LEGENDRE, ADMEN MARIE (1752-1833). A French mathematician, born in Paris. Ile early became professor of mathe matics in the military school. and later in the normal school at Pal:is. Ile was a member of the Academy and of the Bureau of Longitudes, and ill 1816 was appointed examiner for ad mission to the Ecole Polytechnique. In 1824. in an election at the Academy. because he did not vote for the candidate of the Government, he was deprived of his pension. and he died in poverty. Legemlre was one of the lenders in introducing the metric system, and was asso ciated with Prosy ill preparing the great eentesi mal trigonometric tables. TIe contributed ex tensively to the theory of attraction (from 1783), and introduced into the discussion of the at traction of spheroids the special eases of La place's coeflieients which hear his name. HP also wrote important memoirs (1787-S8) on geodesy, introducing a method of treating the spherical triangle as plane, provided certain corrections are made witb respect to the angles. The method of least squares was introduced in his Nourciles methodcs mentioned below, although Gauss had already (1795) used it. The celebrated law of quadratic reciprocity (see NUMBER), which Gauss called 'the gem of arithmetic,' appeared in a memoir of 1785, but the first proof was given in his Thdorie des nombres. The most im
portant of Legendre's works is the Trait(' des fonetions elliptiques, upon which he worked for forty years. It is a tribute to his generosity that just as his work was appearing the labors of Abel and Jacobi became known, and were at once recognized by him as superior to his own. Ile even went so far as to embody them, with due credit, in his last volume. (See FUNCTIONS.) The work which had the greatest popularity, and which was a classic for a century, was his Elements de geometric. (1794. 15th ed. 1881; Ger. trans. by Crelle, 6th ed. 1873; Eng. trans. 186'0). The later editions of this work contain his proof of the irrationality of 7r and 7r His other works are: Essai sur in theorie des nom bres (179S; 4th ed. 1900; Ger. trans. by Maser, 1886) : Nouvelle theorie des parallides (1S03) ; Nourelles methodes pour In determbuition des orbites des coraCtes (1805) ; Exerciees de ealeul integral (1807; new ed., 3 vols., 1819) ; Traitd des fonetions elliptiques et integrales Euleriennes (3 vols., 1S2G-32).