Sinopsis
Explore the foundations of projective geometry and its unifying reach across mathematics. This volume presents the essential ideas that distinguish projective from metric geometry, while showing how analytic and synthetic methods interrelate. It lays a framework for understanding transformations, figures, and their relations in space.
The book emphasizes general concepts such as group actions, duality, and the role of coordinates, without relying on metric assumptions. It introduces homogeneous coordinates and the idea that many geometric theorems hold across different spaces, including finite and rational spaces. Pedagogically, the text aims to reveal the unity of mathematics through projective methods and their connections to later metric topics.
- Foundational concepts: points, lines, planes, and their interrelations.
- The emergence of projective transformations and duality as central tools.
- Introduction to homogeneous coordinates and their use in representing geometric objects.
- A pathway to later metric geometry and a broader view of geometric structure.
Ideal for readers seeking a rigorous, historically informed introduction to projective geometry and its place in the broader landscape of mathematics.
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Reseña del editor
Excerpt from Projective Geometry, Vol. 1
This interpretation is a concrete representation of our assumptions. Every proposition derived from the assumptions must be true of this system of triples. Hence none of the assumptions can be logically inconsistent with the rest; otherwise contradictory statements would be true of this system of triples.
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 Geometry
Geometry, which had been for centuries the most perfect example of a deductive science, during the creative period of the nineteenth century outgrew its old logical forms. The most recent period has however brought a clearer understanding of the logical foundations of mathematics and thus has made it possible for the exposition of geometry to resume the purely deductive form. But the treatment in the books which have hitherto appeared makes the work of laying the foundations seem so formidable as either to require for itself a separate treatise, or to be passed over without attention to more than the outlines. This is partly due to the fact that in giving the complete foundation for ordinary real or complex geometry, if is necessary to make a study of linear order and continuity, - a study which is not only extremely delicate, but whose methods are those of the theory of functions of a real variable rather than of elementary geometry.
The present work, which is to consist of two volumes and is intended to be available as a text in courses offered in American universities to upper-class and graduate students, seeks to avoid this difficulty by deferring the study of order and continuity to the second volume. The more elementary part of the subject rests on a very simple set of assumptions which characterize what may be called "general projective geometry." It will be found that the theorems selected on this basis of logical simplicity are also elementary in the sense of being easily comprehended and often used.
Even the limited space devoted in this volume to the foundations may seem a drawback from the pedagogical point of view of some mathematicians. To this we can only reply that, in our opinion, an adequate knowledge of geometry cannot be obtained without attention to the foundations. We believe, moreover, that the treatment is peculiarly desirable in projective geometry, it is through the latter that the other geometric disciplines are most readily coordinated.
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 Geometry, Vol. 1 (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book offers a fresh and rigorous look at the foundations of geometry, a subject that has captivated mathematicians for centuries. It delves into the historical development of geometry, noting how it evolved beyond traditional deductive methods in the 19th century. The author emphasizes the need to re-establish the logical framework of geometry, highlighting the complexities of linear order and continuity. The book adopts a novel approach, focusing on general projective geometry ââ â a highly abstract and powerful system ââ â in its first volume, delaying the more complex issues of order and continuity for a second volume. This allows readers to grasp the fundamental concepts and theorems of projective geometry without being bogged down by technicalities. By studying projective geometry, readers gain a deeper understanding of its relationship to other geometrical disciplines like Euclidean and non-Euclidean geometries. The author uses both synthetic and analytic methods to illuminate the unifying principles of geometry, revealing the powerful connections between different branches of mathematics. This book serves as a valuable resource for students and scholars seeking a thorough grounding in the principles and methods of projective geometry. 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: 9781330343876_0
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Projective Geometry, Vol. 1 (Classic Reprint)
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