An Introduction To Projective Geometry And Its Applications An Analytic And Synthetic Treatment By Arnold Emch PDF Download

Excerpt from An Introduction to Projective Geometry and Its Applications: An Analytic and Synthetic Treatment Treatises on Projective Geometry are usually written with the object of presenting this science in a purely systematic form; hardly any attention is paid to the applications. As a rule the methods of "arithmetized" mathematics have to be transformed, made more concrete, before they lend themselves to the solution of practical problems; and this, in the judgment of many, disfigures the purely scientific method. In this respect, projective geometry, geometry of position, is no exception. The puristic tendencies of von Staudt, Reye, and others culminate in the modern Italian school of geometer-logicians, headed by Veronese and Enriques. The latter's projective geometry contains an admirable logical presentation of the subject. With Enriques projective geometry is a "visual" science, and everything is foreign to it which cannot be based upon the axioms of vision. It seems doubtful whether the axioms of vision alone can establish a sound projective geometry. Enriques himself, in his book, lets the fundamental elements of the first order be generated by motion! In this visual geometry metrical properties, which are indispensable in the applications, appear as special cases and are of secondary importance. Conics result from the theory of polarity. 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.