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A. SCHUYLER, LL. D.,

Professor of Mathematics and Philosophy in Kansas Wesleyan University;
Author of Principles of Logic, Empirical and Rational Psychology
and of a Series of Mathematical Works.

NEW-YORK CINCINNATI

AMERICAN BOOK COMPANY

CHICAGO

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PREFACE.

THE following treatise on Plane and Spherical Trigonometry and Mensuration first appeared in 1873 as an Introduction to the author's work on Surveying and Navigation.

The general favor with which the Trigonometry has been received renders it probable that its publication in a separate volume would greatly extend its usefulness.

The many studying Trigonometry, who do not care to learn Surveying, ought not to be compelled to purchase a more expensive book than is necessary.

In the application of Logarithms to the processes of Multiplication and Division, Involution and Evolution, the order of treatment is, first, the proposition and its demonstration; next, the rule, then the solution of examples, thus giving the application of the principle in immediate connection with its statement.

The trigonometrical functions are defined, not as ratios, but as linear functions of the angle, thus giving the student clear geometrical conceptions instead of abstract relations, and enabling him the more readily to grasp the laws of the algebraic signs of the functions. The advantages in analytic investigations resulting from defining these functions as ratios have been secured in the. principles relating to the Right Triangle, Art. 64.

Each of the circular functions has, in the first place, been considered by itself, and its value traced for all arcs, from 0° to 360°.

Trigonometry is naturally divided into Plane and Spherical. In Plane Trigonometry triangles are discussed in the order, Right Triangles and Oblique Triangles.

Then, under the general head, Relations of the Circular Func

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