Sinopsis
Excerpt from Projective Differential Geometry of Curves and Ruled Surfaces
The examples collected at the end of each chapter are of two kinds. Some of them are mere exercises. Some, however, (those marked with an asterisk), are of a very different nature. They are essentially suggestions for such further investigations, as appear to me to be of promise and importance. I have, also in the body of the book, taken the privilege of pointing out further problems which seem to be of interest. Many others will readily suggest themselves. It is my sincere wish that these suggestions may be helpful toward a further development of this fascinating subject.
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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.
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Reseña del editor
Excerpt from Projective Differential Geometry of Curves and Ruled Surfaces
The examples collected at the end of each chapter are of two kinds. Some of them are mere exercises. Some, however, (those marked with an asterisk), are of a very different nature. They are essentially suggestions for such further investigations, as appear to me to be of promise and importance. I have, also in the body of the book, taken the privilege of pointing out further problems which seem to be of interest. Many others will readily suggest themselves. It is my sincere wish that these suggestions may be helpful toward a further development of this fascinating subject.
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.
Reseña del editor
Excerpt from Projective Differential Geometry of Curves and Ruled Surfaces
In the geometrical investigations of the last century, one of the most fundamental distinctions has been that between metrical and projective geometry. It is a curious fact that this classification seems to have given rise to another distinction, which is not at all justified by the nature of things. There are certain properties of curves, surfaces, etc., which may be deduced for the most general configurations of their kind, depending only upon the knowledge that certain conditions of continuity are fulfilled in the vicinity of a certain point. These are the so-called infinitesimal properties and are naturally treated by the methods of the differential calculus. The curious fact to which we have referred is that, but for rare exceptions, these infinitesimal properties have been dealt with only from the metrical point of view. Projective geometry, which has made such progress in the course of the century, has apparently disdained to consider the infinitely small parts into which its configurations may be decomposed. It has gained the possibility of making assertions about its configurations as a whole, only by limiting its field to the consideration of algebraic cases, a restriction which is unnecessary in differential geometry.
Between the metrical differential geometry of Monge and Gauss, and the algebraic projective geometry of Poncelet and Plücker, there is left, therefore, the field of projective differential geometry whose nature partakes somewhat of both. The theorems of this kind of geometry are concerned with projeciive properties of the infinitesimal elements. As in the ordinary differential geometry, the process of integration may lead to statements concerning properties of the configuration as a whole. But, of course, such integration is possible only in special cases. Even with this limitation, however, which lies in the nature of things, the field of projective differential geometry is so rich that it seems well worth while to cultivate it with greater energy than has been done heretofore.
But few investigations belonging to this field exist. The most important contributions are those of Halphen, who has developed an admirable theory of plane and space curves from this point of view. The author has, in the last few years, built up a projective differential geometry of ruled surfaces. In this book we shall confine ourselves to the consideration of these simplest configurations. If time and strength permit, a general theory of surfaces will follow.
In presenting the theories of Halphen, I have nevertheless followed my own methods, both for the sake of uniformity and simplicity.
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.
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Projective Differential Geometry of Curves and Ruled Surfaces (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book investigates projective differential geometry, a discipline at the intersection of projective geometry and differential geometry. The author presents an explicit distinction between metrical and projective geometry, highlighting that projective differential geometry is concerned with projective properties of infinitesimal elements. The theorems in this field are related to projective properties of the configuration as a whole, and integration may lead to statements about the configuration's properties. The author's approach and results differ from those presented in other texts on the subject, particularly in the treatment of ruled surfaces. This book also includes numerous examples and suggested further investigations, making it a valuable resource for researchers and students alike. The author's work contributes to the development and understanding of projective differential geometry and its applications to ruled surfaces. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781330379356_0
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Projective Differential Geometry of Curves and Ruled Surfaces Classic Reprint
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