The third of the great trio, of which the first two were Lagrange and Laplace, appeared in the person of Adrien-Marie Legendre 1. He was educated at the College Mazarin in Paris, where he early showed his taste for mathematics, and with the help of his teacher, the Abbe Marie 2, and of d'Alembert, he became (1775) professor of mathematics in the Ecole Militaire at Paris, resigning in 1780. Two years later (1782) he won the prize of the Berlin Academy for his essay on the path of a projectile 3. In elementary mathematics he is known chiefly for his geometry 4, a work which had a generous reception in various countries and which justly ranks as one of the best textbooks ever written upon the subject. In it he sought to rearrange the propositions of Euclid, separating the theorems from the problems and simplifying the proofs, without lessening the rigor of th e ancient methods of treatment. To Legendre is largely due the abandoning of Euclid as a textbook in American schools.

In higher mathematics Legendre is known for his works on the theory of numbers 5 and on elliptic functions 6. He is also known for his treatises on the calculus, higher geometry, mechanics, astronomy and physics. To him is due the first satisfactory treatment of the method of least squares 7, although Gauss had already discovered the method. In his theory of numbers appear the law of quadratic reciprocity which Gauss called the "gem of ari thmetic." The treatise on elliptic functions appeared almost simultaneously with the works by Abel and Jacobi on the same subjects; and although Legendre had spent thirty years on the theory, he recognized at once the superiority of the treatment given t o it by these younger men, and posterity has agreed with his judgment.

Failing to yield to the government in its desire to dictate to the Academie, he was deprived of his pension, and his last days were spent in poverty. His letters of this period are depressing, showing how one of the greatest scientists of France had l ost heart at the failure of a nation to recognize his honesty of purpose and his powers of intellect.

(Smith, pp. 489-490.)