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Gaspard Monge (May 10, 1746 July 28, 1818), was a French mathematician and inventor of descriptive geometry.
He was born at Beaune. He was educated first at the college of the Oratorians at Beaune, and then in their college at Lyon - where, at sixteen, the year after he had been learning physics, he was made a teacher of it. Returning to Beaune for a vacation, he made, on a large scale, a plan of the town, inventing the methods of observation and constructing the necessary instruments; the plan was presented to the town, and preserved in their library. An officer of engineers seeing it wrote to recommend Monge to the commandant of the military school at Mézières, and he was received as a draftsman and pupil in the practical school attached to that institution; the school itself was of too aristocratic a character to allow of his admission to it. His manual skill was duly appreciated: "I was a thousand times tempted," he said long afterwards, "to tear up my drawings in disgust at the esteem in which they were held, as if I had been good for nothing better."
An opportunity, however, presented itself: being required to work out from data supplied to him the défflement of a proposed fortress (an operation then only performed by a long arithmetical process), Monge, substituting for this a geometrical method, obtained the result so quickly that the commandant at first refused to receive it - the time necessary for the work had not been taken; but upon examination the value of the discovery was recognized, and the method was adopted. And Monge, continuing his researches, arrived at that general method of the application of geometry to the arts of construction which is now called descriptive geometry.
But such was the system in France before the Revolution that the officers instructed in the method were strictly forbidden to communicate it even to those engaged in other branches of the public service; and it was not until many years afterwards that an account of it was published.
In 1768 Monge became professor of mathematics, and in 1771 professor of physics, at Mézières; in 1778 he married Mme Horbon, a young widow whom he had previously defended in a very spirited manner from an unfounded charge; in 1780 he (held by him together with his appointments at Mézières), and was received as a member of the Académie; his intimate friendship with C.L. Berthollet began at this time. In 1783, quitting Mézières, he was, on the death of É. Bézout, appointed examiner of naval candidates. Although pressed by the minister to prepare for them a complete course of mathematics, he declined to do so, on the ground that it would deprive Mme Bézout of her only income, from the sale of the works of her late husband; he wrote, however (1786), his Traité élémentaire de la statique.
Monge contributed (17701790) to the Memoirs of the Academy of Turin, the Mémoires des savantes étrangers of the Academy of Paris, the Mémoires of the same Academy, and the Annales de chimie, various mathematical and physical papers. Among these may be noticed the memoir "Sur la théorie des déblais et des remblais" (Mém. de lacad. de Paris, 1781), which, while giving a remarkably elegant investigation in regard to the problem of earth-work referred to in the title, establishes in connection with it his capital discovery of the curves of curvature of a surface. Leonhard Euler, in his paper on curvature in the Berlin Memoirs for 1760, had considered, not the normals of the surface, but the normals of the plane sections through a particular normal, so that the question of the intersection of successive normals of the surface had never presented itself to him. Monge's memoir just referred to gives the ordinary differential equation of the curves of curvature, and establishes the general theory in a very satisfactory manner; but the application to the interesting particular case of the ellipsoid was first made by him in a later paper in 1795. A memoir in the volume for 1783 relates to the production of water by the combustion of hydrogen; but Monge's results had been anticipated by Henry Cavendish.
In 1792, on the creation by the Legislative Assembly of an executive council, Monge accepted the office of minister of the marine, and held this office from August 10, 1792 to April 10, 1793. When the Committee of Public Safety made an appeal to the savants to assist in producing the materiel required for the defence of the republic, he applied himself wholly to these operations, and distinguished himself by his indefatigable activity therein; he wrote at this time his Description de l'art de fabriquer les canons, and his Avis aux ouvriers en fer sur la fabrication de l'acier.
He took a very active part in the measures for the establishment of the normal school (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; his methods in that science were first published in the form in which the shorthand writers took down his lessons given at the normal school in 1795, and again in 17981799.
In 1796 Monge was sent into Italy with C.L. Berthollet and some artists to receive the pictures and statues levied from several Italian towns, and made there the acquaintance of General Bonaparte. Two years afterwards he was sent to Rome on a political mission, which terminated in the establishment, under A. Masséna, of the short-lived Roman Republic; and he thence joined the expedition to Egypt, taking part with his friend Berthollet as well in various operations of the war as in the scientific labours of the Egyptian Institute of Sciences and Arts; they accompanied Bonaparte to Syria, and returned with him in 1798 to France. Monge was appointed president of the Egyptian commission, and he resumed his connection with the École Polytechnique. His later mathematical papers are published (17941816) in the Journal and the Correspondence of the École Polytechnique. 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, and even excluded from the list of members of the reconstituted Institute.
