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

  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},
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… 

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