On the Definitions of the Trigonometric Functions (Classic Reprint) - Hardcover

Alexander Macfarlane

9780266610601: On the Definitions of the Trigonometric Functions (Classic Reprint)

Hardcover

ISBN 10: 0266610609 ISBN 13: 9780266610601

Publisher: Forgotten Books, 2018

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A fresh look at how trigonometric functions are defined and related to space-analysis.

This edition presents Alexander Macfarlane’s exploration of a systematic notation for the partial products of vectors and how these ideas extend beyond circles to space, planes, and more general curves.

The work revisits historical definitions and builds a logical framework that connects traditional circular functions with broader analytical concepts. It argues that trigonometry is not merely an application of space-analysis but a fundamental element of it, capable of encompassing elliptic, hyperbolic, and other functions within a unified approach. The discussion includes the evolution of symbols, the treatment of area and line relationships, and the careful treatment of signs and definitions to support higher mathematics.

Historical origins of sine, cosine, tangent, and related lines in a geometric setup
Introduction of a consistent notation for products of two vectors and for area-based relationships
How space-analysis generalizes trigonometry beyond the circle to ellipses and other curves
Connections between geometric definitions and their analytical expressions

Ideal for readers who enjoy the history and foundations of trigonometry, and for those exploring advanced mathematical analysis.

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