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 Collège Mazarin in Paris, where he began the study of mathematics under Abbé Marie. His mathematical genius secured for him the position of professor of mathematics at the military school of Paris. While there he prepared an essay on the curve described by projectiles thrown into resisting media (ballistic curve), which captured a prize offered by the Royal Academy of Berlin. In 1780 he resigned his position in order to reserve more time for the study of higher mathematics. He was then made member of several public commissions. In 1795 he was elected professor at the Normal School and later was appointed to some minor government positions. Owing to his timidity and to Laplace's unfriendliness toward him, but few important public offices commensurate with his ability were tendered to him.

As an analyst, second only to Laplace and Lagrange, Legendre enriched mathematics by important contributions, mainly on elliptic integrals, theory of numbers, attraction of ellipsoids, and least squares. The most important of Legendre's works is his Fonctions elliptiques, issued in two volumes in 1825 and 1826. He took up the subject where Euler, Landen, and Lagrange had left it, and for forty years was the only one to cultivate this new branch of analysis, until at last Jacobi and Abel stepped in with admirable new discoveries.[52] Legendre imparted to the subject that connection and arrangement which belongs to an independent science. Starting with an integral depending upon the square root of a polynomial of the fourth degree in $\scriptstyle{x}$, he showed that such integrals can be brought back to three canonical forms, designated by $\scriptstyle{F(\phi)}$, $\scriptstyle{E(\phi)}$, and $\scriptstyle{\Xi(\phi)}$, the radical being expressed in the form $\scriptstyle{\Delta(\phi)=\sqrt{1-k^2\sin^2\phi}}$.|undefined He also undertook the prodigious task of calculating tables of arcs of the ellipse for different degrees of amplitude and eccentricity, which supply the means of integrating a large number of differentials.