Publisher's Synopsis
Excerpt from Curves With a Directrix
The definition of the first orthocentre, as extended for 292 - 1 lines, is the point of intersection of the 2n - 1 perpendiculars, let fall from the centres of the 2n - 1 one of which is uniquely determined by every 271 - 2 lines, upon the line left out in each case. By a* A28 is meant a deltoid of order 271 - 2 and class 2n - 3, having 2 n - 3 cusps, and containing the line at infinity as a special (2n - 4)-fold line, being tangent to it n - 2 times at I and 72 - 2 times at J. Thus, in the case of three lines, the three As each of which is determined by two lines of the three, are simply points, the vertices Of the triangle of the three lines, and the orthocentre is the intersection of the perpendiculars dropped from the vertices upon the Opposite sides. But in the case of five lines, every four lines uniquely determine a A, and the perpendiculars dropped from the centres of these five As's upon the line omitted in each case meet in a point, which is the orthocentre of the five given lines. 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.
