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Excerpt from A Course of Plane Geometry for Advanced Students, Vol. 2 The author ))olds very strongly that the educational value of higher geometry lies in that novelty of idea and generality of con ception which is more characteristic of this subject than of any other branch of elementary mathematics. A course of geometrical conics, based on the focus-directrix definition and developed by Euclidean methods, provides excellent practice in rider-work but although the student may gain from it a systematic knowledge of the metrical properties of the conic, yet he will assimilate few, if any, really new ideas. On the other hand a projective treatment introduces the student to a region of geometrical thought, unlike anything he has seen in the past - a transition as abrupt and fertile as the crossing from algebra to the calculus. There are constant surprises, apparent contradictions, features of absorbing interest, and principles which, by the generality of their application and the variety of their expression, cannot fail to fascinate the reader and incite him to investigate their developments for himself. Experience proves incontestably that analytical methods frequently elucidate difficult geometrical conceptions. The theory of ideal elements in pure geometry, the notion of one-to - one correspondence and its application to homography and involution, the principles of conical projection are undoubtedly illuminated by a joint use of geometry and analysis. 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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