Advertisement

Ancient and Modern Statics in the Renaissance

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

Abstract

Statics is the science of equilibrium. The term appears in the Latin version (translated by Snel) of Simon Stevin (1548–1620) most famous textbook, Tomus quartus mathematicorum hypomnematum de statica (Stevin 1605, p 5) This work can be considered the hinge between ancient and modern statics. Ancient statics was the science of equilibrium of weights; modern statics is the science of equilibrium of forces. In ancient Greece statics was part of mechanics, the science of transportation of bodies by means of machines. In the Middle Ages and first Renaissance, statics was known as scientia de ponderibus (science of weights); its main object was the study of principles of equilibrium for heavy bodies suspended from a balance. Presently, statics is part of mechanics, which is the general science studying equilibrium and motion of bodies and their assembly, of any kind.

Keywords

English Translation Incline Plane Heavy Body Simple Machine Latin Translation 
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. Abattouy M (2006) The Arabic transformation of mechanics: the birth of science of weights. Found Sci Tech Civil 615:1–25Google Scholar
  2. Abattouy M, Jurgen R, Weinig P (2001) Transmission as transformation: the translation movements in the Medieval East and West in a comparative perspective. Sci Context 14:1–12MathSciNetzbMATHGoogle Scholar
  3. Alberti LB (15th century) Ex ludis rerum mathematicarum. MS. Typ 422.2. The Houghton Library. The Harvard University Press, Cambridge, MA. via:http://pds.lib.harvard.edu/pds/view/8282412?op=n&n=1&treeaction=expand
  4. Alberti LB (1973) Ludi rerum mathematicarum. In: Greys G (ed) Opere volgari, vol 3. Laterza, Bari, pp 131–173, pp 352–360Google Scholar
  5. Archimedes (2002) On the equilibrium of planes. In: Heath 2002, pp 189–220Google Scholar
  6. Aristotle (1984) The complete works of Aristotle. Barnes (ed). The Princeton University Press, PrincetonGoogle Scholar
  7. Baldi B (1621) Bernardini Baldi Urbinatis Guastallae abbatis in mechanica Aristotelis problemata exercitationes. Ioannis Al-bini, MoguntiaeGoogle Scholar
  8. Benedetti GB (1585) Diversarum speculationum Mathematicarum, & Physicarum liber. Apud Haeredem Nicolai Bevilaquae, TauriniGoogle Scholar
  9. Biener Z (2004) Galileo’s first new science: the science of matter. Perspect Sci 12:262–287MathSciNetCrossRefzbMATHGoogle Scholar
  10. 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
  11. Brown EJ (1976) The science of weights. In: Lindberg 1976 (ed) pp 179–205Google Scholar
  12. Capecchi D (2004) On the logical status of the virtual work principle. Meccanica 39:159–173MathSciNetCrossRefzbMATHGoogle Scholar
  13. Capecchi D (2012a) Historical roots of the rule of composition of forces. Meccanica 47:1887–1901MathSciNetCrossRefzbMATHGoogle Scholar
  14. Capecchi D (2012b) History of virtual work laws. Birkhäuser, MilanoCrossRefGoogle Scholar
  15. Capecchi D (2014a) An historical and epistemological point of view of mathematical physics. Math Mech Solids MMS-13-0143Google Scholar
  16. Capecchi D (2014b) The problem of motion of bodies. Springer, Cham-DordrechtGoogle Scholar
  17. Capecchi D (2014c) A historical reconstruction of mechanics as a mathematical physical science. Math Mech Solids (in press)Google Scholar
