MONGE, GASPAR, the inventor of descriptive geometry, was born at Beaune in 1746. He received his education at the college of the Oratory in his native town, and at a superior school in Lyons. His talent for mathematics gained for him a place as modeller at the age of nineteen in the school founded at Mézières for the instruction of engineers. From this obscure position, however, he soon raised himself by the discovery of a new and easy method of making the calculations of an operation of deployment or defiling, which had been prescribed him as a task. Bossut, who professed mathematics at Mézières, now appointed Monge his assistant; and he was attached, in the same capacity, to Abbé Nollet, professor of natural philosophy, whom he soon afterwards succeeded in that chair. In this situation he made a number of curious experiments on gas, molecular attraction, and the effects of optics and electricity, as well as refined deductions on meteorology, and on the important discovery of the production of water by the combustion of inflammable air; in which, however, he had been anticipated by Cavendish without being aware of it. About the same time Monge extended and generalized his first mathematical essays, and setting out from the principle which refers to the three rectangular co-ordinates the position of any point whatever taken in space, he made it the foundation of a new and fruitful doctrine, indispensable for all the arts of construction, and to which, when completed by successive developments, he applied the name of Descriptive Geometry. More than twenty years elapsed, however, before he succeeded in obtaining the application of his geometry to the tracings of carpentry.
from such a system, it is at all times productive of the greatest inconvenience and trouble. Where there are so many separate and independent banks (about 1400), the sphere of the influence and circulation of each is necessarily circumscribed; and when notes get to any considerable distance from the place where they are issued, especially when they get into a different State, they circulate with difficulty, and generally at a discount. But this is not the only evil by which their circulation is attended. Banks are every now and then suspending payments, or getting into discredit. And lists are regularly published of such defaulting or suspected banks, and of the rates of discount at which their notes are current, without which no traveller can leave his house, and no shopkeeper can venture to transact any business. It is truly astonishing, seeing the extreme inconvenience resulting from such a state of things, that it should be tolerated even for a week. If the general government be not sufficiently strong to suppress local issues, and to substitute in their stead a national paper issued on deposits of bullion, the public may, if they choose, rid themselves of the evil, by refusing to accept payment otherwise than in coin. The banking interest is, however, so very powerful, and embraces so great a number of individuals, that we doubt whether, even with the co-operation of the general government, the time has yet arrived for anything effectual being done for the amendment of the system. But the longer it exists, the more intolerable will it become; and in the end, no doubt, it will be suppressed. It forms, at present, the most gigantic abuse by which an intelligent people ever permitted themselves to be disgraced and oppressed. (J. R. M.)
Through the interest of D'Alembert, Monge was received into the Academy of Sciences in 1780, and was soon after made professor of physics in the Lyceum of Paris.
Like many others, he was at first led away by the promises and hopes of the Revolution; but the terrible events that followed in such rapid succession in some measure dissipated this illusion, which he shared in common with so many others. He was made a member of the Executive Council, but resigned this irksome post in 1793. When the Committee of Public Safety made an appeal to the savans to assist in producing the matériel requisite for the defence of the republic, Monge applied himself wholly to these operations, and distinguished himself by his indefatigable activity. It was at this time he composed his Art de fabriquer les Canons, and his Avis aux Ouvriers en Fer, sur la Fabrication de l'Acier.
At length Monge published his Géométrie Descriptive, which he had so long kept secret, and which unquestionably forms his highest title to distinction. Of all the applications of which his geometry was susceptible, he has only treated of five,—viz., carpentry, stone-cutting, deployment, linear and aerial perspective, and the distribution of light and shadow. To him also France was in a great measure indebted for the establishment of the Polytechnic School. After visiting Italy on an artistic mission, Monge accompanied Napoleon to Egypt, where he was indefatigable in his scientific researches, and in his endeavours to provide for the wants of the army after the naval defeat of Aboukir.
On his return, Monge became president of the Egyptian Commission, and was again placed at the head of the Polytechnic School. On the formation of the Senate he was appointed a member of that body, with an ample provision and the title of Count of Pelusium; but on the fall of Napoleon he was deprived of all his honours. He died on the 28th of July 1818.
The separate publications of Monge are:—Traité Él-
mentaire de Statique, Paris, 1786, in 8vo; Description de l'Art de fabriquer les Canons, Paris, 1795, in 4to; Leçons de Géométrie Descriptive, Paris, 1813, in 8vo; Application de l'Analyse à la Géométrie des Surfaces du Premier et du Deuxième Degré, Paris, 1809, in 4to. Monge likewise inserted four memoirs on Pure Analysis in the Collection des Savants Étrangers de l'Académie des Sciences de Paris (tomes vii., ix., and x.). His name also figures amongst the contributors to the Dictionnaire de Physique of the Encyclopédie Méthodique; and the Annales de Chimie contain several memoirs written by him. (J. B.-E.)