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Loci: Convergence
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Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation
Introduction
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
- Introduction
- A Revolution in France, a Revolution in Calculus
- Foundations of Calculus: Differentials and Limits
- A Third Path
- Lagrange's School
- Differentials via Series
- Limits and Infinitesimals
- Series Expansion and Convergence
- Analogies and Algebraic Properties
- Wronski's Philosophy of Mathematics
- Criticism of Wronski in the “Reflections”
- Conclusions, Recommendations, and Translation
- References
- Acknowledgments and About the Authors
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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