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Mathematical Treasure: Joseph Fenn’s Algebra

Frank J. Swetz (The Pennsylvania State University)

Joseph Fenn was an Irish mathematics master. His New and Complete System of Algebra or Specious Arithmetic (1767) can be considered one of the first “modern” algebra texts. The term “specious arithmetic” is defined as “the calculus of quantities as designated by letters of the alphabet.” This is the title page of the Algebra.

Title page for Joseph Fenn's 1767 algebra textbook.

On page 80 of his text, Fenn demonstrated how to find the square root of a given number. His method appears to be that of Horner, introduced in 1819. Paolo Ruffini introduced a similar method in 1809. That Fenn predated both of these developments seems to indicate that a knowledge and use of the method was prevalent by the end of the 18th century.

Page 80 of Joseph Fenn's 1767 algebra textbook.

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: Joseph Fenn’s Algebra," Convergence (July 2016)