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Excerpt from A Treatise on Plane Trigonometry In the present treatise, I have given an account, from the modern point of view, of the theory of the circular functions, and also of such applications of these functions as have been usually included in works on Plane Trigonometry. It is hoped that the work will assist in informing and training students of Mathematics who are intending to proceed considerably further in the study of Analysis, and that, in view of the fulness with which the more elementary parts of the subject have been treated, the book will also be found useful by those whose range of reading is to be more limited. The definitions given in Chapter III., of the circular functions, were employed by De Morgan in his suggestive work on Double Algebra and Trigonometry, and appear to me to be those from which the fundamental properties of the functions may be most easily deduced in such a way that the proofs may be quite general, in that they apply to angles of all magnitudes. It will be seen that this method of treatment exhibits the formulae for the sine and cosine of the sum of two angles, in the simplest light, merely as the expression of the fact that the projection of the hypothenuse of a right-angled triangle on any straight line in its plane, is equal to the sum of the projections of the sides on the same line. The theorems given in Chapter VII. have usually been deferred until a later stage, but as they are merely algebraical consequences of the addition theorems, there seemed to be no reason why they should be postponed. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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