Author(s):

Frank J. Swetz (The Pennsylvania State University)

Elias Loomis (1811-1889) was an American mathematician. He taught at the University of the City of New York, later to become New York University, and at Yale. He was a prolific author of mathematics texts and his books went on to shape nineteenth century mathematics instruction in the United States. His very influential *Elements of Analytical Geometry and of the Differential* *and Integral Calculus* was first published in 1835 and went through several editions. It also was translated into Chinese and Japanese and used to introduce calculus into China and Japan. This is the title page of the tenth (third American) edition of 1858.

The first page of text on differential calculus follows.

On pages 114-115, Loomis supplied basic definitions recognizable to any student of calculus: implicit and explicit functions; increasing and decreasing functions; limits; etc.

The first page of discussion on integral calculus follows. Note the explanation of the use of Leibnizian notation.

*This material was obtained through the courtesy of the Peabody Library of Johns Hopkins University.*

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: The Calculus of Elias Loomis," *Convergence* (July 2016)