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Mathematical Treasure: l'Hospital's Differential Calculus

Frank J. Swetz (Pennsylvania State University)

Analyse des Infiniment Petits, published by the Marquis de l’Hospital in 1696, was the first calculus text for a popular audience. L’Hospital (1661-1704), a well-respected mathematician, compiled this book while under the tutelage of Johann Bernoulli, from whom he acquired knowledge of Leibniz’s approach to the calculus. The book adheres to Leibniz’s principles. It includes the technique for dealing with indeterminate expressions now known as l’Hospital’s Rule.


The frontispiece portrait of the Marquis de l’Hospital


The first page of the text


Discussion of l’Hospital’s rule begins on page 145.


Discussion of the Rule continues on pages 146-147.

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: l'Hospital's Differential Calculus," Loci (August 2013)