3/2/2023 0 Comments Galileo infinitesimals![]() Il numero era inteso come una misura della quantità tuttavia solo le frazioni e i naturali erano considerati numeri nel vero senso del termine. This conception allowed Euler to consider calculus as a calculus of functions (intended as analytical expressions of quantities) and, at the same time, to handle differentials formally.Nel diciottesimo secolo la classica nozione di quantità fu sviluppata fino ad essere intesa come quantità generale, la quale, analiticamente espressa, era soggetta a manipolazioni formali. ![]() They were symbols that represented a primordial and intuitive idea of limit, although they were manipulated in the same way as numbers. In this context Eulerian infinitesimals should also be considered as fictitious numbers. The other types of numbers were fictitious entities, namely ideal entities firmly founded in the real world which could be operated upon as if they were numbers. Number was understood as the measure of quantity however, only fractions and natural numbers were considered numbers in the true sense of term. The easily available sources (Wiki,etc.) about the condemnation of indivisibles of Galileo and Cavalieri (dated August 10, 1632), led the Revisors General of the Jesuits Jacob Bidermann all ref to Amir Alexander's book.In the 18th-century calculus the classical notion of quantity was understood as general quantity, which was expressed analytically and was subject to formal manipulation. I think that the modern source is Egidio Festa, La querelle de l'atomisme: Galilee, Cavalieri et les jesuites (1990). See also Mordechai Feingold (editor), Jesuit Science and the Republic of Letters (MIT Press, 2002), page 28-29, for details about jesuit Rodrogo de Arriaga's Cursus philosophicus (Anversa, 1632) condemnation of 1632, concerning "mathematical atomism" and "the opinion on quantity made up of indivisibles". The jesuit mathematician Paul Guldin was an harsh critic of Cavalieri's method of indivisibles into his De centro gravitatis (or Centrobaryca, three volumes, 1635-41), on mathematical grounds. Unlike The Assayer, which had recourse to the lethal polemical weapons of satire and the new philosophy, the Ratio used those no-less-lethal weapons of doctrinal and dialectical retort based on religious and philosophical orthodoxy. Grassi's second response to Il Saggiatore, the Ratio ponderum librae et simbellae (1626), focused mainly on doctrinal issues. The beginning of the demonstration of the law of falling bodies.Īnd see : Galileo's Saggiatore (1623) and the reply by the jesuit Orazio Grassi ( Libra, published under the name : Lotario Grassi)Īsserting that Galileo's book advanced an atomic theory of matter, and that this conflicted with the Catholic doctrine of the Eucharist, because atomism would make transubstantiation impossible. Indivisibles are implicitly mentioned in part of the second day of the Dialogo (1632), at In February and March 1626, Cavalieri reminded him of the project: “do you remember the work on indivisibles that you had decided to write?” ![]() On, Galileo wrote, in a letter to the secretary of the Grand Duke of Tuscany, that he was planning a piece of work on the De Compositione continui. See : Vincent Jullien (editor), Seventeenth-Century Indivisibles Revisited (2015, Birkhauser) for details about the works of Kepler (1609), Cavalieri (1635) and Guldin (1640).Ĭavalieri developed his theory of geometry during the years 1620–1622.Īccording to Vincent Jullien's chapter dedicated to Indivisibles in the Work of Galileo : The issue regards more indivisibles than infinitesimals and must be located in the context of the Early Modern European debate about the "revamping" of atomism. ![]()
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