On the in-and-Circumscribed Triangles of the Plane Rational Quartic Curve (Classic Reprint)

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Excerpt from On the in-and-Circumscribed Triangles of the Plane Rational Quartic Curve I. Quartic with three double points. II. Quartic with one double point and a tacnode. III. Quartic with a triple point. IV. Quartic with two double points and a cusp. This discussion was led up to by preliminary work on the three cusped rational quintic. Upon subjection to a quadratic trans formation this curve goes into a rational quartic, which, it will be shown, has triangles Of the kind here mentioned. Accordingly it will first be proved that the quintic can have certain conditions imposed upon its coefficients so that it may acquire an additional cusp or a tacnode without degenerating. It will also be shown that it cannot have a triple point. 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.