# Cauchy's Work on Integral Geometry, Centers of Curvature, and Other Applications of Infinitesimals

@article{Bair2020CauchysWO, title={Cauchy's Work on Integral Geometry, Centers of Curvature, and Other Applications of Infinitesimals}, author={Jacques Bair and Piotr Błaszczyk and Peter Heinig and Vladimir Kanovei and Mikhail G. Katz and Thomas Mcgaffey}, journal={arXiv: History and Overview}, year={2020} }

Like his colleagues de Prony, Petit, and Poisson at the Ecole Polytechnique, Cauchy used infinitesimals in the Leibniz-Euler tradition both in his research and teaching. Cauchy applied infinitesimals in an 1826 work in differential geometry where infinitesimals are used neither as variable quantities nor as sequences but rather as numbers. He also applied infinitesimals in an 1832 article on integral geometry, similarly as numbers. We explore these and other applications of Cauchy's…

## 5 Citations

### Continuity between Cauchy and Bolzano: issues of antecedents and priority

- PhilosophyBritish Journal for the History of Mathematics
- 2020

In a paper published in 1970, Grattan-Guinness argued that Cauchy, in his 1821 Cours d'Analyse, may have plagiarized Bolzano's Rein analytischer Beweis (RB), first published in 1817. That paper was…

### Mathematical Conquerors, Unguru Polarity, and the Task of History

- Philosophy
- 2020

We compare several approaches to the history of mathematics recently proposed by Blasjo, Fraser--Schroter, Fried, and others. We argue that tools from both mathematics and history are essential for a…

### Equality and Near-Equality in a Nonstandard World

- PhilosophyLogic and Logical Philosophy
- 2022

In the context of nonstandard analysis, the somewhat vague equality relation of near-equality allows us to relate objects that are indistinguishable but not necessarily equal. This relation appears…

### Three case studies in current Leibniz scholarship

- PhilosophyAntiquitates Mathematicae
- 2022

We examine some recent scholarship on Leibniz’s philosophy of the infinitesimal calculus. We indicate difficulties that arise in articles by Bassler, Knobloch, and Arthur, due to a denial to…

### A two-track tour of Cauchy's Cours

- Mathematics
- 2021

Cauchy published his Cours d’Analyse 200 years ago. We analyze Cauchy’s take on the concepts of rigor, continuity, and limit, and explore a pair of approaches in the literature to the meaning of his…

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