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The Analysis of Books VII and VIII of Quesiti et inventioni diverse

  • Raffaele Pisano
  • Danilo Capecchi
Chapter
  • 533 Downloads
Part of the History of Mechanism and Machine Science book series (HMMS, volume 28)

Abstract

We analyse Niccolò Tartaglia’s Books VII and VIII of the Quesiti et inventioni diverse. The discussion is organized both from historical and epistemological points of view. Particularly, we will focus on the reasoning proposed by Tartaglia against the arguments of the Aristotelian Problemata mechanica on the accuracy and stability of a balance – with large or small arms, and fulcrum below or above – (Book VII) and concerning the principles of the science of weights (Book VIII). The latter arguments are discussed, taking into account de Nemore’s corpus on the science of weights for exploration of the structure of the shared knowledge of early modern statics, aiming to discuss alternative frameworks, and so distinguishing between individual and shared structures in the literature belonging to early modern mechanics. In this sense, this chapter is devoted to historical epistemology of science, presenting an integrated history and epistemology of scientific methods, which combine epistemological and historical approaches to identify significant historical hypotheses within the relationship between physics and mathematics (physical observations and theoretical mechanical modeling).

Keywords

Horizontal Position Incline Plane Small Balance Physical Argument Large Balance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Aristotle (1525) Conversio mechanicarum quaestionum Aristotelis cum figuris et annotationibus quibusdam. In: Leonico Tomeo 1525Google Scholar
  2. Aristotle (1853) On the definition and division of principles. In: Octavius Freire Porphyry Owen (ed) The organon, or logical treatises, of Aristotle, vol I. Bohn H G, London, pp 263–266Google Scholar
  3. Aristotle (1949) Aristotle’s prior and posterior analytics. A revised text with introduction and commentary. In: Ross WD (ed) The Oxford University Press, OxfordGoogle Scholar
  4. Aristotle (1955a) De Caelo. Translation into English by Stocks JL. The Tech Classics Archive. The Massachusetts Institute of Technology Press, Cambridge, MAGoogle Scholar
  5. Aristotle (1955b) Mechanical problems. In: Hett WS (ed) Aristotle. Minor works. William Heinemann, Cambridge, pp 328–414Google Scholar
  6. Aristotle (1955c) Minor Works (trans: Hett WS). The Harvard University Press/Heinemann W Ltd, Cambridge MA/LondonGoogle Scholar
  7. Aristotle (1984) The complete works of Aristotle. Barnes (ed). The Princeton University Press, PrincetonGoogle Scholar
  8. Aristotle (1996) The principles of nature-physics, vol I. In: Waterfield R (ed). The Oxford University Press, OxfordGoogle Scholar
  9. Aristotle (1999) Physics (trans: Waterfield R). The Oxford University Press, OxfordGoogle Scholar
  10. Aristotle (2000) Problemi meccanici. Bottechia Dehò ME (ed). Rubbettino, CatanzaroGoogle Scholar
  11. Baldi B (1621) Bernardini Baldi Urbinatis Guastallae abbatis in mechanica Aristotelis problemata exercitationes. Ioannis Al-bini, MoguntiaeGoogle Scholar
  12. Benedetti GB (1585) Diversarum speculationum Mathematicarum, & Physicarum liber. Apud Haeredem Nicolai Bevilaquae, TauriniGoogle Scholar
  13. Biener Z (2008) The unity of science in early-modern philosophy: sub-alternation, metaphysics and the geometrical manner in scholasticism, Galileo and Descartes. PhD dissertation. The University of Pittsburg Press, PennsylvaniaGoogle Scholar
