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Mathematical Treasures - William Frend's Algebra and Arithmetic

Frank J. Swetz (The Pennsylvania State University)

William Frend (1757–1841) was a British clergyman, an active social reformer, and a sometime mathematician. Frend contributed to some of the algebra tracts published by Francis Maseres and shared his mathematical discomfort on the concept of negative numbers. In his The Principles of Algebra (1796), Frend denied the existence of these numbers. The controversy over this claim helped force a more formal, logical examination of the foundations of the real numbers. The established “Laws of Arithmetic” eventually welcomed the negative numbers into mathematics.

The “Table of Contents” for Frend’s Algebra.

In 1805, Frend published Tangible Arithmetic in which he introduced an “arithmetical toy” to assist in the learning of the subject.

These images from its George Arthur Plimpton Collection are presented through the courtesy of the Columbia University Libraries.

Index to Mathematical Treasures


Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasures - William Frend's Algebra and Arithmetic ," Convergence (January 2020)

Mathematical Treasures from the Smith and Plimpton Collections at Columbia University