The Trigonometry of Angles: An Introduction

The theories of the Pythagoreans (the philosophical school of Pythagoras and his followers) in the late sixth century B.C. taught that, in its essence, everything is a number, and that all relationships can be expressed arithmetically. They believed that, using mathematical ideas, everything could be predicted and measured in rhythmic patterns or cycles. The reduction of angular measure to a triad of fractions using the sides of right triangles was just one of the achievements which underscored their philosophical beliefs. However, if Pythagoras could have envisioned the truly rhythmic and cyclical waves which the sine and cosine functions etch out on the Cartesian plane when the radian angular measure of Roger Cotes is used, he could not have failed to have been impressed by the profoundness of that prediction. Their discoveries about triangles and the ensuing implications of triangular measure have today become encapsulated into the study of Trigonometry.

However, despite the long history of the study of the triangular measure of angles, it is somewhat surprising that the term 'trigonometry' first appeared in the late sixteenth century as the title of a book Trigonometria. It was published in 1595 by a German/Polish mathematician, astronomer and theologian called  Bartholomaeus Pitiscus (1561-1613). 

Last Updated by SAS October 07, 2026, 16:01:00