MONGE, GASPARD (1746-1818), French mathematician, the inventor of descriptive geometry, was born at Beaune on May 1o, 1746. He was educated first at the college of the Oratorians at Beaune, and then in their college at Lyons. He was a draftsman in the practical school attached to the military school at Mezieres.
In 1768 Monge became professor of mathematics, and in 1771 professor of physics, at Mezieres; in 178o he was appointed to a chair of hydraulics at the Lyceum in Paris (held by him together with his appointments at Mezieres), and was received as a mem ber of the Academie ; his intimate friendship with C. L. Berthollet began at this time. In 1783, quitting Mezieres, he was, on the death of E. Bezout, appointed examiner of naval candidates. Although pressed by the minister to prepare for them a com plete course of mathematics, he declined to do so, on the ground that it would deprive Mme. Bezout of her only income, from the sale of the works of her late husband; he wrote, however (1786), his Traits elementaire de la statique.
Monge contributed (177o-179o) to the Memoires of the Aca demy of Turin, the Memoires des savants strangers of the Academy of Paris, the Memoires of the same Academy, and the Annales de chimie, various mathematical and physical papers. Among these may be noticed the memoir "Sur la theorie des deblais et des remblais" (Mem. de l'acad. de Paris, 1781), which, while giving a remarkably elegant investigation in regard to the problem of earth-work referred to in the title, establishes in con nection with it his capital discovery of the curves of curvature of a surface. The memoir gives the ordinary differential equation of the curves of curvature, and establishes the general theory; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795.
In 1792 Monge became minister of marine, but he remained so only until 1793. When the Committee of Public Safety made an appeal to the savants to assist in producing the materiel re quired for the defence of the republic he applied himself wholly to these operations, and distinguished himself by his indefatigable activity; he wrote at this time his Description de Part de fabriquer les canons, and his Avis aux ouvriers en fer sur la fabrication de l'acier. He took a very active part in the measures for the estab
lishment of the normal school (which existed only during the first four months of the year 1795) and of the Ecole Polytechnique and was at each of them professor for descriptive geometry ; his methods in that science were first published in the form in which the shorthand writers took down his lessons given at the normal school in 1795, and again in 1798-1799. His later mathematical papers are published (1794-1816) in the Journal and the Corre spondance of the polytechnic school. On the formation of the Senate he was appointed a member of that body, with the title of Count of Pelusium ; but on the fall of Napoleon he was de prived of all his honours, and even excluded from the list of members of the reconstituted Institute. He died at Paris on July 28, 1818.
See B. Brisson, Notice historique sur Gaspard Monge; Dupin, Essai historique sur les services et les travaux scientifiques de Gaspard Mange (Paris, 1819), which contains (pp. 162-166) a list of Monge's memoirs and works; and the biography by F. Arago (Oeuvres, t. 1854). Mange's various mathematical papers are to a considerable extent reproduced in the Application de l'analyse a la geometrie (4th ed., last revised by the author, Paris, 1819) ; the pure text of this is reproduced in the 5th ed. (revue, corrigee et annotee par M. Liouville) (Paris, 185o), which contains also Gauss's Memoir, "Disquisitiones generales circa superficies curvas," and some valuable notes by the editor. The other principal separate works are Traits elementaire de la statique, 8e edition, conformie a la precidente, par M. Hachette, et suivie d'une note, etc., par M. Cauchy (Paris. 1846) ; and the Geometrie descriptive (originating, as mentioned above, in the lessons given at the normal school) . The 4th edition, published shortly after the author's death, seems to have been substantially the same as the 7th (Geometrie descriptive par G. Monge, suivie d'une theorie des ombres et de la perspective, extraite des papiers de l'auteur, par M. Brisson (Paris, 1847).