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Mathematical Treasure: Letter from Leibniz to Huygens

Frank J. Swetz (The Pennsylvania State University)

Carl Immanuel Gerhardt (1816-1899), a German mathematician and historian of mathematics, served as editor of Leibniz’s unpublished papers. As editor of Leibniz’s writings, he is best known for Leibnizens mathematische Schriften (1859), and, as a historian, for his monumental 17-volume work, Geschichte der Wissenschaften Deutschland (1877). Gerhardt published a copy of Leibniz’s 1674 letter to Huygens in which he claimed to have found a method for the quadrature of the circle: De Quadratura Arithmetica Circuli, Ellipseos et Hyperbolae.

Title page of Leibniz's published manuscripts.

On page 25, Leibniz discussed his work using series to accomplish quadratures. In particular, he employed the series of reciprocals of the triangular numbers.

Page 25 of Leibniz's 1674 letter to Huygens.

The images above are presented courtesy of the University of Pennsylvania Libraries.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Letter from Leibniz to Huygens," Convergence (August 2016)