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Excerpt from An Elementary Treatise on Pure Geometry: With Numerous Examples In this treatise, the author has attempted to bring together all the well-known theorems and examples connected with Harmonics, Anharmonics, Involution, Projection (including Homology), and Reciprocation. In order to avoid the difficulty of framing a general geometrical theory of Imaginary Points and Lines, the Principle of Continuity is appealed to. The properties of Circular Points and Circular Lines are then discussed, and applied to the theory of the Foci of Conies. The examples at the ends of the articles are intended to be solved by the help of the article to which they are appended. Among these examples will be found many interesting theorems which were not considered important enough to be included in the text. At the end of the book there is, besides, a large number of Miscellaneous Examples. Of these, the first part is taken mainly from examination papers of the University of Oxford. Scattered throughout the book will be found examples taken from that admirable collection of problems called Mathematical Questions and Solutions from the 'Educational Times.' For permission to make use of these, I am indebted to the kindness of the able editor, Mr. W. J. C. Miller, B.A., Registrar of the General Medical Council. 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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