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Mathematical Treasure: Leslie's Geometry and Trigonometry

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

John Leslie (1766-1832) was a Scottish mathematician and physicist. He spent much of his career at the University of Edinburgh where he assumed the Chair of Mathematics previously occupied by John Playfair. Leslie wrote several textbooks, including Elements of Geometry, Geometrical Analysis, and Plane Trigonometry (1809). In his consideration and teaching of Euclidean geometry, he was a reformer moving away from the traditional approach to Euclid that had for so long been followed in England. The images viewed here are from the 1817 third edition of this work (note that “Geometrical Analysis” was removed from the title in the third and subsequent editions). The title page is signed by a previous owner of the book, Florian Cajori (1859-1930), whose last academic post was at the University of California, Berkeley, where he held a chair in the history of mathematics from 1918 onward.

Title page of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

In the "Preface," Leslie stated his objectives.

Page one of preface to Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

Page two of preface to Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

Page three of preface to Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

The introductory pages of the text initiate instruction by considering the overall definition of the subject of geometry.

Page one of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

Page two of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

Basic definitions and precepts are given:

Page five of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

Page 11 of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

A “Theorem-Proof” format is followed throughout the text.

Page 14 of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

Page 15 of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

 Trigonometry follows the discussion on geometry and stands as a separate book.

Page 225 of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

Page 226 of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

Page 227 of Elements of Geometry and Plane Trigonometry by John Leslie, third edition, 1817

The images above are supplied through the courtesy of the University of California Libraries. The work may be viewed in its entirety in the Internet Archive.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Leslie's Geometry and Trigonometry," Convergence (August 2018)

Dummy View - NOT TO BE DELETED