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Mathematical Treasure: The Arithmeticae practicae of Gemma Frisius

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

Gemma Frisius (1508–1555) was a Dutch mathematician and medical doctor who served as Professor of Medicine and Mathematics at the University of Louvain. In 1540, he published his arithmetic textbook, Arithmeticae practicae. The title page of a 1556 edition is shown below.

Title page of Arithmeticae practicae by Gemma Frisius, 1556

On page 18 of this work, Frisius gave a table of the basic multiplication facts up to 9 x 9. Note that the table was constructed to emphasize the commutative property of multiplication, and that the main diagonal is labeled as square numbers, or “Quadrati numeri”:

Page 18 of Arithmeticae practicae by Gemma Frisius, 1556

The squares and cubes of the numbers 1-9 are shown on page 89:

Page 89 of Arithmeticae practicae by Gemma Frisius, 1556

Here on page 104 of his Arithmeticae practicae, Frisius discussed “Regula Falsi,” or the Rule of False Position:

Page 104 of Arithmeticae practicae by Gemma Frisius, 1556

The images above are supplied through the courtesy of the United States Library of Congress and may be viewed at its website.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: The Arithmeticae practicae of Gemma Frisius," Convergence (January 2020)

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