  18. Ciocci A (2011) Le matematiche tra Medio Evo e Rinascimento. In: Proceedings of the 2nd international meeting, Sansepolcro-Perugia-Firenze. The Fondazione Cassa di Risparmio Perugia, Perugia, pp 253–285Google Scholar
  19. Clagett M (1959) The science of mechanics in the middle ages. The University of Wisconsin Press, MadisonzbMATHGoogle Scholar
  20. Cuomo S (2004) Pappus of Alexandria and the mathematics of late antiquity. The Cambridge University Press, CambridgezbMATHGoogle Scholar
  21. 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. Hoepli, MilanoGoogle Scholar
  22. De Nemore I (fl. 13th) Ms. Elementa Jordani super demonstratione de ponderibus. Oxford, Bodleian Library, Ms. Auct. F.5.28. Folia 125v–133rGoogle Scholar
  23. 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
  24. De Roberval Personne G (1636) Traité de mechanique des poids soustenus par des puissances sur les plans inclinez al’horizon. Charlemagne, ParisGoogle Scholar
  25. 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
  26. 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
  27. 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
  28. Dijksterhuis EJ (1961) The mechanization of the world picture (English translation, Dikshoorn C). The Oxford University Press, New YorkGoogle Scholar
  29. Drachmann AG (1963) Fragments from Archimedes in Heron’s mechanics. Centaurus 8:91–146ADSMathSciNetCrossRefzbMATHGoogle Scholar
  30. Drake S (1999) Essays on Galileo and the history of philosophy of science. The University of Toronto Press, TorontoGoogle Scholar
  31. Drake S (2000) Two new sciences. A history of free fall, Aristotle to Galileo. Wall and Emerson, TorontoGoogle Scholar
  32. 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
  33. Duhem PMM (1905–1906) Les origines de la statique, 2 vols. Hermann, ParisGoogle Scholar
  34. Duhem PMM (1906–1913) Etudes sur Léonard de Vinci. Hermann, ParisGoogle Scholar
  35. Galilei G (1590) De motu. In: Galilei 1890–1909, vol I, pp 243–419Google Scholar
  36. Galilei G (1612) Discorsi intorno alle cose che stanno in su l’acqua e o che in quella si muovono. In: Galilei 1890–1909, vol IV, pp 57–141Google Scholar
  37. Galilei G (1638) Discorsi e dimostrazioni matematiche intorno a due nuove scienze. In: Galilei 1890–1909, vol VIII, pp 38–362Google Scholar
  38. Galilei G (1649) Le Mecaniche. In: Galilei 1890–1909, vol II, pp 147–191Google Scholar
  39. Galilei G (2002) Le Mecaniche. Gatto R (ed). Olschki, FirenzeGoogle Scholar
  40. Galluzzi P (1979) Momento. Ateneo e Bizzarri, RomaGoogle Scholar
  41. Garin E (1993) L’umanesimo Italiano. Laterza, BariGoogle Scholar
  42. Garin E (2008) L’uomo del Rinascimento. Laterza, BariGoogle Scholar
  43. Gatto R (1988) Un matematico sconosciuto del primo Seicento: Davide Imperiali. Bollettino di Storia delle Scienze Matematiche 8:71–135MathSciNetGoogle Scholar
  44. Gatto R (1996) La meccanica a Napoli ai tempi di Galileo. In appendice De Gli Elementi Mechanici di Colantonio Stigliola e le inedite Mechaniche mie di Davide Imperiali. La Città Del Sole, NapoliGoogle Scholar
  45. Gillispie CC (ed) (1971–1980) Dictionary of scientific biography (1971–1980). Scribner & Son, New YorkGoogle Scholar
  46. Grendler PF (2002) The universities of the Italian renaissance. The John Hopkins University Press, BaltimoraGoogle Scholar
  47. Heath TL (1896) Apollonius, Treatise on Conic Sections. The Cambridge University Press, CambridgeGoogle Scholar
