しい HARVARD COLLEGE LIBRARY GIFT OF GEORGE ARTHUR PLIMPTON JANUARY 5, 1924 Copyright, 1898, by HARPER & BROTHERS. All rights reserved. W. P. 4 PREFACE IN this work the trigonometric functions are defined as ratios, but their representation by lines is also introduced at the beginning, because certain parts of the subject can be treated more simply by the line method, or by a combination of the two methods, than by the ratio method alone. Attention is called to the following features of the book: The simplicity and directness of the treatment of both the Plane and Spherical Trigonometry. The emphasis given to the formulas essential to the solution of triangles. The large number of exercises. The graphical representation of the trigonometric, inverse trigonometric, and hyperbolic functions. The use of photo-engravings of models in the Spherical Trigonometry. The recognition of the rigorous ideas of modern mathematics in dealing with the fundamental series of trigonometry. The natural treatment of the complex number and the hyperbolic functions. The graphical solution of spherical triangles. Our grateful acknowledgments are due to our colleague, Professor James Pierpont, for valuable suggestions regarding the construction of Chapter VI. We are also indebted to Dr. George T. Sellew for making the collection of miscellaneous exercises. YALE UNIVERSITY, December, 1898. ANDREW W. PHILLIPS, WENDELL M. STRONG. Functions of an Acute Angle of a Right Triangle Functions of Complementary Angles |