# Guillaume François Antoine, Marquis de l'Hôpital

**Guillaume François Antoine, Marquis de l'Hôpital** (1661 - February 2, 1704) was a French mathematician. He is perhaps best known for the rule which bears his name for calculating the limiting value of a fraction whose numerator and denominator approach zero.

He is also the author of the first known book on differential calculus, *L'Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes*. Published in 1696, the text includes the lectures of his teacher, Johann Bernoulli, in which Bernoulli discusses the indeterminate form 0/0.

His name is also spelled **l'Hospital**. The circumflex in "l'Hôpital" is an anachronism; it was not in use at the time l'Hôpital was alive.

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