Reprint of the original, first published in 1877.

Excerpt from An Elementary Geometry: Plane, Solid, and Spherical; With Numerous Exercises Illustrative of the Principles of Each Book The favor with which the author's smaller work on Elemen tary Geometry has been received has induced him to under take the present more complete work, in the hope that it may prove equally useful to the higher classes Of learners for whom it is intended. While each Book has been made fuller, the same plan has, for the most part, been followed as in the former work: as in that, numerous practical questions illustrative of each Book, and theorems for original demonstration are introduced, serv ing as practical applications of the principles of the Book, and for discipline in discovering methods Of demonstration. In addition to the exercises at the end of each Book many more, arranged in proper order, have been added at the close Of the whole. These features are believed to be of special value in securing a real acquaintance with Geometry and its practical application. 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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Excerpt from A Treatise on Special or Elementary Geometry: Including Plane, Solid, and Spherical Geometry, and Plane and Spherical Trigonometry, With the Necessary Tables This treatise on the Special or Elementary Geometry consists of four parts. Part I. is designed as an introduction. In it the student is made familiar with the geometrical concepts, and with the fundamental definitions and facts of the science. The definitions here given, are given once for all It is thought that the pupil can obtain his first conception of a geometrical fact, as well, at least, from a correct, scientific statement of it, as from some crude, colloquial form, the language of which he will be obliged to replace by better, after the former shall have become so firmly fixed in his mind, as not to be easily eradicated. No attempt at demonstration is made in this part, although most of the fundamental facts of Elementary Plane Geometry are here presented, and amply and familiarly illustrated. This course has been taken in obedience to the canon of the teacher's art, which prescribes "facts before theories." Moreover, such has been the historic order of development of this, and most other sciences; viz., the facts have been known, or conjectured, long before men have been able to give any logical account of them. And does not this indicate what may be the natural order in which the individual mind will receive science ? When the student has become familiar with the things (concepts) about which his mind is to be occupied, and knows some of the more important of their properties and relations, he is better prepared to reason upon them. Part II. contains all the essential propositions in Plane, Solid, and Spherical Geometry, which are found in our common text-books, with their demonstrations. The subject of triedrals and the doctrine of the sphere are treated with more than the ordinary fullness. The earlier sections of this part are made short, each treating of a single subject, and the propositions are made to stand out prominently. At the close of each section are Exercises designed to illustrate and apply the principles contained in the section, rather than to extend the pupil's knowledge of geometrical facts. These features, together with the synopses at the close of the sections, practical teachers cannot fail to appreciate. 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.