Gaspar, the inventor of descriptive geometry, and one of the founders of the Polytechnic School, was born at Beaune in 1746. His father was a dealer in small wares, who had much difficulty in supporting his family, consisting of three sons, all of whom were inclined to the sciences; but having the good sense to appreciate the importance of instruction, he employed every means in his power to procure this benefit to his children. The subject of this notice, being the eldest, received the rudiments of his education at the college of the Oratory in his native town, where he was initiated in the elements of mathematics, and whence, having completed the usual course, he was removed to a superior school at Lyons, where his precocious talents quickly developed themselves. At the age of sixteen, he was judged qualified to assist his new masters in teaching physics; and before he had completed his nineteenth year, he had been admitted into the school which had been founded at Mézières for the instruction of engineers. But this establishment was only opened to privileged scholars, twenty in number, of whom one half left, and as many joined it, every year. In order to participate in its advantages, it was essential to possess an elevated station in society; and the humble fortune of Monge was therefore a title of exclusion. He was placed as a pupil and modeller in the class, with the superintendence and direction of works in fortification; and amidst these obscure labours, where dexterity was of more importance than intelligence, the qualities of his mind remained unobserved. He was considered merely as an expert modeller, and he longed to escape from a reputation which was equally unworthy of his genius and offensive to his self-love.

Meanwhile, the commandant of the school selected him to make the practical calculations of an operation of deployment, or defiling, which had been prescribed as a task. But Monge, dissatisfied with the tentative means by which the problem was usually resolved, and impressed with the importance of signalizing the commencement of his career, imagined a more expeditious and not less certain, though far more scientific method, for attaining the result desired, by the instrumentality of geometry. His solution was contested, upon the ground that he had not made allowance for the time required to exhaust the series of calculations; but its merit was nevertheless recognised, and the capacity of the pupil strongly exemplified. The latter was then nineteen. 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. Anticipated by Cavendish, without being aware of it, he examined this phenomenon with scrupulous attention, and assigned the share of caloric and light in its production. About the same time Monge extended and generalised his first mathematical essays, and setting out from the principle which refers to three rectangular coordinates 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. This collection of simple and uniform methods was, however, at variance with the incoherent practices which had been sanctioned by time; the attempt made by the inventor to introduce his innovations into the course of instruction in the school encountered strenuous opposition; and more than twenty years elapsed before he succeeded in obtaining the application of his geometry to the tracings of carpentry.

Monge generally passed his vacations at Paris, where he mingled in the society of men who then held the first rank in the sciences. Being already a correspondent of the Academy, to the honours of which he aspired, he found active patrons in Lavoisier, Condorcet, La Rocheleoucaud, and the President Bochart de Sarson; and, through the interest of D'Alembert, he was received into the Academy of Sciences in 1780. The same year he was associated with Bossut, who had been appointed to deliver the course of hydrodynamics established at the Louvre by Turgot. To perform these double functions, he was obliged to be alternately at Paris and at Mézières; but the situation of examiner of the pupils of the naval school, to which he was appointed after the death of Bezout in 1783, withdrew him from Mézières, where he had laid the foundation of his fame, and initiated in the sciences such men as Meusnier, Tinsseau, Carnot, Coulomb, and others scarcely inferior to them. For the benefit of the naval school he composed a treatise on statics, in which he proceeded synthetically, in order to get rid of equations, and rendered the principles more accessible by relaxing the rigour of demonstration. His next appointment was that of professor of physics in the Lyceum of Paris; an institution which had for its object to disguise instruction under agreeable forms, and present it in an attractive shape to a number of indolent amateurs. To interest such frivolous auditors he would have required the peculiar talents of Fontenelle; but if he failed to impart that fascination to science which formed the distinguishing attribute of the illustrious man just named, he knew how to render his lessons attractive by piquant views and ingenious illustrations, independently of the graces of language.

Like many others, he was at first led away by the promises and hopes of the revolution. Adopting those notions of political perfectibility, which then filled all heads, he conceived that the barriers which arrested generous emulation were for ever removed, and that talents would henceforth command that distinction which of right belonged to them; but the terrible events that followed in such rapid succession in some measure dissipate this illusion, which he shared in common with so many others. Called to the ministry of marine after the 10th of August 1792, he accepted the appointment, being determined, he said, by the presence of the Prussians on the French soil; he was thus a member of the government, which then formed the ministers into one body, under the denomination of the Executive Council; and it was in this capacity that he concurred with his colleagues in causing the judgment which condemned Louis XVI. to death to be carried into execution. But he soon discovered that, amidst the exasperation of faction, his place was not tenable, and ac- Monge accordingly, in the month of April 1793, he tendered his resignation, which was accepted. Some time afterwards, the committee of public safety made an appeal to the savans to assist in the defence of the French territory. Nine hundred thousand men were ready to march to the frontier to repulse the European crusade which menaced the republic; but the existing manufactories were insufficient to produce the tenth part of the matériel requisite for so mighty preparations. It was necessary to multiply manufactures, to describe and simplify their processes, to direct the operations of the workshops, to decompose innumerable metallic alloys for the wants of the artillery, to extract copper, to prepare steel, and to draw from the resources of the country alone a prodigious quantity of powder. The progress of the enemy required extraordinary celerity. Monge applied himself wholly to these operations, and distinguished himself by his indefatigable activity. He directed his attention to the manufacture of arms, the founderies, the boring of cannon, and the powder-mills, superintending and simplifying the various processes; he gave instructions for the preparation of saltpetre, and composed, at intervals, his Art de fabriquer les Canons, which was soon followed by his Aris aux Ouvriers en Fer, sur la Fabrication de l'Acier, containing an exposition of the means of obtaining steel by combining iron with a little charcoal.

