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Mathematical Treasure: Jacques Peletier’s l’Algebra

Frank J. Swetz (Pennsylvania State University)

Jaques Peletier of Mans (1517-1582) was a French poet and mathematician. His l’Algebra, published in 1554, became a standard text in France for the next thirty years.

On these pages, Peletier discussed how to obtain the solutions for problems involving square roots. First, he cited a problem given by Stifel that was insufficient for the purpose:

[Given two numbers such that their sum is 15; and the larger of the two divided by the smaller equals 19.] What are the numbers?

In the solution process for this problem, all expressions are linear and there is no need to extract a root. Peletier then gave his similar but more appropriate problem:

Given two numbers where the sum of their squares equals 340 and the product of the two numbers is equal to 6/7 of the square of the larger number. Find the numbers.

He then took the reader through a procedure to obtain the correct answers, 12 and 14.

On page 103, Peletier presented a second problem involving four men, who among them had an unknown amount of money. It was known that the amounts possessed by the first, second, and third men totaled 149; by the second, third, and fourth, 110; and by the third, fourth, and first, 125. In order to complete the problem, another set of conditions was given on the following page and the reader was asked to find the amount of money jointly possessed by these men. 

Page 130 of l’Algebra features a discussion of irrational numbers.

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: Jacques Peletier’s l’Algebra," Loci (September 2013)