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Excerpt from Lectures on the Geometry of Position, Vol. 1 In preparing this translation of Professor Reye's Geometric der Lage, my sole object has been to place within easy reach of the English-speaking student of pure geometry an elementary and systematic development of modern ideas and methods. The increasing interest in this study during recent years has seemed to demand a text-book at once scientific and sufficiently comprehensive to give the student a fair view of the field of modern pure geometry, and also sufficiently suggestive to incite him to investigation. The recognized merit of Professor Reye's work in all these regards is my only apology for offering this translation as an attempt to satisfy our present needs. It has been my aim to present in fair readable English the geometric ideas contained in the text, rather than to hold myself, at all points, to a literal translation; yet I trust that I have not altogether destroyed the charm of the original writing. Some changes have been made; the articles have been numbered, the examples set at the end of the lectures to which they are related and a few new ones added, explanatory notes have been inserted where they seemed necessary or helpful, and an index has been compiled. I have not deemed it advisable to omit from this edition any part of the original prefaces or introduction, even though, at this distance from their first publication, they might not be demanded in their entirety. For the most part I have endeavoured to hold rigorously to well-established terminology. A few instances of deviation from this principle, however, may be mentioned. 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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