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Topic: [HM] Cauchy and his Resume des Lecons sur le calcul infinitesimal
Replies: 4   Last Post: Oct 27, 2003 2:56 PM

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Judy Grabiner

Posts: 22
Registered: 12/3/04
Re: [HM] Cauchy and his Resume des Lecons sur le calcul infinitesimal
Posted: Oct 27, 2003 11:32 AM
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Dear Professor Villeneuve,

One place you can find a discussion of some of the ideas in the
Resume is in my book, Origins of Cauchy's Rigorous Calculus (MIT 1981).
There is an article in Historia Mathematica just focusing
on the derivative, "The Origins of Cauchy's Theory of
the Derivative." Hist. Math. 5, 1978, pp. 379-409.
Perhaps these will address some of your questions.

In fact the 1821 Cours d'analyse by Cauchy is more accurately
characterized as the source of much of his work on
19th-century analysis, notably the theory of convergence
and, in an appendix, a proof of the intermediate-value
theorem for continuous functions (which actually assumes
uniform continuity). These are also treated in my book.
I commend also to you the writings of Umberto Bottazzini
and Ivor Grattan-Guinness on this subject.

Best wishes,

Judith V. Grabiner
Flora Sanborn Pitzer Professor of Mathematics
Pitzer College (909) 607-3160

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