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.

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