Das velocidades às fluxões
DOI:
https://doi.org/10.1590/S1678-31662010000400002Keywords:
Newton, Theory of fluxions, History of mathematical analysis, Analysis/synthesis, History of rational mechanicsAbstract
Newton's De methodis (written in 1671) results from a revision of an uncompleted treatise that he had written in October-November 1666 (The October 1666 tract on fluxions, as Whiteside called it). In 1666, Newton already had the main results that he would expound 5 years later in the text that is unanimously considered the best presentation of his theory of fluxions. However, the term "fluxion" itself did not appear however in The October 1666 tract on fluxions, where the question addressed had to do with motions or velocities. From the strict point of view of mathematical formalism, the shift from (punctual) velocities to fluxions is not especially relevant: the mathematical methods of the De methodis are essentially the same as those of The October 1666 tract on fluxions. Still, this terminological change is, I think, the symptom of a different way to understand these methods and the objects they apply to. This is quite explicitly said by Newton in a crucial passage at the beginning of the De methodis, where he claims that the term "time" in his treatise does not refer to the time formaliter spectatum, but to "another quantity" for the "fluxion of which the time is expressed and measured". In this paper, I discuss this passage and try to clarify the essential differences between the 1666 notion of velocity and the new notion of fluxion introduced in 1671. This also enables me to discuss the role of Newton in the origin of 18th century analysis.Downloads
References
Adam, C. & Tannery, P. (Ed.). Oeuvres de Descartes. Vrin: Paris, 1897-1910. 12 v.
Al-Khwãrizmi, M. Le commencement de l’algébre. Tradução e introdução R. Rashed. Paris: Blanchard, 2007.
Auger, L. Gilles Personne de Roberval (1602-1675). Paris: Blanchard, 1962.
Backer, R (Ed.). Euler reconsidered. Tercentenary essays. Heber City: Kendrick, 2007.
Barrow, I. Lectiones geometricæ (...). Londini: Typi G. Godbid, & prostantvenales apud J. Dunmore, & O. Pulleyn Juniorem, 1670.
Cerrai, P. F. & Pellegrini, C. (Eds.) The application of mathematics to the sciences of nature. Critical moments and aspects. New York: Kluwer/Plenum, 2002.
Child, J. M. (Ed.) The geometrical lectures of Isaac Barrow. Chicago/London: Open Court, 1916.
Descartes, R. Discours de la méthode [...]. Plus La dioptrique. Les météores. Et La géométrie qui sont des essaies de cette méthode. Leyde: I. Maire, 1637.
Descartes, R. Geometria, à Renato des Cartes anno 1637 Gallicè edita [...] Operâ atque studio Francisci à Schooten [...]. Amstelodami: Elzevirios, 1659-1661. 2 v.
Descartes, R. Principia philosophiæ. Amstelodami: Elzevirium, 1644.
Descartes, R. Les principes de la philosophie. Paris: Le Gras, 1647.
Euler, L. Introductio in analysis infinitorum. Lausanne: Bousquet & Soc., 1748. 2 v.
Freguglia, P. Viète reader of diophantus. An analysis of Zeteticorum libri quinque. Bollettino di Storia delle Scienze Matematiche, 28, p. 51-95, 2008.
Grattan-Guinness, I. (Ed.) From the calculus to set theory, 1630-1910. London: Duckworth, 1980.
Guicciardini, N. Reading the Principia. The debate on Newton’s mathematical methods for natural philosophy from 1687 to 1736. Cambridge: Cambridge University Press, 1999.
Hara, K. Etude sur la théorie des mouvements de Roberval. Paris, 1965, Tese (Doutorado em filosofia). Faculté des Lettres, Université de Paris.
Hoskin, M. (Ed.). Cambridge illustrated history of astronomy. Cambridge: Cambridge University Press, 2000.
Kinckhuysen, G. Algebra ofte stel-konst. Harlem: Passchier van Wesbusch, 1661.
