HOPITAL. GUILLAUME FRANÇOIS ANTOINE, MARQUIS DE L', a celebrated French mathematician, was born at Paris in 1661. Entering the army, he served for some time in a cavalry regiment, but his bad eyesight, and a strong desire to pursue the study of mathematics, induced him to retire into private life. At a very early age he had given proof of a strong bent as well as of a large capacity for the pure sciences. One day at the table of the Duc de Rohan, a problem was mentioned, for which it was said that Pascal after long thinking had found an elegant solution. De l'Hôpital, then a lad of fifteen, astonished the savants who were admiring the neatness of Pascal's method by de-
Hôpital. claiming that he believed he could solve it otherwise, and in a few days he did send in a correct solution on a totally different principle. Towards the close of the seventeenth century the calculus was beginning slowly, and amid fierce opposition, to force its way into general acceptance among the mathematicians of Europe. One of its ablest advocates, John Bernoulli, coming to Paris, was engaged by De l'Hôpital to give him instructions in it, and spent some time in the marquis's house, teaching him the higher mathematics. So great was De l'Hôpital's progress, that when his tutor propounded to the mathematicians of Europe his famous problem of the curve of quickest descent he was the only Frenchman who sent in a solution. De l'Hôpital now became one of the warmest supporters of the calculus, and indeed wrote the first systematic treatise on it, which appeared at Paris in 1696, under the title of L'Analyse des Infinitement Petits. In the preparation of this work De l'Hôpital is said, though apparently on insufficient grounds, to have been unduly aided by his old tutor Bernoulli. This work, which may be fairly regarded as marking an era in the history of mathematical science, was frequently reprinted in the course of the eighteenth century. Not long after De l'Hôpital's death, which took place in 1704, a treatise on the conic sections, which he had left in MS., was published, and long maintained its ground as the standard work on this department of mathematics. See Playfair's DISSERTATION, prefixed to this work.