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Mathematical Treasure: Euler's Elements of Algebra

Frank J. Swetz (Pennsylvania State University)

Leonhard Euler (1707-1783) was one of the most prolific and influential mathematicians of all time. Among his many works was Elements of Algebra, originally written in German around 1765 but not published until 1770, when a Russian language edition appeared soon followed by one in German. Elements of Algebra was translated into French by Johann Bernoulli and supplemented by a 120-page contribution by Joseph Lagrange. Francis Horner, the brother of William Horner of “Horner’s Method” fame, undertook the English translation of this work as a student project. Unfortunately, he died before completing the task and it was finished by John Hewlett in 1822. The edition shown above is from 1828. For over fifty years, Euler’s Elements of Algebra remained a popular book in British universities.

Partial view of “Table of Contents” of Euler’s 1828 Elements of Algebra

Page xxx of “Contents” listing Lagrange’s contributions

On page 312 of Elements of Algebra, the author considered Regula Caeci, literally “The Rule of the Middle,” but more commonly known as “The Rule of False Position.”

The Special Collections staff at the Linderman Library of Lehigh University in Bethlehem, Pennsylvania, is pleased to cooperate with the Mathematical Association of America to exhibit this and other items from the Library’s holdings in “Mathematical Treasures.” In particular, Convergence would like to thank Lois Fischer Black, Curator, Special Collections, and Ilhan Citak, Archives and Special Collections Librarian, for their kind assistance in helping to make this display possible. You may use these images in your classroom; all other uses require permission from the Special Collections staff, Linderman Library, Lehigh University.

Frank J. Swetz (Pennsylvania State University), "Mathematical Treasure: Euler's Elements of Algebra," Loci (August 2013)