BEZOUT, STEPHEN, a celebrated French ma thematician, was born at Nemours, in the department of the Seine and Marne, on the 19th of March 1730. His attention was accidentally directed to the study of mathematics, by some elementary works on geo metry which fell into his hands, and by the perusal of Vontenelle's Lives of the Academicians, from which he saw, that tranquillity and glory were the high re wards of a successful study of the sciences. The youthful ardour which was thus inspired was at first checked by the opposition of his father ; but every restraint was found to be unavailing, and Bezout was at length permitted to give his undivided attention to the study of geometry.
Before he had reached his 28th year, he presented to the Academy of Sciences two memoirs on the in tegral calculus, in consequence of which lie was ap pointed adjunct mechanic on the 8th of April 1758. In the first of these memoirs he determined the form of similar functions, in which the variable quantities are connected by an equation, and which, multiplied by constant factors, and added together, become al gebraically rectifiable ; and in the second memoir he gave the general equation of rectifiable curves. By • these memoirs the fame of Bezout was so much ex tended, that in the year 1763, the Duke de Choiseul appointed him examiner to the marine, and requested him to draw up a course of mathematics for the use of those destined for the navy. In 1768, he was chosen associate to the Academy of Sciences, and member of the Marine Academy ; and upon the death of Camus, he succeeded him as examiner to the royal corps of artillery. In 1779, he published his General Theory of Equations ; a work on which he had laboured with unremitting assiduity since the year 1762. During these researches, Bezout ob tained a solution of a particular class of equations of all degrees. This method, which was entirely new, was general for equations of the third and fourth or der, and became particular in equations of the fifth degree. By means of several new theorems on the calculus of finite differences, he discovered a general method for the extermination of unknown quantities, by which lie was enabled to avoid the tedious and complicated calculations which would otherwise have been necessary, and to determine beforehand the form and degree of the final equation. His Course of Ma thematics for the Marine was completed in 6 vols 8vo in 1761. ; and in 1770, he finished his Course for the Corps of Artillery, in 4 vols 8vo. These ele
mentary works have passed through several editions, and have been used in a great number of seminaries as peculiarly adapted for initiating the young in the elements of mathematics. The private studies of Bezout were greatly interrupted by the nature of his public duties. The examination of the marine and artillery schools, and the frequent journies which he was on this account compelled to take, occupied much of his time ; but harassing as these duties must have been to a man of genius, they were discharged by Bezout with the most unremitting assiduity, and with the utmost tenderness and affection for his pit pils. During an examination at Toulon, two of his pupils were prevented by the small-pox from attend ing it publicly. In' consequence of this misfortune, their progress would have been retarded a whole year, had not Bezout, at the risk of catching the infection, examined them in their own apartments. Though the attention of this able writer was chiefly directed to geometry, he found leisure to study mineralogy and several branches of physics. He was the first who gave any account of the crystallized stones of Fontainbleau, of which more full and recent accounts have been given by M. de Lasonne.
Bezout married when he was very young, and was the father of a family whom he rendered happy by his domestic virtues. Fond of retirement and stu dy, his manners were reserved and cold, and his con versation marked by no uncommon qualities ; but the warmth and sensibility of his heart were apparent to those who knew him well, and the natural sagacity and extensive knowledge which he possessed were displayed only to his particular friends. The regu lar and abstemious life which he led, held out to him the prospect of a long life ; but the fatigues of his public duties, the severity of his private studies, and the. bitterness of personal chagrins, triumphed • over the natural strength of his constitution. A ma lignant fever, to which he fell a victim on the 27th September 17S3, carried him off from the cares and labours by which it was engendered.
Besides the works of Bezout which we have al ready mentioned, he published several mathematical papers among the Memoirs of the Academy for 1758 and 1762. He also wrote a paper on the Integra tion of Differentials, in the Mr:noires des Syarans Etrangeres, vol. iii. ; and another containing Experi ments on Cold, in the Memoirs of the Academy for 1770. (a)