Joseph Louis Lagrange, count de, a French geometrician, born in Turin, of French parents, Jan. 25, 1736, died in Paris, April 10, 1813. His first publication was a letter to C. J. Fagna-no, June 23, 1754, which contained a series of fluxions and fluents of different orders, somewhat resembling the binomial theorem of Newton. In 1755 he was made professor of geometry in the royal school of artillery at Turin, where many of his pupils were his seniors. In conjunction with several of them, he established a scientific society, whose memoirs, owing particularly to his contributions, afterward acquired a high reputation, his essays on the propagation of sound being especially noticed. He meanwhile corresponded with Euler, to whom he communicated his first ideas of the solution of the isoperimetrical problems. In 1764 he won a prize from the French academy of sciences for a memoir on the libration of the moon. In 1766 a second prize, on the subject of the satellites of Jupiter, was awarded him by the French academy; and he was invited to become a mathematical director of the Prussian academy.

In Berlin he was treated with great distinction by Frederick the Great, and spent there 20 years, during which he prepared his great work, the Mecanique analy-tique. On the death of Frederick, yielding to a secret desire and to the entreaties of Mirabeau, notwithstanding liberal offers from the courts of Naples, Sardinia, and Tuscany, he went to France, where he was welcomed by Queen Marie Antoinette, received as a veteran pensioner of the academy an income equal to that which he had enjoyed at Berlin, and was provided with apartments in the Louvre. His Mecanique analytique appeared a few months after his arrival in Paris in 1787, and commanded general admiration. Though now in the zenith of his fame, he was seized with fits of morbid melancholy, during which he lost all taste for his wonted pursuits. His spirits revived about the beginning of the revolution, and his treatment by the revolutionists was perhaps still more flattering than that which he had obtained from kings and princes. His pension was unanimously confirmed by the national assembly, and he was appointed member of a committee for examining useful inventions, and director of the mint in conjunction with Monge and Berthollet. In 1793, when a decree of the convention ordered all persons not born in France to leave the country, an exception was made in favor of Lagrange. On the establishment of the normal school and of the polytechnic school he was appointed professor in those institutions.

For his pupils he wrote his Theorie des fonctions analytiques (4to, 1797; new ed., 1813), and his Legons sur le calcul des fonctions (last ed., 1806); but the ideas in these books are far from being as perfect as the method of fluxions and its kindred doctrines. On the foundation of the institute and the board of longitude, he was placed among the members of the former, and at the head of the latter. On the entrance of the French army into Turin, the generals and many high functionaries, headed by the civil commissary, went in procession, by order of the directory, to congratulate Lagrange's father, then 90 years of age, on the merits of his son. Napoleon made him a senator and a count of the empire, and styled him the " high pyramid of mathematical sciences." His last years were devoted to preparing new editions of his Mecanique analytlque (2 vols. 4to, 1811 - '15), and Theorie des fonctions analytiques (4to, 1813). An edition of his complete works was published in 1867-'70, at the cost of the government.