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Guillaume-François-Antoine, Marquis de l'Hôpital, Marquis de Sainte-Mesme, Comte d'Entremont and Seigneur d'Ouques-la-Chaise was born in Paris in 1661, the exact date is unknown. His family was very prominant, dating back to the 12th century.
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His father was Anne-Alexandre de l'Hôpital, a Lieutenant-general in the King's Army; he was Comte de Sainte-Mesme and Duc d'Orleans. Guillaume's mother was Elisabeth Gobelin, the daughter of Claude Gobelin who was an Intendant in the King's Army and a Councillor of State. To put it simply: he had bank.
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His wife is said to have been associated with him in his work. L'Hôpital married Marie-Charlotte de Romilley de La Chesnelaye; they had one son and three daughters.
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As a child, l'Hôpital had no talent for subjects like Latin, but he developed strong mathematical abilities and a real passion for the subject.
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Bernard de Fontenelle recounts that when l'Hôpital was fifteen years old he was discussing mathematics with the Duke of Roannès and a Mr Arnaud. They told him about a very difficult problem on the cycloid that Blaise Pascal had proposed. A few days later l'Hôpital had solved the problem.
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He was a Captain in the King's cavalry, like most of the men in his family, so it was no surprise. But he still studied mathematics in his tent. Because of extreme near-sightedness, he had to resign from the military, and devote himself entirely to his math.
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Johann agreed to supplement his Paris talks on infinitesimal calculus with private lectures to l'Hôpital.
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On this day, l'Hôpital made the following proposal to Johann Bernoulli: in exchange for an annual payment of 300 Francs, Bernoulli would inform L'Hôpital of his latest mathematical discoveries, withholding them from correspondence with others, including Varignon. Bernoulli's immediate response has not been preserved, but he must have agreed soon, as the subsequent letters show.
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Answering l'Hôpital's question, in a letter of 22 July 1694 Johann Bernoulli described the rule of computing the limit of a fraction whose numerator and denominator tend to 0 by differentiating the numerator and denominator. A commonly made claim that l'Hôpital attempted to get credit for discovering the l'Hôpital's rule is inaccurate, since in the preface to his textbook, l'Hôpital generally acknowledged Leibniz, Jakob Bernoulli and Johann Bernoulli as the sources of the results in it.
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"I must own myself very much obliged to the labours of Messieurs Bernoulli, but particularly to those of the present Professor at Groningen. I have made free use of their discoveries, as well as those of Mr Leibniz, so that I frankly return to them whatever they please to claim as their own. "
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This book ontains an account of the differential calculus as conceived by Leibniz and learned from Bernoulli. In its preface l’Hôpital freely acknowledges his debt to the two mathematicians, saying, "I have made free use of their discoveries."
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He soon rivaled Newton, Huyghens, Leibniz, and the Bernoulli prothers in the propounding and solving of problems involving calculus.
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In Paris, France
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Ttraite anlytique des sectios coniques
Analytical treatise of conic sections
Published 1707 posthumous -
new editions made scene until 1781, exact date unknown
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