Projective Geometry (Classic Reprint) - Tapa blanda

Mathews, George Ballard Ballard

 
9781451000085: Projective Geometry (Classic Reprint)

Sinopsis

A rigorous, self-contained introduction to projective geometry that builds intuition without using distance.

It explores space, duality, and projections through clear explanations, abundant diagrams, and concrete examples.

This edition presents the core ideas of projective geometry, starting from intuitive notions of points, lines, and planes, and developing them with ten primitive propositions. It emphasizes the principle of duality and guides readers toward a solid understanding of space up to three dimensions. The book also introduces complex elements of space, discusses fundamental theorems, and connects theory with classical and modern perspectives. Throughout, exercises reinforce learning and illustrate how projective methods apply to a wide range of geometric problems.
What you’ll experience
  • A step-by-step path from basic definitions to advanced topics in projective geometry
  • Clear treatment of duality and its consequences in space and projections
  • Connections to historical and contemporary approaches, with practical examples
  • Exercises that build problem-solving skill and deepen understanding
Ideal for students and self-learners seeking a rigorous yet accessible entry to projective geometry, with a focus on structure and reasoning.
{ "genre": "nonfiction", "confidence": 0.78 }

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Reseña del editor

Excerpt from Projective Geometry

A Handbook/or 1h: teach, to accomfiuy the Excrdra. Exercises IN arithmetic and mensura tion. By P. Abbott, ba.. Head of the Mathe matical D'spanment. The Polytechnic, Regent Street, London, With Diagrams. Crown 8vo. Without Answers, 35. 6d.; With Answers. 45.

About the Publisher

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Reseña del editor

The two main objects of this work have been to develop the principles of projective geometry without making use of the theory of distance, and to give a satisfactory discussion of complex elements of space, up to three dimensions. No attempt has been made to start with the smallest sufficient number of indefinable terms and primitive propositions ;there are ten primitive propositions, involving quite a large number of indefmables (besides point, plane, line, the indefinable entities), and these propositions have been chosen because they seem to be obvious to the ordinary intuition, and fall into five correlative pairs. Thus the principle of duality appears at the outset, and is emphasized more and more as we proceed. The proof of the fundamental theorem (after that of Liiroth and Zeuthen) involves the notion of a converging sequence of points, as well as that of order: so it is by no means the most rigorous that could be given, but I believe it is as near to a rigorous proof as an ordinary student is likely to appreciate. The beginner is recommended to assume the theorem of A rt. 51, and treat the rest of Chap. VII. as something to ruminate upon. In dealing with complex elements I have constantly consulted v. Staudt and Liiroth {M ath. A nn. viii.
(Typographical errors above are due to OCR software and don't occur in the book.)

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Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text. Read books online for free at www.forgottenbooks.org

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