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Mathematical Treasure: Lacroix and Bézout on Trigonometry

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

Title page for Farrar's translation of Bézout's and Lacroix's trigonometry textbook.

Silvestre François Lacroix (1779-1843) and Étienne Bézout (1730-1783) were French mathematicians professors, and popular textbook writers. John Farrar, an American mathematics professor at Harvard University, translated many French mathematics books for the use of his students. An Elementary Treatise on Plane and Spherical Trigonometry was one such book. This is the cover of the third edition (1833), in which the contributions of both Lacroix and Bézout appear. Note the signature of Florian Cajori (1859-1930), noted historian of mathematics, on the cover, indicating that, at one time, this copy belonged to Cajori, who was Professor of the History of Mathematics at the University of California, Berkeley, from 1918 onward.

Advertisement for Farrar's translation of Bézout's and Lacroix's trigonometry textbook.Advertisement for Farrar's translation of Bézout's and Lacroix's trigonometry textbook.

The “Advertisement” at the beginning of this book is equivalent to a modern preface. Here Farrar explained his compilation of the text.

Table of contents for Farrar's translation of Bézout's and Lacroix's trigonometry textbook.

The Table of Contents provides the scope of the material considered.

Page 108 of Farrar's translation of Bézout's and Lacroix's trigonometry textbook.

On page 108, we find the derivation of the formula for the volume of a frustum of a pyramid. A technique employing proportions is used to arrive at the result.

 

This material is obtained through the courtesy of the University of California Libraries. A complete digital copy can be read on the Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Lacroix and Bézout on Trigonometry," Convergence (January 2017)

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