The following pages embrace, in the main, the substance of lectures which for some years past I have been giving to students of applied science. Fragments of this work have also been given to students to whom a general knowledge of the principles of Analytical Geometry was part of a liberal education.<br><br>It is important that the beginner should not think the terms "Analytical Geometry" and "Conic Sections" are synonymous. Analytical Geometry is the application of Analysis, or algebra, to Geometry, the principal quantities involved in the equations having reference to and receiving their meaning from certain lines known as axes of co-ordinates, or their equivalents. The principles of Analytical Geometry are developed in the first two chapters of this book. It is usual to illustrate these principles by applying them to the straight line, and to obtaining the properties of the simplest yet most important curves with which we are acquainted, - the Conic Sections. Hence the remainder of the book is occupied in applying the principles and methods of Analytical Geometry to the straight line, circle, parabola, etc.<br><br>Throughout the effort has been to limit the size of the book, while omitting nothing that seemed essential. Many important properties of the Conics are given as exercises, the solutions being made simple by the results of previous exercises, as well as by hints and suggestions.