buonaiuto Lorini In Cuzzolin (Ed.), 3 Convegno di Storia dell’ingegneria, vol. II (pp. 797-808). Napoli.
[87] Pisano, R., & Gaudiello, I. (2009). Continuity and discontinuity. An epistemological inquiry based on the use of categories in history of science. Organon, 41, 245-265.
[88] Pisano, R., & Rougetet, L. (2013-forthcoming). Quelles mathématiques trouve-t-on chez Leonardo da Vinci et chez Luca Pacioli? In press.
[89] Renn, J., Damerow, P. & McLaughlin, P. (2003). Aristotle, Archimedes, Euclid, and the origin of mechanics: The perspective of historical epistemology. Berlin: The Max Planck Institute for the history of science of Berlin.
[90] Rogers, K. (2005). On the metaphysics of experimental physics. New York: Palgrave Macmillan.
[91] Rose, P. L. (1975). The Italian renaissance of mathematics. Geneve: Droz.
[92] Sarton, G. (1953). Leonardo de Vinci, ingenieur et savant. Paris: Colloques Internationaux.
[93] Schneider, J. H. J. (2011). Philosophy and theology in the Islamic culture: Al-Farabi’s de scientiis. Philosophy Study, 1, 41-51.
[94] Tartaglia, N. (1554). La nuova edizione dell’opera Quesiti et inventioni diverse de Nicolo Tartaglia brisciano Riproduzione in facsimile dell'edizione del 1554. In A. Masotti (Ed.), Commentari dell’Ateneo di Brescia. Brescia: Tipografia La Nuova cartografica.
[95] Tartaglia, N. (1565a). Archimedes De insidentibus aqueae, Lib. I et II, in Iordani Opvscvlvm de Ponderositate. Venetia: Apud Curtium Troianum Navò.
[96] Tartaglia, N. (1565b). Iordani opvscvlvm de ponderositate, nicolai tartaleae stvdio correctvm novisqve figvrisavctvm. Cvm Privilegio Traiano Cvrtio, Venetiis, Apvd Curtivm Troianvm.
[97] Truesdell, C. (1968). Essay in the history of mechanics. New York: Spinger. doi:10.1007/978-3-642-86647-0
[98] Vanderputten, S. (2005). Exploring the book of nature? Human history and natural history in monastic historiography from the Middle Ages. In K. van Berkel, & A. Vanderjagt (Eds.), Book of Nature in Antiquity and the Middle Ages (pp. 151-166). Leuven: Peeters.

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