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Although this may seem a paradox, all exact science is dominated by the idea of approximation.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.
Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation
Many historians of mathematics consider the nineteenth century to be the Golden Age of mathematics. During this time period many areas of mathematics, such as algebra and geometry, were being placed on rigorous foundations. Another area that experienced fundamental change was analysis. Grabiner  considers Joseph-Louis Lagrange (1736-1813) to be the first mathematician to treat the eighteenth century foundations of calculus as a serious mathematical issue. The publication of his Fonctions analytiques  can be seen as the first attempt to resolve these foundational issues. However, many other mathematicians also contributed to the foundational debates of the eighteenth and nineteenth centuries. One such figure was François-Joseph Servois (1767-1847). Servois was a priest, artillery officer during the French Revolutionary period, professor of mathematics, and supporter of Lagrange’s algebraic formalism. This paper provides an examination and English translation of Servois’ “Essay on a new method of exposition of the principles of differential calculus” [1814a], in which Servois continued the work of Lagrange by attempting to place calculus on a foundation of algebraic analysis without recourse to infinitesimals.
Download the authors’ English translation of Servois’ “Essay.”
Table Of Contents
Bradley, Robert E. and Salvatore J. Petrilli, Jr., "Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation," Loci (November 2010), DOI: 10.4169/loci003597