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 done with the ruler and compass, but I am not allowed to reveal these secrets to you." But Lacroix set himself to examine what the secret could be, discovered the processes, and published them in 1795. The method was published by Monge himself in the same year, first in the form in which the shorthand writers took down his lessons given at the Normal School, where he had been elected professor, and then again, in revised form, in the Journal des écoles normales. The next edition occurred in 1798–1799. After an ephemeral existence of only four months the Normal School was closed in 1795. In the same year the Polytechnic School was opened, in the establishing of which Monge took active part. He taught there descriptive geometry until his departure from France to accompany Napoleon on the Egyptian campaign. He was the first president of the Institute of Egypt. Monge was a zealous partisan of Napoleon and was, for that reason, deprived of all his honours by Louis XVIII. This and the destruction of the Polytechnic School preyed heavily upon his mind. He did not long survive this insult.

Monge's numerous papers were by no means confined to descriptive geometry. His analytical discoveries are hardly less remarkable. He introduced into analytic geometry the methodic use of the equation of a line. He made important contributions to surfaces of the second degree (previously studied by Wren and Euler) and discovered between the theory of surfaces and the integration of partial differential equations, a hidden relation which threw new light upon both subjects. He gave the differential of curves of curvature, established a general theory of curvature, and applied it to the ellipsoid. He found that the validity of solutions was not impaired when imaginaries are involved among subsidiary quantities. Monge published the following books: Statics, 1786; Applications de l'algèbre à la géométrie, 1805;