Gaspard Monge died at Paris on July 28, 1818 and was interred in Le Père Lachaise Cemetery in Paris - see Gaspard Monge's mausoleum.
Monge was a man of considerable merit as a geometrician, and, while living, stood preeminent above his contemporaries in the French school of that day. He is the author of several works, but his most popular one is entitled "Gèomètrie Descriptive. par G. Monge, de l'Institut des Sciences, Lettres et Arts, de l'Ecole Polytechnique; Membre du Sénat Conservateur, Grand Officier de la Legion d'Honeur et Cointe de l'Empire."
The programme to this work is interesting, as it urges the necessity of making geometry a branch of the national education, and points out the beneficial results that would arise therefrom. The following is the translation:
- To draw the French nation from the dependence, which, even in the present day it is obliged to place in foreign industry, it is necessary first to direct the national education towards the knowledge of those objects which require a correctness which hitherto has been totally neglected; to accustom the hands of our artists to the management of the various instruments that are necessary to measure the different degrees of work, and to execute them with precision; then the finisher becomes sensible of the accuracy it will require in the different works, and he will be enabled to set the necessary value on it. For our artists to become, from their youth, familiar with geometry, and to be in a condition to attain it, it is necessary in the second place to render popular the knowledge of a great number of natural phenomena that are indispensable to the progress of industry; they will then profit for the advancement of the general instruction of the nation, which by a fortunate circumstance it has at its disposal, the principal resources that are necessary for it. Lastly, it is requisite to extend among our artists the knowledge of the advancement of the arts and that of machines, whose object is either to diminish manual labour or to give to the result of labour more uniformity and precision; and on those heads it must be confessed we have much to draw from foreign nations (Monsieur Monge has drawn much from Hamilton's work on Stereography but he has not mentioned his work.). All these views can only be accomplished by giving a new turn to national education.
- This is to be done, in the first place, by making all intelligent young men (who are born with a fortune) familiar with the use of descriptive geometry, so that they may be able to employ their capital more profitably both for themselves and the nation, and also for those who have no other fortune than their education, so that their labour will bring them the greater reward. This art has two principal objects, the first to represent with exactness, from drawings which have only two dimensions, objects which have three, and which are susceptible of a strict definition; under this point of view it is a language necessary to the man of genius when he conceives a project, and to those who are to have the direction of it; and lastly, to the artists who are themselves to execute the different parts.
- The second object of descriptive geometry, is to deduce from the exact description of bodies all that necessarily follows of their forms and their respective positions; in this sense it is a means of seeking truth, as it offers perpetual examples of the passage from what is known to what is unknown, and as it is always applied to objects susceptible of the minutest evidence, it is necessary that it should form part of the plan of a national education. It is not only fit to exercise the intellectual faculties of a great people, and to contribute thereby to the perfection of mankind, but it is also indispensable to all workmen, whose end is to give to certain bodies determined forms, and it is principally owing to the methods of this art having been too little extended, or in fact almost entirely neglected, that the progress of our industry has been so slow. We shall contribute then to give an advantageous direction to national education, by making our young artist familiar with the application of descriptive geometry, to the graphic constructions which are necessary in the greater number of the arts, and in making use of this geometry in the representation and determination of the elements of machinery, by means of which, man by the aid of the forces of nature, reserves for himself, in a manner, in his operations no other labour than that of his intellects. It is no less advantageous to extend the knowledge of those phenomena of nature which may be turned to the profit of the arts. The charm which accompanies them will overcome the repugnance that men have in general for manual operations, (which most regard as painful and laborious,) as it will make them find pleasure in the exercise of their intellect; thus there ought to be in the formal school a course of descriptive geometry.
- As yet we have no well compiled elementary work on that art, because till this time learned men have taken too little interest in it, or it has only been practised in an obscure manner by persons whose education had not been sufficiently extended, and were unable to communicate the result of their lucubrations. A course simply oral would be absolutely without effect. It is necessary then, for the course of descriptive geometry, that practice and execution be joined to the hearing of methods; thus pupils will be exercised in graphic construction of descriptive geometry. The graphic arts have general methods with which we can only become familiar by the use of the rule and compass. Among the different applications that may be made of descriptive geometry, there are two which are remarkable, both for their universality and their ingenuity; these are the constructions of perspective and the strict determination of the shadows. These two parts may finally be considered as the completion of the art of describing objects.
This article incorporates text from the public domain 1911 Encyclopædia Britannica.
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