HOSPITAL, William-Francis-Antony, Marquis of, a great mathematician of France, was born of an ancient family in 1661. He was a geometrician almost from his infancy; for one day being at the duke of Rohan's, where some able mathematicians were speaking of a problem of Paschal's which appeared to them extremely difficult, he ventured to say, that he believed he could solve it. They were amazed at such presumption in a boy of 15, for he was then no more; nevertheless, in a few days he sent them the solution. He entered early into the army, and was a captain of horse; but being extremely short-sighted, and exposed on that account to perpetual inconveniences and errors, he at length quitted the army, and applied himself entirely to his favourite amusement. He contracted a friendship for Malebranche, and took his opinion upon all occasions. In 1693, he was received an honorary member of the academy of sciences at Paris; and he published a work upon Sir Isaac Newton's calculations, entitled, L'Analyse des infiniment petits. He was the first in France who wrote upon this subject; and on this account was regarded almost as a prodigy. He engaged afterwards in another work of the mathematical kind, in which he included Les Sections Coniques, les Lieux Geometriques, la Construction des Equations, et Une Theorie des Courbes Mechaniques: but a little before he had finished it, he was seized with a fever, of which he died Feb. 2. 1704, aged 43. It was published after his death.