Lagrange, JOSEPH LOUIS, COMTE, the great algebraist, was born at Turin, 25th January 1736. His father, who, as well as his mother, was of French descent, was war-treasurer to the Piedmontese government. In later life Lagrange explained his first application to the study of mathematics by the fact that the family property had been lost in speculations. At the age of seventeen a paper of Halley's in the Philosophical Transactions turned him towards algebra and analytical geometry, and then his powers developed with striking precocity. In 1754 he was appointed mathematical professor in the Royal School of Artillery; at the same time he discovered a series for differential expansion analogous to the binomial theorem of Newton, and attracted Euler's attention by a letter on the general solution of certain isoperimetrical problems which had been proposed to the best mathematicians in Europe. He also corresponded with D'Alembert, then the leader of French scientific society. At Euler's suggestion Frederick the Great appointed Lagrange to succeed him as director of the Academy of Berlin. Before leaving Piedmont he did much original work in integration and partial differences, applying mathematical methods to physics and astronomy, and assisted, in 1758, to found the Turin Academy of Sciences. In 1762, by his completion of the Calculus of Variations, the main theory of which had been foreshadowed in his discussion of isoperimetricals, and his investigations of sound, harmonics, &c. by new analytical methods, Lagrange gained a European reputation, though at the expense of his health, which was never afterwards robust. His memoir on the moon's libration, which in 1764 obtained the prize of the French Academy, brought into prominence his great 'principle of virtual velocities,' which was presently to be so largely utilised in dynamical problems. Lagrange gave the first complete proof of Laplace's generalisation, that, so far as the laws of motion are concerned, our solar system is necessarily stable and permanent, because all the changes of the planetary orbits, caused by their reciprocal gravitation, are periodic. While in Prussia, from 1766 to 1787, Lagrange read before the Berlin Academy about sixty dissertations on the application of the higher analysis to mechanics and dynamics. From the leading results of these memoirs and of his previous work, duly marshalled and systematised, arose Lagrange's principal work, the Mécanique Analytique, which was published (1788) in Paris under the supervision of Legendre. The central theory, unifying the science of dynamics in all its developments, was the principle of virtual velocities which he had established in 1764.
Just before the issue of the Mécanique Analytique, Lagrange arrived in Paris, to be welcomed by the court and lodged in the Louvre with a pension of 6000 francs. In 1791 he was elected foreign member of the Royal Society of London.
He commanded universal respect even in the crisis of the Revolution, and was appointed professor in the Normal and Polytechnic Schools, one of the first members of the Bureau des Longitudes, and was enthusiastically in favour of the new decimal and metrical system. He was appointed member of the senate under Bonaparte, who also bestowed on him the title of Count and the Grand Cross of the Legion of Honour. He did more than any other, except Euler, to develop the applications of the infinitesimal calculus.
Partly owing to his weak constitution, Lagrange was extremely regular in his habits, abstemious in food, with his work ever most systematically distributed. His various treatises, read to the Academies of Turin, Berlin, and Paris, now fill seven quarto volumes. Other important works are Théorie des Fonctions (2d ed. 1813), Leçons sur le Calcul des Fonctions, Résolution des Équations Numériques. Lagrange died at Paris, 10th April 1813, and was buried in the Panthéon. A new edition of his works, in 16 vols., was undertaken in 1867.