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Mathematical Treasure: Legendre’s Integral Calculus

Author(s): 
Frank J. Swetz (The Pennsylvania State University)

Exercices de Calcul Intégral by Adrien-Marie Legendre (1752-1833) appeared in three volumes published a bit out of order in 1811 (Vol. I), 1817 (Vol. II), and 1816 (Vol. III). It is considered one of his most important works. The first volume introduces the concept of elliptic functions and integrals, and discusses beta and gamma functions. The other volumes in the series expand on elliptic integrals and their solutions. Below is the title page for the third volume published in 1816:

Title page for Exercises de Calcul Integral by Adrien-Marie Legendre, third volume, published in 1816

Within this third volume is a section on methods for the construction of elliptic functions.

Second title page which emphasizes tables of elliptical functions in Exercises de Calcul Integral by Adrien-Marie Legendre, third volume, published in 1816

These images were obtained through the courtesy of the University of California’s Digital Library. The book may be viewed in its entirety in the Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University) , "Mathematical Treasure: Legendre’s Integral Calculus," Convergence (March 2018)

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