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Excerpt from Elements of Plane and Spherical Trigonometry: With the First Principles of Analytic Geometry The first edition of this work was intended chiefly as a text-book for the use of the students in the belfast institution, when the Author was Professor of Mathematics in that establishment; and it was therefore written, not as a regular and complete treatise on Trigonometry, but as an outline to be filled up, and illustrated orally in the Lectures. It was received, however, by other readers in a more favourable manner than the Author could have anticipated from its nature and form; and, in consequence of this, he has been induced, in the subsequent editions, to make various alterations, and, it is hoped, im provements. The investigations, though still concise, are given at such length as to be easily understood by readers of ordinary talents and attainments; and various interesting additions are introduced, some from the best recent works on the subject, and others that have occurred to the Author himself. Of the latter kind are the improvements in the numerical resolution of tri angles, established in Nos. 57, 58, 73, and 74, and'exemplified in Nos. 62, 63, and 1 10; which, with the modes of operation previously known, seem to render the subject as simple and easy as can be desired. In the present edition, also, a scholium of considerable interest will be found at the end of the third section and the last four pages of the ninth section contain some curious propositions in Spherical Geometry, most of which the Author believes to be new. It has been everywhere the aim of the Author, to comprise in a small com pass much useful and interesting matter; and, whatever may be the imper fections of the work, he trusts that the person who shall make himself well acquainted with what it contains, will find it easy to acquire a knowledge of all that is yet known in Trigonometry, and to apply it in Astronomy, and other branches of science. 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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