> Does anyone know when the term "Fundamental Theorem of Calculus" first > came into use and when it was first used to refer to the two results: > equality of the definite integral and the change in an anti-derivative, > the derivative of a definite integral with variable upper limit of > integration is the integrand.
In Cauchy's 1823 course on the calculus, he proves the second statement but does not even state it as a theorem; it seems to be treated just as a convenient property of integrals. See pages 151 and 152 of Oeuvres compeltes d'Augustin Cauchy, 2nd series, volume IV (which is available online at gallica.bnf.fr).
In a quick search, I couldn't find any occurrences in gallica of "theoreme fondamental" pointing to FTC. (There are lots of other "fundamental theorems", of course, including the one that says that the complex numbers are algebraically closed.)
-- Fernando Q. Gouvea Department of Mathematics Editor, FOCUS and FOCUS Online Colby College Mathematical Association of America Waterville, ME 04901 http://www.maa.org http://www.colby.edu/~fqgouvea ==========================================================
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