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[T]o characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.
"Geometry and Empirical Science" in J. R. Newman (ed.), The World of Mathematics, New York: Simon and Schuster, 1956.
Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation
What were the philosophical foundations of the differential calculus at the turn of the nineteenth century? There were three competing notions: differentials, limits, and power series expansions. François-Joseph Servois (1768-1847), a disciple of Lagrange, supported the power series formalism and was sympathetic to a foundation based on limits. On the other hand, he claimed that the use of infinitesimals in mathematics would "one day be accused of having slowed the progress of the mathematical sciences, and with good reason." In this paper, we provide an analysis and an English translation of Servois' philosophical paper "Reflections on the various systems of exposition of the principles of the differential calculus."
Download the authors' English translation of Servois' “Reflections.”
Table Of Contents
Bradley, Robert E. and Salvatore J. Petrilli, Jr., "Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation," Loci (April 2010), DOI: 10.4169/loci003487