Math 150A ProjectSpring 2013

L’Hospital’s Rule was first published in 1696 in the Marquis de l’Hospital’s calculus textbook Analyse des Infiniment Petits, but the rule was discovered in 1694 by the Swiss mathematician John (Johann) Bernoulli. The explanation is that these two mathematicians had entered into a curious business arrangement whereby the Marquis de l’Hospital bought the rights to Bernoulli’s mathematical discoveries. The details, including a translation of l’Hospital’s letter to Bernoulli proposing the arrangement, can be found in the book by Eves [1].

Write a report on the historical and mathematical origins of l’Hospital’s Rule. Start by providing brief biographical details of both men (the dictionary edited by Gillispie [2] is a good source) and outline the business deal between them. Then give l’Hospital’s statement of his rule, which is found in Struik’s sourcebook [4] and more briefly in the book of Katz [3]. Notice that l’Hospital and Bernoulli formulated the rule geometrically and gave the answer in terms of differentials. Compare their statement with the version of l’Hospital’s Rule given in Section 3.7 and show that the two statements are essentially the same.

1. Howard Eves, In Mathematical Circles (Volume 2: Quadrants III and IV) (Boston: Prindle, Weber and Schmidt, 1969), pp. 20–22.

2. C. C. Gillispie, ed., Dictionary of Scientific Biography (New York: Scribner’s, 1974). See the article on Johann Bernoulli by E. A. Fellmann and J. O. Fleckenstein in Volume II and the article on the Marquis de l’Hospital by Abraham Robinson in Volume VIII.

3. Victor Katz, A History of Mathematics: An Introduction (New York: HarperCollins, 1993), p. 484.

4. D. J. Struik, ed., A Sourcebook in Mathematics, 1200 –1800 (Princeton, NJ: Princeton University Press, 1969), pp. 315–316.

WRITING PROJECT THE ORIGINS OF L’HOPITAL’S RULE ■ 1

This project can be completed anytime after you have studied Section 3.7 in the textbook.

WRITING PROJECT: THE ORIGINS OF L’HOSPITAL’S RULE3.7

■ www.stewartcalculus.com The Internet is another source of information for this project. See the website and click on History of Mathematics.

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