  48. Hoyrup J (1988) Jordanus de Nemore, 13th century mathematical innovator. Arch Hist Exact Sci 38:307–363MathSciNetCrossRefzbMATHGoogle Scholar
  49. Jaouiche K (1976) Le livre du Qarastun de Thabit Ibn Qurra. EJ Brill, LeidenzbMATHGoogle Scholar
  50. Koyré A (1996) Études Galiléennes. Hermann, ParisGoogle Scholar
  51. Lagrange JL (1853) Mecanique Analytique. Betrand MJ (ed), 2 vols, 3rd edn. Mallet-Bachelier, ParisGoogle Scholar
  52. Lennox JG (1985) Aristotle, Galileo and the mixed sciences. Wallace, W (ed). Washington, DC, pp 29–51Google Scholar
  53. Machamer P (1978) Galileo and the causes. In: Butts RE, Pitt JC (eds) New perspectives on Galileo. Reidel, Dordrecht, pp 161–180CrossRefGoogle Scholar
  54. Marcolongo R (1937) Studi vinciani. Memorie sulla geometria e la meccanica di Leonardo da Vinci. Stabilimento Industrie Editoriali Meridionali, NapoliGoogle Scholar
  55. Moody E, Clagett M ([1952] 1960) The medieval science of weights (Scientia de ponderibus). The University of Wisconsin Press, MadisonGoogle Scholar
  56. Nastasi P ([1985] 1988) (ed) Sviluppi della ricerca sui principi meccanici. Proceeding of Il meridione e le scienze, (secoli XVI–XIX). Istituto Gramsci Siciliano, Palermo, pp 177–193Google Scholar
  57. Pacioli L (1494) Summa de arithmetica, geometria, proportioni et proporzionalità. Paganino de’ Paganini, VeneziaGoogle Scholar
  58. Pacioli L (1509a) De Divina proportione Opera a tutti gli ingegni perspicaci e curiosi necessaria […]. Paganino de’ Paganini, VeneziaGoogle Scholar
  59. Pacioli L (1992) Summa de arithmetica geometria proportioni et proportionalita (1494). Pistolesi, SienaGoogle Scholar
  60. Panza M (2008) The role of algebraic inferences in Na’īm Ibn Mūsā’s collection of geometrical propositions. Arab Sci Philos 18(2):165–191MathSciNetCrossRefzbMATHGoogle Scholar
  61. Pisano R (2009a) Continuity and discontinuity. On method in Leonardo da Vinci’ mechanics. Organon 41:165–182Google Scholar
  62. Pisano R (2009b) Il ruolo della scienza archimedea nei lavori di meccanica di Galilei e di Torricelli. In: Giannetto E, Giannini G, Capecchi D, Pisano R (eds) Da Archimede a Majorana: La fisica nel suo divenire. Guaraldi Editore, Rimini, pp 65–74Google Scholar
  63. Pisano R (2009c) On method in Galileo Galilei’ mechanics. In: Hunger H (ed) Proceedings of ESHS 3rd conférence. The Austrian Academy of Science, Vienna, pp 147–186Google Scholar
  64. Pisano R (2009d) Galileo Galileo. Riflessioni epistemologiche sulla resistenza dei corpi. In Giannetto E, Giannini G, Toscano M (eds). Relatività, Quanti Chaos e altre Rivoluzioni della Fisica. Guaraldi Editore Rimini, 61–72Google Scholar
  65. Pisano R (2013a) Reflections on the scientific conceptual streams in Leonardo da Vinci and his relationship with Luca Pacioli. Adv Hist Stud 2(2):32–45CrossRefGoogle Scholar
  66. Pisano R (2013b) Historical Reflections on Newton’s First Law and Carnot’s Première Hypothèse In: 5th International Conference of the European Society for the History of Science. The Hellenic Foundation of Science Press. Athens, pp 214–220Google Scholar
  67. Pisano R (2013c) Note sulle Fortificazioni nei Quesiti di Tartaglia. Libro Sesto e sua Gionta. D’agostino S (ed). In: Proceedings of the 5th International Conference History of Engeenering (AISI 2014). Cuzzolin, Napoli, pp 813–826Google Scholar
