CARNOT, LAZARE NICIIOLAS MARGUERITE, wee born of respectable ancestry at Nolay, in Burgundy, ou the 13th of May 1753. He entered the nrmy in the corps of engineer, in 1771, and at the time the revolution began was known as a respectable and well informed officer, who had gained the prize of the Academy of Dijon for an Mega of Vauban, and had refused large offers to cuter the service of Frederick of Prussia. In 1791 ho was elected to represent the Pas de Calais in the legislative assembly, and became a member of the military committee. He was one of those who voted the death of the ex-king. In 1793 lie became a member of the committee of public safety. His name does not directly appear as an advocate of, or an agent in, any of the excesses of the violent republicans ; but he stood high in place during those times of fury. So far as his acts are evi dence, his attention was entirely directed to the affairs of his profession ; he was in truth the war-minister of the committee. The most glorious period (in a military sense) of the republic) was that in which he directed the raisiug of all the tnnteriel of the army, and it was after wards said of him that he had "organise la vietoire." lu 1793 ho joined the army of the north with other deputies; the inefficiency of another general called him into action, and he was mainly instrumental in gaining the victory of Watignies. In 1795 lie was elected for four teen different places, but was shortly afterwards proscribed, and sought refuge io Germany. lie was recalled by the First Cousul, and was made minister of war. This post he lost when he voted against the consulate for life, and et the game time all the other military situa tions which he held. But after the Russian campaign, when Franco was on the eve of invasion, ho offered hie services to Napoleon, and received the command of Autwerp, which he held until the abdication of 1814. When Napoleon returned from Elba, he wished to return to Antwerp, but the emperor is said to have told him that a machine would answer the purpose there : ho was again appointed minister of war. After the restoration ho retired first to Warsaw, and thou to Magdeburg, where ho died on the 2nd of August, 1823. lie was twice n member of tho Institute, and twice expelled ; the first time by the Directory, and afterwards on the restoration of 1814.
He published in 1786 an Ego& cur les Machines en general,' and in 1808 his work ' De la Defense dea Places Fortes.' The latter is n remonstrance to the officers of the army upon the disposition which existed to consider a place untenable after the enemy had gained the glacis. Ile endeavours to show that the most serious part of an officer's duty only begins when the body of the place is attacked, and brings a large number of illustrations from ancient and modern warfare. He also explains the system of defence which goes by his name, namely, that of covering the guns from the enemy, and using them for vertical firing only, until the attack upon the body of the place begins.
The mathematical works of Carrot are remarkable for the elegance of his geometry and the clearness of his mode of expression. In his ‘R dflexiona sur la Metaphysique du Calcul Infinitesimal,' he enters upon the consideration of the system of Leibnitz; and the main point of his theory is, that there is a compensation between the infinitesimals of inferior orders which are rejected on both aides of an equation. In his Gdometrie de Position' (Paris, 1803), his object is to explain the meaning of the negative sign in geometry, but at the same time he gives a large number of new and very general theorems. Here he is the inventor of that class of general theorems which have since been pushed to a great extent by Messrs. Poncelet, Dandelin, Quetelet, Chasles, &c. There is also his memoir upon the relation of five points taken in apace, followed by his theory of transversals, Paris, 1806. The essay on machines in general was enlarged and republished in 1803, under the title Principea fondamentaux d'Equilibre et du Mouvement: He published also some political tracts, and in particu lar, a justification of his public conduct in 1815.
The fullest and best account of Carnet yet published is Arago's 'Notice Biographique,' read before the Acaddmie des Sciences, August 21, 1837, and published in the first volume of his cEuvres, pp. 511 633 ; hut it will be well to bear in mind that although M. Amgo says " it is a biography, not a panegyric," it is in fact an dloge, and as such it must be read.