Augustin Cauchy: "Sur les intégrales qui s'étendent à tous les points d'une courbe fermée" (On integrals that extend over all of the points of a closed curve). In: Comptes rendus, volume 23, 1846, on 251-255 in the weekly issue. Extracted from a larger bound volume. Nice copy, fresh and crisp. $200
“In 1846, the form of "Green's theorem" which appears in this article was first published, without proof, in an article by Augustin Cauchy (in 1846, this article). (The equation appears at the bottom of page 254, where (S) denotes the line integral of a function k along the curve s that encloses the area S.) A proof of the theorem was finally provided in 1851 by Bernhard Riemann in his inaugural dissertation: Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse (Basis for a general theory of functions of a variable complex quantity), 1851...“--Wiki, “Green's Theorem”. ["George Green, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (Nottingham, England: T. Wheelhouse, 1828. Green did not actually derive the form of "Green's theorem" which appears in this article; rather, he derived a form of the "divergence theorem", which appears on pages 10-12 of his Essay."--Wiki] See also: Weisstein, Eric W. "Cauchy Integral Theorem." From MathWorld--A Wolfram Web Resource.
Comments