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 de l'analyse à la géométrie, The last two contain most of his miscellaneous papers.

Monge was an inspiring teacher, and he gathered around him a large circle of pupils, among which were Dupin, Servois,, Hachette, Biot, and Poncelet.

Charles Dupin (1784–1873), for many years professor of mechanics in the Conservatoire des Arts et Métiers in Paris, published in 1813 an important work on Développements de géométrie, in which is introduced the conception of conjugate tangents of a point of a surface, and of the indicatrix.[55] It contains also the theorem known as "Dupin's theorem." Surfaces of the second degree and descriptive geometry were successfully studied by Jean Nicolas Pierre Hachette (1769–1834), who became professor of descriptive geometry at the Polytechnic School after the departure of Monge for Rome and Egypt. In 1822 he published his Traité de géométrie descriptive.

Descriptive geometry, which arose, as we have seen, in technical schools in France, was transferred to Germany at the foundation of technical schools there. G. Schreiber, professor in Karlsruhe, was the first to spread Monge's geometry in Germany by the publication of a work thereon in 1828–1829.[54] In the United States descriptive geometry was introduced in 1816 at the Military Academy in West Point by Claude Crozet, once a pupil at the Polytechnic School in Paris. Crozet wrote the first English work on the subject.[2]

Lazare Nicholas Marguerite Carnot (1753–1823) was born at Nolay in Burgundy, and educated in his native province. He entered the army, but continued his mathematical studies, and wrote in 1784 a work on machines, containing the earliest proof that kinetic energy is lost in collisions of bodies. With the advent of the Revolution he threw himself into politics, and when coalesced Europe, in 1793, launched against France a million soldiers, the gigantic task of organising fourteen