A Collection of Examples on the Analytical Geometry of Plane Conics, Vol. 1

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Excerpt from A Collection of Examples on the Analytical Geometry of Plane Conics, Vol. 1: To Which Are Added Some A part of this collection of examples has boon published by me before in a Collection of Examples and Problem on Conics and some of the Higher Plane Curves. In this volume I have added a good many more examples, besides giving solutions of the more difficult ones which were left unsolved. I believe that either the examples themselves, or the methods of their solution, are to a great extent original. A large number of the examples contain properties of circles connected with a conic, and especially of those which have double contact with the curve. In proving the properties of the latter systems of circles I have made frequent use of their differential equations in elliptic co-ordinates, the given curve being one of the system of confocal conics. In the same co-ordinates I have also made use of the differential equations of the tangents to a conic, and the systems of conics having double contact with two fixed confocal conics. The method of elliptic co-ordinates simplifies greatly the study of relations involving the angles of intersection of such systems, whoso differential equations take a simple form. 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.