  14. Biringucci VO (1582) Parafrasi di monsignor Alessandro Piccolomini sopra le meccaniche di Aristotele, tradotta da Oreste Vannocci Biringucci, gentilomo senese. Francesco Zanetti, RomaGoogle Scholar
  15. Bolletti I (1958) Nicolò Tartaglia. La sua vita, le sue opere, i suoi tempi. Etude Tecnique Bolceraf, BresciaGoogle Scholar
  16. Bolton R (1976) Essentialism and semantic theory in Aristotle: Posterior analytics, II, 7–10. Phil Rev 85(4):514–544CrossRefGoogle Scholar
  17. Brown EJ (1967–1968) The scientia de ponderibus in the later middle ages. Ph.D. doctoral thesis. The University of Winscosin. Tutor: Prof. Clagett M. UMI – ProQuest Company: www.il.proquest.com
  18. Brown EJ (1976) The science of weights. In: Lindberg 1976 (ed) pp 179–205Google Scholar
  19. Capecchi D (2009) Aristotle’s mechanics and virtual work principle. In: Gianetto E (ed) Proceedings of XXIX SISFA Congress. Guaraldi, Rimini, pp 139–146Google Scholar
  20. Capecchi D (2011) Weight as active or passive principle in the Latin and Arabic scientia de ponderibus. Organon 43:29–58Google Scholar
  21. Capecchi D (2012a) Historical roots of the rule of composition of forces. Meccanica 47:1887–1901MathSciNetCrossRefzbMATHGoogle Scholar
  22. Caverni R (1891–1900a) Storia del metodo sperimentale in Italia [copia anastatica]. Forni, Bologna vol I, pp 53–54, vol IV, pp 190–198Google Scholar
  23. Caverni R (1891–1900b) Storia del metodo sperimentale in Italia. Civelli, FirenzeGoogle Scholar
  24. Clagett M (1956) The liber de Motu of Gerard of Brussels and the origin of kinematics in the West. Osiris 12:73–175MathSciNetCrossRefzbMATHGoogle Scholar
  25. Clagett M (1959) The science of mechanics in the middle ages. The University of Wisconsin Press, MadisonzbMATHGoogle Scholar
  26. Clagett M (1964–1984). Archimedes in the middle ages, Madison-Philadelphia, Memoirs of the American Philosophical Society, 5 vols., 10 Tomes. The Clarendon University Press, OxfordGoogle Scholar
  27. Corbini A (2006) La teoria della scienza nel XIII secolo. I commenti agli analitici secondi. Edizioni del Galluzzo, FirenzeGoogle Scholar
  28. Crombie AC (1959) Medieval and early modern science. II. Science in the later middle ages and early modern times, XIII-XVII centuries. Doubleday Anchor Books, New YorkGoogle Scholar
  29. Cuomo S (1998) Nicolò Tartaglia, mathematics, ballistics and the power of possession of knowledge. Endeavour 22(1):31–35MathSciNetCrossRefGoogle Scholar
  30. De Nemore I (fl. 13th) Ms. Elementa Jordani super demonstratione de ponderibus. Oxford, Bodleian Library, Ms. Auct. F.5.28. Folia 125v–133rGoogle Scholar
  31. De Nemore I (1533) Liber Iordani Nemorarii viri clarissimi, de ponderibus propositiones XIII & earundem demonstrationes, multarumque rerum rationes sane pulcherrimas complectens. [edited by Apianus] Ioh Petreium, NorimbergaeGoogle Scholar
  32. De Nemore (1565) Iordani Opusculum de Ponderositate, Nicolai Tartaleae Studio Correctum Novisqve Figuris avctum. Tartaglia N (ed) Cum Privilegio Traiano Curtio, Venetiis, Apud Curtium Troianum. MDLXVGoogle Scholar
  33. De Pace A (1993) Le matematiche e il mondo. Ricerche su un dibattito in Italia nella seconda metà del Cinquecento. Franco Angeli, MilanozbMATHGoogle Scholar
  34. Del Monte G ([1577] 1581) Le Meccaniche dell’Illustrissimo Sig. Guido Ubaldo dè Marchesi del Monte, tradotto in volgare dal Sig. Filippo Pigafetta. Evangelista Deuchino, Venezia [1577: Mechanicorum Liber]Google Scholar