  68. Pisano R (2013d) Notes on the historical conceptual streams for mathematics and physics teaching. International proceedings of the 53° mathematical society congress. Series A. The Vilnius University Press, Vilnius A/54, pp iv–xviiGoogle Scholar
  69. Pisano R, Bussotti P (2012) Galileo and Kepler. On Theoremata Circa Centrum Gravitatis Solidorum and Mysterium Cosmographicum. Hist Res 2(2):110–145Google Scholar
  70. 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
  71. Pisano R, Bussotti P (2013b) Open problems in mathematical modelling and physical experiments: exploring exponential function. Prob Educ 21st Century 50:56–69Google Scholar
  72. 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
  73. Pisano R, Bussotti P (2014b) Novelty of the concept of force in Johannes Kepler’s Corpus (Submitted to Studies in History and Philosophy of Science)Google Scholar
  74. Pisano R, Bussotti P (2014c) The emergencies of mechanics and thermodynamics in the Western society during 18th–19th century. In: Pisano R (2014) (ed) (in press)Google Scholar
  75. Pisano R, Capecchi D (2008) La meccanica in Italia nei primi anni del Cinquecento. Il contributo di Niccolò Tartaglia. In: Tucci P (ed) Proceedings of XXV SISFA congress, pp C17.1–C17.6, Milano (also available in .pdf via:http://www.brera.unimi.it/sisfa/atti/index.html)
  76. Pisano R, Capecchi D (2009) Il ruolo della meccanica ne Le fortificationi di Buonaiuto Lorini In: D’Agostino S (ed) 3rd Convegno di Storia dell’ingegneria, Cuzzolin editore, Napoli, vol II, pp 797–808Google Scholar
  77. Pisano R, Capecchi D (2010a) Galileo Galilei: Notes on Trattato di Fortificazione. In: Altamore A, Antonini G (eds) Galileo and the renaissance scientific discourse. Edizioni Nuova Cultura, Roma, pp 28–41Google Scholar
  78. Pisano R, Capecchi D (2010b) On Archimedean roots in Torricelli’s mechanics. In: Paipetis SA, Ceccarelli M (eds) The genius of Archimedes. Springer, Dordrecht, pp 17–28Google Scholar
  79. Pisano R, Capecchi D (2012) Historical reflections on scale ratio in Galilean Tratattto di Fortificazione. In: Koetsier T, Ceccarelli M (eds) Explorations in the history of machines and mechanisms. Springer, Dordrecht, pp 463–473CrossRefGoogle Scholar
  80. Pisano R, Capecchi D (2013) Conceptual and mathematical structures of mechanical science in the Western civilization around the 18th century. Almagest 4(2):86–121CrossRefzbMATHGoogle Scholar
  81. Pisano R, Rougetet L (2014) Quelles mathématiques trouve-t-on chez Leonardo da Vinci et chez Luca Pacioli? Les nouvelles d’Archimède (in press)Google Scholar
  82. Pulte H (1998) Jacobi’s criticism of Lagrange: the changing role of mathematics in the foundations of classical mechanics. Hist Math 25(2):154–184MathSciNetCrossRefzbMATHGoogle Scholar
  83. Radelet-de Grave P (1996) Entries: Stevin, Kepler, Leibniz, Huygens. In: Dictionnaire du patrimoine littéraire européen, Patrimoine Littéraire Européen, vol VIII. Avènement de l’Equilibre européen 1616–1720. De Boeck Université, p 18, pp 745–755, pp 1020–1027Google Scholar
  84. Rose PL (1975) The Italian renaissance of mathematics. Droz, GeneveGoogle Scholar
  85. Rowland D, Howe TN (1999) Vitruvius. Ten books on architecture. The Cambridge University Press, CambridgeGoogle Scholar
  86. Salusbury (1661–1665a) Galileus, his mechaniks, weights and from its instruments. In Salusbury 1661–1665, II, pp 271–310Google Scholar
  87. Salusbury (1661–1665b) Mathematical collections and translations, 2 vols. Leybourn W, LondonGoogle Scholar
