HOSPITAL, William-Francis-Antony, Marquis of, an eminent French mathematician, 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 Pascal'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 fifteen, for he was then no more; nevertheless, in a few days he sent them the solution. He entered early into the army, and rose to be a captain of horse; but being extremely shortsighted, and exposed on that account to perpetual inconveniences and errors, he at length quitted the army, and applied himself entirely to his favourite pursuit. He contracted a friendship for Malebranche, whose opinion he followed upon all occasions. In 1693 he was received as 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 Infinimens 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 Géométriques, la Construction des Equations, et Une Théorie des Courbes Mécaniques; but a little before he had finished it, he was seized with a fever, of which he died on the 2d of February 1704, at the age of forty-three. It was published after his death.