Title page of Turner's trigonometry book 

Dedication page of Turner's trigonometry book.

     The third book of Richard Turner's compendium is titled "Plain Trigonometry."  Here Turner aims to explain the basics of solving triangles.  This book is addressed to "those Gentlemen, whose genius may incline, or employment lead them to the study of Mathematicks" [1].  In the dedication page that follows, Turner promotes the practicality and usefulness of trigonometry since it is relied on for navigating, surveying, map-making, and astronomy, among many other professions and sciences.  While trigonometry is a key skill for members of the army or navy, Turner's dedication page shows us that it is also becoming a widespread part of a gentleman's education in this period.

     Turner describes that one of the most common ways to go about solving triangles is by using sine and cosine functions.  At this time these would be calculated out in large and bulky tables that were expensive.  Instead, Turner's methods use "easy calculation in arithemtick only" [2].  This means that Turner's system of solving triangles only requires the use of multiplication and division, addition and subtraction, and the odd exponent and square root. "Plain Trigonometry," therefore, keeps calculations simple by avoiding unnecessary functions.  Turner's goal is to make Trigonometry more convenient for his contemporaries that use it on a daily basis, and those who are interested in learning it for its own sake [3].