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Mathematical Treasure: Williams’s Translation of Dechales’s Paraphrase of Euclid’s Elements

Frank J. Swetz (The Pennsylvania State University)

Shortly before his death, the French Jesuit mathematician Claude Dechales (1621–1678) prepared a paraphrase of Euclid’s Elements. In 1685 Reeve Williams, an Englishman of whom nothing is known except that he termed himself a “philomath,” or lover of knowledge, translated this work into English. He made ambitious claims in the title: The elements of Euclid, explained and demonstrated in a new and most easie method: with the uses of each proposition in all the parts of the mathematicks by Claude Francois Milliet D'Chales, a Jesuite; done out of French, corrected and augmented, and illustrated with nine copper plates, and the effigies of Euclid. Note that the frontispiece of this book depicts a hardworking Euclid surrounded by the mathematical instruments of the 17th century.

Frontispiece and title page of Reeve Williams's 1685 English translation of Dechales's French Euclid.

Williams preserved the arithmetical, symbolic language of Dechales, which is generally said to have been unpopular with English audiences, although his book did go through at least five printings by 1748. For more information, see Diana M. Simpkins, “Early editions of Euclid in England,” Annals of Science 22 (1966): 225–249.

This image is from the copy owned by the Dibner Library of the Smithsonian Institution Libraries.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Williams’s Translation of Dechales’s Paraphrase of Euclid’s Elements," Convergence (March 2022)