Geometrical Conic Sections, An Elementary Treatise in Which the Conic Sections Are Defined as the Plane Sections of a Cone, and Treated by the Method of Projections (Classic Reprint)

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Excerpt from Geometrical Conic Sections, An Elementary Treatise in Which the Conic Sections Are Defined as the Plane Sections of a Cone, and Treated by the Method of Projections The following pages have been written with a view to give the student the benefit of the Method of Projections as applied to the Ellipse and Hyperbola. This Method is calculated to produce a material simplification in the treatment of those curves and to make the proof of their properties more easily understood in the first instance and more easily remembered. It is also a powerful instrument in the solution of a large class of problems relating to these curves. When the Method of Projections is admitted into the treatment of the Conic Sections there are many reasons why they should be defined, not as has been the case of late years with reference to the focus and directrix, but according to the original definition from which they have their name, as plane Sections of a Cone. First and principally, because this definition gives an immediate proof of the relation by projection of the Ellipse and Circle and of the General and Rectangular Hyperbolas: and in the second place, it naturally divides the properties that may be proved by projection from those connected with the focus and directrix, and thus introduces a valuable simplification into the treatment of the subject. 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.