[5] In 1762 he went to the Collège de la Trinité at Lyon, where, one year after he had begun studying, he was made a teacher of physics[5] at the age of just seventeen.

[5] An officer of engineers who saw it wrote to the commandant of the École Royale du Génie at Mézières, recommending Monge to him and he was given a job as a draftsman.

After Bossut left the École Royale du Génie, Monge took his place in January 1769, and in 1770 he was also appointed instructor in experimental physics.

[5] Although pressed by the minister to prepare a complete course of mathematics, he declined to do so on the grounds that this would deprive Mme Bézout of her only income, that from the sale of the textbooks written by her late husband.

[7] When the Committee of Public Safety made an appeal to the academics to assist in the defence of the republic, he applied himself wholly to these operations, and distinguished himself by his energy, writing the Description Le l'art de Fabriquer Les canons and Avis aux ouvriers en fer sur la fabrication de l'acier.

[5] He took a very active part in the measures for the establishment of the Ecole Normale (which existed only during the first four months of the year 1795), and of the school for public works, afterwards the École Polytechnique, and was at each of them professor for descriptive geometry.

Upon his return to France, he was appointed as the Director of the École Polytechnique, but early in 1798 he was sent to Italy on a mission that ended in the establishment of the short-lived Roman Republic.

de Paris, 1781),[5] which is an elegant investigation of the problem with earthworks referred to in the title and establishes in connection with it his capital discovery of the curves of curvature of a surface.

[5] It is also noteworthy to mention that in his Mémoire sur quelques phénomènes de la vision Monge proposed an early implicit explanation of the color constancy phenomenon based on several known observations.

Related to that, the Monge soil-transport problem leads to a weak-topology definition of a distance between distributions rediscovered many times since by such as L. V. Kantorovich, Paul Lévy, Leonid Vaseršteĭn, and others; and bearing their names in various combinations in various contexts.

[5] It was also in this time, from 1783 - 1784, that Monge worked with (Jean-François, Jean-Baptiste-Paul-Antoine, or Abbé Pierre-Romain) Clouet to liquefy sulfur dioxide by passing a stream of the gas through a U-tube sunken in a refrigerant mixture of ice and salt.