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Bair, Jacques; Błaszczyk, Piotr; Heinig, Peter; Kanovei, Vladimir; Katz, Mikhail G.; McGaffey, Thomas

Cauchy’s work on integral geometry, centers of curvature, and other applications of infinitesimals. (English) Zbl 1442.01010

Real Anal. Exch. 45, No. 1, 127-150 (2020).
The authors discuss the technique and contribution of Cauchy to integral geometry. Most attention is paid to elucidating his views on the structure of the continuum, the concepts of limit and continuity, and applications to elasticity. Relationship is elaborated with the modern understanding of infinitesimals in nonstandard analysis.
Reviewer: S. S. Kutateladze (Novosibirsk)

Cited in 3 Documents

MSC:

01A55 History of mathematics in the 19th century
26-03 History of real functions

Keywords:

Cauchy-Crofton formula; continuity; infinitesimals; integral geometry; de Prony; Petit; Poisson

Biographic References:

Cauchy, Augustin-Louis
Cite Review PDF
Full Text: DOI arXiv Euclid

References:

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