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Mathematical Treasure: Early French Commercial Arithmetic

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

One of the best early French commercial arithmetics was l’Arithmetique by Jean Trenchant. First published in 1557, it underwent many editions. Little is known of its author, but it can be surmised that he was a reckoning master of the time. This is the title page of the 1602 edition.

Title page of L'Arithmetique by Jean Trenchant, 1602

On page 36 of this volume is found a rather interesting and innovative table of multiplication facts for the numbers 0–9 and 12. In this listing, the squares of the various numbers are given in the second column of the configuration.

Mulitiplication table from L'Arithmetique by Jean Trenchant, 1602

Another unusual feature of l’Arithmetique is its consideration of calculation methods employing a counting table and jetons. At this period of European history, one might think that the use of a counting table was antiquated. Obviously not! On page 363, Trenchant introduced the section, “The Art and Method of Calculating with Jetons.”

Page 363 of L'Arithmetique by Jean Trenchant, 1602

In the following pages, Trenchant discussed the designation of values for jetons and their positioning. A monetary entry of 3647 liure, 18 souz, and 9 deniers is illustrated with jetons.

Page 364 of L'Arithmetique by Jean Trenchant, 1602

Page 366 of L'Arithmetique by Jean Trenchant, 1602

Page 368 of L'Arithmetique by Jean Trenchant, 1602

Page 369 of L'Arithmetique by Jean Trenchant, 1602

For images of and more information about counting boards, see the Convergence article, Counting Boards.

This material is obtained through the courtesy of the University of California Libraries. A complete copy of this work can be viewed in the Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Early French Commercial Arithmetic," Convergence (June 2018)

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