Marquis de Sainte-Mesme and Comte d'Entremont, French mathematician; b. at Paris, 1661; d. at Paris, 2 February, 1704. Being the son of the lieutenant-general of the king's armies he was intended for a military career, and served for some time as captain in a cavalry regiment. He had no talent for Latin, but early displayed extraordinary ability for mathematics. At the age of fifteen he had solved a number of problems proposed by Pascal, and while an army officer, he studied mathematics in his tent. Owing to extreme near-sightedness he was forced to resign and then devoted himself entirely to his favourite studies. In 1692 he became acquainted with Jean Bernoulli, one of the three or four men of the day who understood the new methods of differential calculus. During four months he studied with Bernoulli, whom he had invited to his estate of Oucques near Vendôme, and learned from him this branch of the science of numbers. In 1693 he was elected honorary member of the Academy of Sciences of Paris and soon rivalled Newton, Huyghens, Leibniz, and the Bernoullis in the propounding and solving of problems involving the calculus. He is remembered because he made it possible for others to learn this new system. His work on the analysis of the infinitesimal for the study of curves was published in 1696 and was received with great satisfaction by many who were trying to solve the mystery surrounding these advanced problems, for the book contained a clear and careful exposition of the methods employed. The rule for the evaluation of a fraction whose numerator and denominator both have a limit value of zero is named after L'Hôpital. His wife is said to have been associated with him in his work. His published works are: "Analyse des infiniment petits pour l'intélligence des lignes courbes" (Paris, 1696; last ed. by Lefèvre, Paris, 1781); "Traité anlytique des sections coniques" (Paris, 1707; 2nd ed., 1720); several memoirs and notes inserted in the "Recueil de l'Académie des sciences" (Paris, 1699-1701), and in "Acta Eruditorum" (Leipzig, 1693-1699).
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