Mathematical Treasure: Bourdon’s Elements of Algebra

Louis Pierre Marie Bourdon (1779–1854) was a French mathematician who began his career as one of the first graduates from the École Polytechnique in Paris. He held several positions at his alma mater and served as well at other French military academies and the Académie des Sciences. He wrote at least four textbooks, but he is probably best known for his 1817 Élémens d'algèbre. The title page of the 1820 second edition is shown below.

The beginning of Bourdon’s introduction to the subject.

Augustus De Morgan (1806–1871) translated the first three chapters in 1828:

Three years later, George Barrell Emerson (1797–1881) translated half of Bourdon’s text, in part using De Morgan’s translation. After Nathaniel Bowditch (1773–1838) made corrections, it was published as part of the series of mathematics textbooks associated with John Farrar (1779–1853) of Harvard College.

Also in 1831, Lt. Edward C. Ross (1801–1851) completed a translation of Bourdon’s algebra textbook at the United States Military Academy at West Point. In 1835, his colleague Charles Davies (1798–1876), the head of the Mathematics Department, began publishing that translation under his own name and as part of his series of mathematics textbooks.

This version appeared in 41 printings by the end of the 19th century. A later printing may be seen here in Convergence. As algebra transitioned from a college to a high school subject, and as teaching practices changed, publishers started to issue teachers’ manuals, or “keys”. In 1856 Davies created such a volume for Bourdon’s algebra. Pages from an 1866 printing are shown, although a copy of the first edition owned by Harvard has also been digitized.

The images above are courtesy of the GoogleBooks digitizations of copies owned by the University of Lausanne, the British Library, and Harvard University; and of the Internet Archive’s digitization of copies of Elements of Algebra and Key to Davies’ Bourdon owned by the University of California.

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