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 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 $\scriptstyle{\int\frac{dx}{\sqrt{1-x^4}}}$.|undefined From this Jacobi[83] concluded that Gauss had thirty years earlier considered the nature and properties of elliptic functions and had discovered their double periodicity. The papers in the collected works of Gauss confirm this conclusion.

Carl Gustav Jacob Jacobi[84] (1804–1851) was born of Jewish parents at Potsdam. Like many other mathematicians he was initiated into mathematics by reading Euler. At the University of Berlin, where he pursued his mathematical studies independently of the lecture courses, he took the degree of Ph.D. in 1825. After giving lectures in Berlin for two years, he was elected extraordinary professor at Königsberg, and two years later to the ordinary professorship there. After the publication of his Fundamenta Nova he spent some time in travel, meeting Gauss in Göttingen, and Legendre, Fourier, Poisson, in Paris. In 1842 he and his colleague, Bessel, attended the meetings of the British Association, where they made the acquaintance of English mathematicians.

His early researches were on Gauss' approximation to the value of definite integrals, partial differential equations, Legendre's coefficients, and cubic residues. He read Legendre's Exercises, which give an account of elliptic integrals. When he returned the book to the library, he was depressed in spirits and said that important books generally excited in him new ideas, but that this time he had not been led to a single original thought. Though slow at first, his ideas flowed all the richer afterwards. Many of his discoveries in elliptic functions were made independently by Abel. Jacobi communicated his first researches to Crelle's Journal. In 1829, at the age