MONGE. 
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consequent representation of points, lines, and figures in space by means of their plan 
and elevation, placed in a determinate relative position. 
In 1768 Monge became professor of mathematics, and in 1771 professor of physics, 
at Mézières; in 1778 he married Madame Horbon, a young widow whom he had 
previously defended in a very spirited manner from an unfounded charge; in 1780 he 
was appointed to a chair of hydraulics at the Lyceum in Paris (held by him together 
with his appointments at Mézières), and was received as a member of the Academy ; 
his intimate friendship with Berthollet began at this time. In 1783, quitting Mézières, 
he was, on the death of Bezout, 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 Madame Bezout of her only 
income, arising from the sale of the works of her late husband ; he wrote, however 
(1786), his Traité élémentaire de la Statique. 
Monge contributed (1770—1790) to the Memoirs of the Academy of Turin, the 
Mémoires des Savants 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 VAcad, de Paris, 1781), which, while giving a remarkably elegant investi 
gation in regard to the problem of earthwork referred to in the title, establishes in 
connexion with it his capital discovery of the curves of curvature of a surface. 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 in this matter had been anticipated by Watts and Cavendish. 
In 1792, on the creation by the Legislative Assembly of an executive council, 
Monge accepted the office of minister of the marine, but retained it only until April 
1793. When the Committee of Public Safety made an appeal to the savants to assist 
in producing the matériel 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 Vart 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 Polytechnic School, and was at each of them professor of 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 1798—99. In 1796 Monge was sent into Italy with Berthollet and some 
artists to receive the pictures and statues levied from several Italian towns, and made 
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