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Mathematical Treasure: Emerson's Cyclomathesis

Frank J. Swetz (Pennsylvania State University)

William Emerson (1701-1782) was an English mathematician. While Emerson may have failed as a teacher of mathematics, he was a prolific and knowledgeable author of mathematics texts. He wrote several books on the method of fluxions that were well received. In 1770, he completed the ambitious project of compiling Cyclomathesis, a ten-volume series of texts that would supply a complete course of mathematical studies for a young person. The texts highlighted here were the property of John Adams, the third president of the United States. They were passed on to his son Charles and Charles’ signature marks some of the books. The title page for Volume I of this series:

A listing of the books in the series and their specific disciplines is given for reference:

In the following “Introduction,” Emerson provided formal definitions for the technical terms that would be used throughout.

Besides prefacing the Cyclomathesis series, the first volume is devoted to the study of Arithmetic.

The fifth volume in the series, The Arithmetic of Infinites (1767), concerned infinite series.

The Doctrine of Combinations, Permutations, … (1770) is the tenth volume in the series:

The material in this text is an overflow from the book on algebra. Note the signature at the top of the page:

The “Table of Contents” for this last volume reveals a rather “mixed bag” of topics.

Emerson had published a Doctrine of Fluxions (differential calculus) in 1748, which is also featured in Convergence's Mathematical Treasures.

The images above are presented courtesy of the John Adams Library at the Boston Public Library, and are available via Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Emerson's Cyclomathesis," Convergence (July 2018)