  88. Sarton G (1953) Leonardo de Vinci, ingenieur et savant. Léonard de Vinci et l’expérience scientifique au XVIe siècle. Colloques internationaux du Centre de la Recherche Scientifique, Sciences Humanes. Presses Universitaires de France, Paris, s. 11–29Google Scholar
  89. Singer (1954–1958) A history of technology, vols 2–3. The Clarendon Press, OxfordGoogle Scholar
  90. Solmi E (1908) Le fonti dei manoscritti di Leonardo da Vinci e altri scritti Giornale storico della letteratura italiana. Supplemento 10–11Google Scholar
  91. Stevin S (1586a) De Beghinselen der Weegconst. Tot Leyden, Inde Druckerye van Christoffel Plantijn, By Francoys van RaphelinghenGoogle Scholar
  92. Stevin S (1586b) De Beghinselen des Waterwichts.Tot Leyden, Inde druckerye van Christoffel Plantijn, by Françoys van RaphelinghenGoogle Scholar
  93. Stevin S (1605) Tomus quartum mathematicorum hypomnematum de statica. Lugodini Batavorum [Translation into Latin by Willebrord Snel van Royen]. Ex Officina Ioannis Patii, Academiae TypographiGoogle Scholar
  94. Stevin S (1605–1608a) Memoires mathematiques: contenant ce en quoy s’est exercé le très-illustre, très-excellent Prince & Seigneur Maurice, Prince d’ Orange, Conte de Nassau, Catzenellenboghen, Vianden, Moers. [Translated into French by Jean Tuning]. Chez Ian Paedts Iacobsz. Marchand Libraire, & Maistre Imprimeur de l’Université de ladite VilleGoogle Scholar
  95. Stevin S (1605–1608b) Hypomnemata Mathematica, hoc est eruditus ille pulvis, in quo se exercuit […] Mauritius, princeps Auraïcus […] a Simone Stevino [Translation into Latin by Willebrord Snel van Royen]. Lugodini Batavorum. Ex Officina Ioannis Patii, Academiae TypographiGoogle Scholar
  96. Stevin S (1605–1608c) Wisconstige Gedachtenissen. Tot Leyden, Inde Druckerye van Ian BouvvenszGoogle Scholar
  97. Stevin S (1634) Les Œuvres Mathematiques de Simon Stevin de Bruges. Le tout reveu, corrigé, & augmenté Par Albert Girard. Samielois, Mathematicien. Bonaventure & Abraham Elsevier Imprimeurs ordinaires de L’Université, LeydeGoogle Scholar
  98. Stevin S (1955) The principal works of Simon Stevin. Mechanics. Committee of Dutch scientists, Dijksterhuis EJ (eds), vol 1. Swets & Zeitkinger, AmsterdamGoogle Scholar
  99. Taisbak C M (1981–1982) Errata: An Archimedean proof of Heron’s formula for the area of a triangle; reconstructed, Centaurus 25(1/2):160Google Scholar
  100. 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
  101. Tenenti A (1990) Les hommes et leurs cités. In: Bec C, Choulas I, Jestaz B, Tenenti A (eds) L’italie de la Renaissance. Un monde en mutation (1378–1494). Fayard, ParisGoogle Scholar
  102. Truesdell C (1968) Essay in the history of mechanics. Spinger, New YorkCrossRefzbMATHGoogle Scholar
  103. Tybjerg K (2000) Doing philosophy with machines: Hero of Alexandria’s Rhetoric of mechanics in relation to the contemporary philosophy. The Cambridge University Press, CambridgeGoogle Scholar
  104. Ulivi E (2002) Scuole e maestri d’abaco in Italia tra Medioevo e Rinascimento. In: Giusti E et al (eds) Un ponte sul Mediterraneo. Leonardo Pisano, la scienza araba e la rinascita della matematica in occidente, Polistampa, Firenze, pp 121–159Google Scholar
  105. Van Dyck M (2006) An archaeology of Galileo’s science. Ph.D. dissertation, a.y 2005–2006. The University of Ghent, GhentGoogle 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

Personalised recommendations