Of the two leading problems of descriptive geometry, the one–-to represent by drawings geometrical magnitudes–-was brought to a high degree of perfection before the time of
Monge; the other–-to solve problems on figures in space
by constructions in a plane–-had received considerable attention before his time. His most noteworthy predecessor in descriptive geometry was the Frenchman Frézier (1682–1773).
But it remained for Monge to create descriptive geometry as a distinct branch of science by imparting to it geometric generality and elegance. All problems previously treated in a special and uncertain manner were referred back to a few general principles. He introduced the line of intersection of the horizontal and the vertical plane as the axis of projection. By revolving one plane into the other around this axis or ground-line, many advantages were gained.54
Gaspard Monge (1746–1818) was born at Beaune. The construction of a plan of his native town brought the boy under the notice of a colonel of engineers, who procured for him an appointment in the college of engineers at Mézières. Being of low birth, he could not receive a commission in the army, but he was permitted to enter the annex of the school, where surveying and drawing were taught. Observing that all the operations connected with the construction of plans of fortification were conducted by long arithmetical processes, he substituted a geometrical method, which the commandant at first refused even to look at, so short was the time in which it could be practised; when once examined, it was received with avidity. Monge developed these methods further and thus created his descriptive geometry. Owing to the rivalry between the French military schools of that time, he was not permitted to divulge his new methods to any one outside of this institution. In 1768 he was made professor of mathematics at Mézières. In 1780, when conversing with two of his pupils, S. F. Lacroix and Gayvernon in Paris, he was obliged
to say, "All that I have here done by calculation, I could have
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 short-hand 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