Luckey, P. Tãbit b. Qurra über den geometrischen Richtigkeitsnachweis der Auflösung der quadratischen Gleichungen. Berichte über die Verhandlungen der Sächsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-physikalische Klasse, 93, p. 93–114, 1941.
Mercator, N. Logarithmothechnia; sive methodus construendi logarithmos nova, accurata & facilis [...]. Cui accedit vera quadratura hyperbolæ et inventio summæ logarithmorum. Londini: M. Pitt, 1668.
Mersenne, M. Cogitata physico-mathematica [...]. Paris: Sumptibus A. Bertier, 1644.
Newton, I. Analysis per quantitatum, series, fluxiones, ac differentias cum enumeratio linearum tertii ordinis. ex officina paersoniana. Londini: W. Jones, 1711.
Newton, I. The method of fluxions and infinite series: with its application to the geometry of curve-lines. Tradução J. Colson. Cambridge: H. Woodfall/J. Nourse, 1736.
Otte, M. & Panza, M. (Ed.) Analysis and synthesis in mathematics. History and philosophy. Dordrecht: Kluwer, 1997. (Boston Studies in the Philosophy, 196).
Panza, M. Classical sources for the concepts of analysis and synthesis. In: Otte, M. & Panza, M. (Ed.) Analysis and synthesis in mathematics. History and philosophy. Dordrecht: Kluwer, 1997. p. 365–414. (Boston Studies in the Philosophy, 196).
Panza, M. Mathematisation of the science of motion and the birth of analytical mechanics: a historiographical note. In: Cerrai, P. F. & Pellegrini, C. (Eds.) The application of mathematics to the sciences of nature. Critical moments and aspects. New York: Kluwer A. P./ Plenum P., 2002. p. 253–71.
Panza, M. Newton et les origines de l’analyse: 1664-1666. Paris: Albert Blanchard, 2005.
Panza, M. Euler’s introductio in analysis infinitorum and the program of algebraic analysis: quantities, functions and numerical partitions. In: Backer, R (Ed.). Euler reconsidered. Tercentenary essays. Heber City (Utah): Kendrick Press, 2007. p. 119-66.
Panza, M. What is new and what is old in Viète’s analysis restituita and algebra nova, and where do they come from? Some reflections on the relations between algebra and analysis before Viète. Revue d’Histoire des mathématiques, 13, p. 83–151, 2008.
Pedersen, K. M. Roberval’s method of tangents. Centaurus, 13, p. 151-82, 1968.
Pedersen, K. M. Techniques of the calculus, 1630-1660. In: Grattan-Guinness, I. (Ed.) From the calculus to set theory, 1630-1910. London: Duckworth, 1980. p. 10-48.
Rigaud, S. J. (Ed.) Correspondance of scientific men of the seventeenth century. Oxford: Oxford Unversity Press, 1841.
Roberval, G. P. Observations sur la composition des mouvemens, et sur le moyen de trouver les touchantes des lignes courbes. In: _____. Divers ouvrage de M. de Roberval. Paris: Académie Royale des Sciences, 1963. p. 67-302.
Skinner, Q. Thomas Hobbes and his disciples in France and England. Comparative Studies in Society and History, 8, p. 153-67, 1966.
Torricelli, E. Opera geometrica. Florentiæ: Landis/Massæ, 1644.
Turnbull, H. W. (Ed.) The correspondence of Isaac Newton. Cambridge: Cambridge University Press, 1959-1977. 7 v. (Correspondence)
Viète, F. In artem analyticem isagoge: seorsim excussa ab opere restitutae mathematicae analyseos, seu algebra
nova. Turonis: Mettayer, 1591.
Westfall, R. Never at rest. A biography of Isaac Newton. Cambridge: Cambridge University Press, 1980.
Whiteside, D. T. (Ed.). The mathematical papers of Isaac Newton. Cambridge: Cambridge University Press, 1967-1981. 8 v. (MP)
Wolfson, P. R. The crooked made straight: Roberval and Newton on tangents. The American Mathematical Monthly, 108, 3, p. 206-16, 2001.
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