Excerpt from A Treatise on Conic Sections and the Application of Algebra to Geometry Rectangular and oblique coordinates. Polar co-ordinates. 1. In order to determine the position of a point in a plane, some fixed point in the plane is taken for the origin of co-ordinates; and through it are drawn two fixed lines, called the co-ordinate axes, at right angles to one another. Then if the perpendicular distances of a point from each of the co-ordinate axes be given, its position will be completely determined. For let A (fig.l), be the origin of co-ordinates, X' AX, Y'AY, the co-ordinate axes, P any point, and PM, PN the perpendiculars let fall from it upon the co-ordinate axes; these perpendiculars are called the rectangular co-ordinates of P, and as their values change for the different points of the plane, they are denoted by the variables x and y. 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.