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Mathematical Treasure: Tacquet’s Geometry and Arithmetic

Frank J. Swetz (The Pennsylvania State University)

Title page for English translation of Tacquet's geometry textbook.Frontispiece for English translation of Tacquet's geometry textbook.

Andrea Tacquet (1612–1660) was a Dutch mathematician trained in the Jesuit schools. He became a Jesuit himself and wrote many texts for use in Jesuit mathematics teaching. His most influential work, Elementa geometriae (1654), offered a simplified presentation of Euclid’s Elements and introduced works of Archimedes to produce a more general approach to the study of the subject. The book became very popular and was used for many years for geometry instruction. The title page and the frontispiece for a 1752 English edition of this work are shown above.

For images from another copy of this book, see Mathematical Treasure: Tacquet’s Euclid and Archimedes and Mathematical Treasure: Tacquet’s Geometry.

Title page of Tacquet's arithmetic.

Tacquet’s arithmetics were also very popular. These images are from a 1704 edition of his 1656 Practical and Theoretical Arithmetic.

Pythagorean table from Tacquet's arithmetic.

In Table I, page 153, a “Pythagorean Table” of multiplication facts is used to demonstrate the process of carrying out the operation of multiplication using a set of Napier’s rods. The illustration on the bottom left of the page above shows the rod arrangement to find the product: \(597\times 9.\) The answer, \(5373,\) is read across the bottom of the configuration.

For a demonstration of multiplication using Napier’s rods, see “John Napier: His Life, His Logs, and His Bones” in Convergence.

The images above are presented courtesy of the University of Pennsylvania Libraries.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Tacquet’s Geometry and Arithmetic," Convergence (July 2016)