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This led Jacobi to inquire Post Date: Sun, 27 Jul 2008 4:03:39 +0000 Cauchy and Legendre were appointed to examine it ; but said nothing about it until after Abel s death. In a brief statement of the discoveries in question, published by Abel in Crette s Journal, 1829, reference is made to that memoir. This led Jacobi to inquire of Legendre whafr had become of it. Autor of the post: Undefined It was not published until Post Date: Sun, 27 Jul 2008 3:52:51 +0000 Le- gendre says that the manuscript was so badly written as to be illegible, and that Abel was asked to hand in a better copy, which he neglected to do. The memoir remained in Canchy ; hands. It was not published until 1841. Autor of the post: Undefined Abelian integrals depend upon Post Date: Sun, 27 Jul 2008 3:42:47 +0000 By a singular mis hap, the manuscript was lost before the proof-sheets were read. In its form, the contents of the memoir belongs to the inte gral calculus. Abelian integrals depend upon an irrational function y which is connected with x by an algebraic equa tion F(x } y) = 0. Autor of the post: Undefined The addition theorems of elliptic Post Date: Sun, 27 Jul 2008 3:23:17 +0000 Abel s theorem asserts that a sum of such integrals can be expressed by a definite number p of similar integrals, where p depends merely on the properties of the equation F(x, y) = 0. It was shown later that p is the defi ciency of the curve F(x, y) = 0. The addition theorems of elliptic integrals are deducible from Abel s theorem. Autor of the post: Undefined Two editions of Abel s Post Date: Sun, 27 Jul 2008 3:06:18 +0000 The hyperelliptic integrals introduced by Abel, and proved by him to possess multiple periodicity, are special cases of Abelian integrals whenever p= or gt; 3. The reduction of Abelian to elliptic integrals has been studied mainly by Jacobi, Hermite, Konigsberger, Brioschi, Goursat, Picard, and Bolza of the University of Chicago. Two editions of Abel s works have been published : the first by Holmboe in 1839, and the second by Sylow and Lie in 1881. Autor of the post: Undefined " During the few years Post Date: Sun, 27 Jul 2008 2:55:25 +0000 Abel s theorem was pronounced by Jacobi the greatest dis covery of our century on the integral calculus. The aged Legendre, who greatly admired Abel s genius, called it "mon- umentum aere perennius." During the few years of work allotted to the young Norwegian, he penetrated new fields of research, the development of which has kept mathematicians busy for over half a century. Autor of the post: Undefined Erom this Jacobi 83 concluded Post Date: Sun, 27 Jul 2008 2:39:14 +0000 Some of the discoveries of Abel and Jacobi were anticipated by Gauss. In the Disqidsitiones Arithmeticce he observed that the principles which he used in the division of the circle were applicable to many other functions, besides the circular, and particularly to the transcendents dependent on the integral. Erom this Jacobi 83 concluded that Gauss had thirty years earlier considered the nature and properties of elliptic functions and had discovered their double periodicity. Autor of the post: Undefined Like many other mathematicians Post Date: Sun, 27 Jul 2008 2:26:41 +0000 The papers in the collected works of Gauss confirm this con clusion. Carl Gustav Jacob Jacob! (1804-1851) was born of Jewish parents at Potsdam. Like many other mathematicians he was initiated into mathematics by reading Euler. Autor of the post: Undefined After the publication Post Date: Sun, 27 Jul 2008 2:11:30 +0000 At the Univer sity of Berlin, where he pursued his mathematical studies independently of the lecture courses, he took the degree of Ph in 1825. After giving lectures in Berlin for two years, he was elected extraordinary professor at Konigsberg, and two years later to the ordinary professorship there. After the publication of his Fimdamenta Nova he spent some time in travel, meeting Gauss in Gottingen, and Legendre, Courier, Poisson, in Paris. Autor of the post: Undefined He read Legendre s Exercises Post Date: Sun, 27 Jul 2008 1:53:41 +0000 In 1842 he and his colleague, Bessel, at tended the meetings of the British Association, where they made the acquaintance of English mathematicians. His early researches were on Gauss 7 approximation to the value of definite integrals, partial differential equations, Le- gendre s coefficients, and cubic residues. He read Legendre s Exercises, which give an account of elliptic integrals. 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