  35. Del Monte G (1615) Le mechaniche dell’illustriss. Sig. Guido Ubaldo de’ marchesi del Monte tr. Tradotto in volgare da Filippo Pigafetta (1581). Evangelista Deuchino, VeneziaGoogle Scholar
  36. Del Monte G (2013) Guidobaldo del Monte (1545–1607) Theory and practice of the mathematical disciplines from Urbino to Europe. Becchi A, Bertoloni Meli D, Gamba E (eds) The Open Access Edition Press, BerlinGoogle Scholar
  37. Drake S, Drabkin IE (1969) Mechanics in sixteenth-century Italy: selections from Tartaglia, Benedetti, Guido Ubaldo, and Galileo. The University of Wisconsin Press, MadisonGoogle Scholar
  38. Duhem PMM (1905–1906) Les origines de la statique, 2 vols. Hermann, ParisGoogle Scholar
  39. Duhem PMM (1906–1913) Etudes sur Léonard de Vinci. Hermann, ParisGoogle Scholar
  40. Galilei G (1649) Le Mecaniche. In: Galilei 1890–1909, vol II, pp 147–191Google Scholar
  41. Gomez-Lobo A (1977) Aristotle hypotheses and the Euclidean postulates. The review of metaphysics, 30(3):430–439Google Scholar
  42. Høirup J (1989) Sub-scientific mathematics: observations on a pre-modern phenomenon. Hist Sci 28:1–79MathSciNetGoogle Scholar
  43. Laird WR (2000) The unfinished mechanics of Giuseppe Moletti. The University of Toronto Press, TorontoCrossRefGoogle Scholar
  44. Leonici Thomei [Leonico Tomeo] N (1530) Opuscula nuper in lucem aedita Parisiis Apud Simonem ColieaeumGoogle Scholar
  45. Leonico Tomeo N (1525) Opuscula nuper in lucem aedita quorum nomina proxima habentur pagella. Bernardino Vitali, Venice (see also English Translation by Walter Stanley Hett: Aristotle, Mechanical Problems. Nicolao Leonico Thomaeo interprete, Venise 1525)Google Scholar
  46. Moody E, Clagett M ([1952] 1960) The medieval science of weights (Scientia de ponderibus). The University of Wisconsin Press, MadisonGoogle Scholar
  47. Pisano R, Bussotti P (2012) Galileo and Kepler. On Theoremata Circa Centrum Gravitatis Solidorum and Mysterium Cosmographicum. Hist Res 2(2):110–145Google Scholar
  48. Pisano R, Bussotti P (2013a) On popularization of scientific education in Italy between 12nd and 16th centuries. Prob Educ 21st Century 57:90–101Google Scholar
  49. Pisano R, Bussotti P (2013b) Open problems in mathematical modelling and physical experiments: exploring exponential function. Prob Educ 21st Century 50:56–69Google Scholar
  50. Pisano R, Bussotti P (2014a) Fibonacci and the reception of the Abacus schools in Italy. Mathematical conceptual streams and their changing relationship with society (Submitted to Almagest)Google Scholar
  51. Renn J, Damerow P (2010b) The equilibrium controversy. Edition open access, BerlinGoogle Scholar
  52. Tartaglia N (1537) Nova scientia inventa da Nicolo Tartalea. B. Disciplinae mathematicae loquuntur[.] Qui cupitis rerum varias cognoscere causas disate nos cunctis hac patet una via. In Vinegia per Stefano Nicolini da Sabio. Ad instantia di Nicolo Tartalea Brisciano il qual habita a San Saluador. MDXXXVIIGoogle Scholar
  53. Tartaglia N (1543a) Euclide Megarense acutissimo philosopho: solo introduttore delle scientie mathematice: diligentemente rassettato, et alla integrita ridotto, per il degno professore di tal Scientie Nicolo Tartalea, Brisciano, Secondo le due tradottioni: e per commune commodo & utilita di latino in volgar tradotto, con una ampla esposizione dello istesso tradottore di novo aggionta. Talmente chiara, che ogni mediocre ingegno, senza la notitia, over suffragio di alcun’altra scientia con facilità, sera capace a’ poterlo intendere. Stampato in Vinegia per Venturino Rossinelli ad instantia e requisitione de Guilielmo de Monferra, & de Pietro di Facolo da Vinegia libraro, & de Nicolo Tartalea Brisciano Tradottore: Nel Mese di Febraro. Anno no nostra salute MDXLIIIGoogle Scholar
