# Mathematical Treasure: Bachet's Arithmetic of Diophantus

Author(s):
Frank J. Swetz (The Pennsylvania State University)

This is the title page of a 1670 edition of The Arithmetic of Diophantus of Alexandria in Six Books. Diophantus is thought to have lived in the third century CE. One of the very earliest translations from Greek into Latin of his Arithmetic was by Claude-Gaspard Bachet (1581-1638), who first published it in 1621. The 1670 edition was published by Samuel Fermat, son of Pierre de Fermat (1601-1665). This edition also considers figurate numbers and contains observations of the elder Fermat on “new discoveries,” including his famous “Last Theorem.”

These pages describe some of Fermat’s observations and discoveries.

Editor's note: Fermat's own statement of his famous Last Theorem appears on page 61 as an observation on Question VIII of Book II. The observation, originally made by Fermat as a marginal note in a 1637 edition of Bachet’s book, translates (from Latin) as:

A cube into two cubes, a fourth power into two fourth powers, and in general to infinity, none other than square powers can be divided into two squares (literally, “two of its own name”), a fact of which I have discovered a truly remarkable proof. This margin is too small to contain it.

Want to see it? As of 1 June 2015, an image of this page was included in the Wikipedia article on Fermat’s Last Theorem.

The images above are supplied through the courtesy of the Rare Books and Manuscripts Collection of the Pennsylvania State University Library and the assistance of Dr. Sandra Stelts, Curator of the Collection. The online MacTutor History of Mathematics Archive has been helpful in describing them.

See "Mathematical Treasure: Arithmetic of Diophantus" for images from another copy of this book.

Index to Convergence's Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Bachet's Arithmetic of Diophantus," Convergence (June 2015)