Services so important having raised in public estimation men of science, against whom the axe of proscription was soon whetted, they obtained, after the fall of Robespierre, a tardy protection for public instruction. The Normal School was created, and a pure light diffused on the exposition of scientific truths. At length Monge published his Géométrie Descriptive, which he had so long kept secret, and which unquestionably forms his highest title of distinction. In explaining this collection of ingenious methods, where the modifications of extension are developed and combined by the aid of design, and where, from a sort of imitative language, are deduced, by an exact description, the truths which result from the forms of bodies and their respective positions, he dilated with pleasure on the advantages which might be derived from his work for rectifying the judgment and improving the dexterity of workmen, as well as for simplifying machines, and adding to the comforts of society. Of all the applications of which his geometry was susceptible, he has only treated of five, viz., carpentry, cutting stones, 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; for, although Berthollet and Guyton-Morveau were associated with him in this undertaking, it was he who arranged the system of studies ultimately adopted, and which remained unaffected by the rapid mobility of the revolutionary creations. This was not only a central school, where aspirants might imbibe the general principles that connect all the branches of the public service, and establish a fraternal communication and free transmission of ideas between different classes; it was also open to all those whose scientific conceptions were calculated to improve the useful arts, to economise labour, and to enlighten industry; and although the system of instruction was perhaps too extensive and profound, there can be no doubt that it proved of immense benefit to France. From these labours Monge was called to Italy, with the sculptor Moïse, the painter Barthélémy, and Berthollet, Thouin, and La-billardière, his colleagues in the Institute, to collect those masterpieces of art, the cession of which had been stipulated by the treaty of Tolentino. This mission lasted more than a year, and Monge, by his experience in mechanical processes, ably seconded the zeal of his associates for the conservation and removal of the conquered monuments.

Having completed his labours in this department, he was charged, along with General Berthier, to lay before the Directory the treaty of Campo Formio; and, not long afterwards, he was sent to Rome, along with Daunou, there to organize a republic; an undertaking which had scarcely been completed when Bonaparte sailed for Egypt. Monge, having been ordered to join the expedition, embarked at Civita-Vecchia, along with Desaix, and, in June 1798, overtook the army at Malta. In Egypt his labours were incessant. He examined the pyramids; visited the obelisk and walls of Heliopolis; explored the antiquities scattered round Cairo and Alexandria; described the state of the Mekias, or wells constructed in the isle of Raou-dah by the Kalif Almamoun, to measure the rise of the Nile; superintended the geodesical and monumental description of Egypt; and was at length appointed president of the Institute formed at Cairo upon the model of that of France. In this last capacity his exertions were prodigious. When the naval defeat of Aboukir had cut off all communication with Europe, the savans assembled at Cairo had to provide for wants still more numerous than those of France in the year 1793; as, independently of military resources, they had in fact to create the utensils necessary for the usages of life and the operations of the arts. The members of the Institute, however, divided these labours amongst them, and the attempts of individuals were guided and facilitated by the inquiries and researches of commissions formed out of the same learned body. On this trying occasion Monge and Berthollet were equally distinguished; and when a revolt broke out at Cairo, they proved that their courage and presence of mind, in the midst of danger, were not surpassed by their zeal for the advancement of science. In a journey to Suez, undertaken by Napoleon, Monge recognised the traces of the canal which by the Nile established a communication between the Red Sea and the Mediterranean; he visited the ruins of Pelusium, and, at the opening of the valley through which it is believed that the Hebrews proceeded towards Mount Sinai, he observed the fountain of Moses. He also accompanied Bonaparte to Syria, and was seized with a dangerous illness at Acre, where, in his tent, he had the affliction to receive the last sighs of his pupil, General Caffarelli.

On his return to Europe with Bonaparte, Monge became president of the Egyptian Commission, and was again placed at the head of the Polytechnic School, where he resumed his place amongst the professors, and often defended, against the prejudices of Bonaparte, the generous youth, whom the despotic instinct of that military chief had led him to dislike. 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. The grief occasioned by the fall of Napoleon was augmented by the dissolution of the Polytechnic School, and the banishment of the surviving members of the Convention who had sent Louis XVI. to the scaffold; a measure which inferred the expatriation of M. Eschasseraux, one of his sons-in-law. The erasure of his name from the roll of the Institute, in consequence of the expurgations of 1816, gave the last blow to his sensibility. Repeated attacks of apoplexy had already shaken his naturally robust frame, whilst the obliteration of his ideas, and all the symptoms of a rapid decline, announced his approaching dissolution. He died on the 28th of July 1818, in the seventy-second year of his age.

The separate publications of Monge are, 1. Traité Élémentaire de Statique, Paris, 1786, in 8vo; 2. Description expatiée de l'Art de fabriquer les Canons, Paris, 1795, in 4to; 3. Leçons de Géométrie Descriptive, Paris, 1813, in 8vo; 4. Application de l'Analyse à la Géométrie des Surfaces du Premier et du Deuxième Degré, Paris, 1809, in 4to. In this last work he presents the equations of lines, planes,