  54. Tartaglia N (1543b) Opera Archimedis Syracusani philosophi et mathematici ingeniosissimi per Nicolaum Tartaleam Brixianum (mathematicarum scientiarum cultorem) multis erroribus emendata, expurgata, ac in luce posita, multisque necessariis additis, quae plurimis locis intellectu difficillima erant, commentariolis sane luculentis & eruditissimis aperta, explicata atque illustrata existunt, appositisque manu propria figuris quae graeco exemplari deformatae ac depravatae erant, ad rectissimam symetriam omnia instaurata reducta & reformata elucent, apud Venturinum Ruffinellum, sumptu & requisizione Nicolai de Tartaleis Brixiani, mense ApriliGoogle Scholar
  55. Tartaglia (1543c) Archimedis Siracusani Tetragonismus In: Tartaglia 1543b, 19v–29rGoogle Scholar
  56. Tartaglia (1543d) Archimedis Syracusani Liber In: Tartaglia 1543b, 29v–31rGoogle Scholar
  57. Tartaglia (1543e) Archimedis de Insidentibus Aquae In: Tartaglia 1543b, 31v–[36r]. See also: Tartaglia 1565–Insidentibus, 1rv–16rvGoogle Scholar
  58. Tartaglia N (1546) Quesiti et inventioni diverse de Nicolo Tartalea Brisciano. Stampata in Venetia per Venturino Ruffinelli ad instantia et requisitione, & a proprie spese de Nicolo Tartalea Brisciano Autore. Nel mese di luio L’anno di nostra salute. M.D.XLVIGoogle Scholar
  59. Tartaglia N (1554) Quesiti et inventioni diverse de Nicolo Tartaglia, di novo restampati con una gionta al sesto libro, nella quale si mostra duoi modi di redur una citta inespugnabile. In: Venetia per Nicolo de Bascarini, ad istantia & requisistione, & a proprie spese de Nicolo Tartaglia Autore. Nell’anno di nostra Salute. MDLIIIIGoogle Scholar
  60. Tartaglia N (1569) Euclide Megarense acutissimo philosopho, solo introduttore delle scientie mathematice. Diligentemente rassettato, et alla integrita ridotto, per il degno professore di tal Scientie Nicolo Tartalea, Brisciano. Secondo le due tradottioni. Con una ampla esposizione dello istesso tradottore di nuono aggiunta. Talmente chiara, che ogni mediocre ingegno, senza la notitia, over suffragio di alcun’altra scientia con facilità, sera capace a’ poterlo intendere. In Venetia, appresso Giovanni Bariletto, 1569Google Scholar
  61. Tartaglia N (1876) I sei scritti di matematica disfida di Lodovico Ferrari coi sei contro–cartelli in risposta di Niccolò Tartaglia, comprendenti le soluzioni de’ quesiti dall’una e dall’altra parte proposti. Raccolti, Autografi e Pubblicati da Enrico Giordani, Bolognese. Premesse notizie bibliografiche ed illustrazioni sui Cartelli medesimi, estratte da documenti già a stampa ed altri manoscritti favoriti dal Comm. Prof. Silvestro Gherardi, Preside del’Istit. Tecn. Prov. di Firenze. R. Sabilimento litografico di Luigi Ronchi e tipografia degl’Ingegneri, MilanoGoogle Scholar
  62. Tartaglia N (2007) Euclide Megarense. Pizzamiglio P (ed). Ateneo di Brescia, BresciaGoogle Scholar
  63. Truesdell C (1968) Essay in the history of mechanics. Spinger, New YorkCrossRefzbMATHGoogle Scholar
  64. Upton TV (1985) Aristotle on hypothesis and the unhypothesized first principle. Rev Metaphys 39(2):283–301Google Scholar

Copyright information

© Springer Netherlands 2016

Authors and Affiliations

  • Raffaele Pisano
    • 1
  • Danilo Capecchi
    • 2
  1. 1.Department of PhysicsLille 1 University Science and TechnologyVilleneuve d’AscqFrance
  2. 2.Dipartimento di ingegneria strutturale e geotecnicaRoma La Sapienza UniversityRomaItaly

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