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Excerpt from The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Two Books and Portions of the Eleventh and Twelfth Books; With Notes and Exercises Polars, Orthogonal Circles, Pedal Triangles, The Pedal Line, The nine-point Circle, Co-axal Circles, Harmonic Ranges, Inversion, and the Properties of a Complete Quadrilateral. Out of the large number of Propositions on these subjects it is clear that only a selection could be made, but I have endeavoured within the range chosen to omit no important Proposition. Without unduly increasing the size of_ the book it was impossible to prove all such important Proposi tions in the text. It is hoped, however, that the hints attached to those given as Exercises will be sufficient or any fairly intelligent student. 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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