Gaspard Monge

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Monge, Gaspard


Born May 10, 1746, in Beaune, C–ted’Or; died July 28, 1818, in Paris. French mathematician and public figure. Member of the Paris Academy of Sciences (1780).

Monge was appointed a professor at the Mézières School of Military Engineering in 1768. He was one of the founders of the Ecole Polytechnique in Paris, and he taught as a professor there from 1794. Monge’s chief works dealt with geometry. Proceeding from the concept of the projection of objects onto two mutually perpendicular planes, he devised a general method for representing three-dimensional figures in a plane. Monge carried out these studies during the first years of his work at the Mézières School (before the mid-1770’s), but his work Géometric descriptive (Descriptive Geometry) was not published until 1799. In Mémoire sur les développées, les rayons de courbure, et les différents genres d’inflexions des courbes à double courbure (1771, published 1785) and Sur les propriétés des plusieurs sorts des courbes des surfaces (1775, published 1780), Monge thoroughly discussed the differential geometry of space curves and surfaces. He studied the evolutes of space curves and the curvatures of surfaces and investigated envelopes and developable surfaces. In 1781 he examined the general properties of normal congruences and introduced the concept of the curves of curvature of surfaces. In Application de l’analyse à la géometrie (Application of Analysis to Geometry; 1795), in addition to presenting important discoveries on differential geometry, Monge gave a geometrical interpretation of partial differential equations and, on the other hand, presented geometrical facts in the language of partial differential equations. Monge also wrote works on mathematical analysis, chemistry, optics, meteorology, and applied mechanics.

During the French Revolution, Monge was a member of a commission to establish a system of weights and measures, and from 1792 to 1793 he was minister of the navy. In 1793 he became director of gunpowder and cannon works of the republic. Monge actively participated in the founding of the Ecole Normale Superieure (1794) and the Ecole Polytechnique (1794). During the Directory, he accompanied Napoleon on the Egyptian expedition (1798–1801). Monge returned to France with Napoleon and resumed teaching at the Ecole Polytechnique. Monge became a senator during the First Empire and was made a count. He was stripped of all his rights during the Restoration and was expelled from the Ecole Polytechnique and the Academy of Sciences.


Géometrie descriptive. Paris, 1799.
Feuilles d’analyse appliquée à la géometrie. Paris, 1795.
Application de l’algèbre à la géometrie. Paris, 1805.
In Russian translation:
Prilozhenie analiza k geometrii Moscow-Leningrad, 1936.
Nachertatel’naia geometriia. Moscow, 1947.


Gaspar Monzh: Sb. st. k dvukhsotletiiu so dnia rozhdeniia. Edited by Academician V. I. Smirnov. Moscow, 1947.
Struik, D. J. Ocherk istorii differentsial’noi geometrii do XX stoletiia. Moscow-Leningrad, 1941. (Translated from English.)
Arago, D. F. Biografiia znamenitykh astronomov, fizikov igeometrov, vol. 1. St. Petersburg, 1859. Pages 499–589 (Translated from French.)
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But parallel projections did not exist in the fifteenth century, and plans, elevations, side views, and sections long remained a practice without a mathematical theory: The rules of parallel projection were formalized by French mathematician Gaspard Monge only at the end of the eighteenth century.
Gaspard Monge, Geometrie descriptive (Paris: Baudouin, 1799).
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