Guillaume de l'Hôpital

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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 either both approach zero or both approach infinity.

l'Hôpital is commonly spelled as both "l'Hospital" and "l'Hôpital." The Marquis spelled his name with an 's'; however, the French language has since dropped the 's' (it was silent anyway) and added a circumflex to the preceding vowel.

l'Hôpital was born in Paris, France. He initially had planned a military career, but poor eyesight caused him to switch to mathematics. He solved the brachistochrone problem, independently of other contemporary mathematicians, such as Isaac Newton. He died in Paris.

He is also the author of the first known textbook 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. It is the method for solving such indeterminate forms through repeated differentiation that bears his name.

In 1694 he forged a deal with Johann Bernoulli. The deal was that l'Hôpital paid Bernoulli 300 Francs a year to tell him of his discoveries, which l'Hôpital described in his book. In 1704, after l'Hôpital's death, Bernoulli revealed the deal to the world, claiming that many of the results in l'Hôpital's book were due to him. In 1922 texts were found that give support for Bernoulli. The widespread story that l'Hôpital tried to get credit for inventing de l'Hôpital's rule is false: he published his book anonymously, acknowleged Bernoulli's help in the introduction, and never claimed to be responsible for the rule.

[edit] See also

l'Hôpital's rule

[edit] External links

• O'Connor, John J., and Edmund F. Robertson. "Guillaume de l'Hôpital". MacTutor History of Mathematics archive.
• C. Truesdell The New Bernoulli Edition Isis, Vol. 49, No. 1. (Mar., 1958), pp. 54-62, discusses the strange agreement between Bernoulli and de l'Hôpital on pages 59-62.
• This article incorporates text from the 1913 Catholic Encyclopedia article "Guillaume-François-Antoine de L'Hôpital" by William Fox, a publication now in the public domain.