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."Sinopsis" puede pertenecer a otra edición de este libro.
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.
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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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Librería: Forgotten Books, London, Reino Unido
Paperback. Condición: New. Print on Demand. This book is concerned with the study of projective geometry from first principles. It develops its subject without the use of the theory of distance, giving a particularly detailed examination of the behavior of complex geometrical elements in spaces of up to three dimensions. Unlike Euclidean geometry, projective geometry is concerned not just with the measurement of lengths and angles, but with the connections between the elements of a figure. The author mostly avoids the use of analytical formulations, opting for a direct and visual construction of every idea. This allows the author to present a great deal of material in a quick and coherent manner, including the famous Desargues' Theorem and an in-depth consideration of harmonic elements. This book will provide an accessible introduction to an important but often opaque branch of mathematics. Those who appreciate this book will include not only those interested in geometry but those who seek a good foundation in the subject for other technical and scientific disciplines. 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: 9781451000085_0
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Librería: PBShop.store US, Wood Dale, IL, Estados Unidos de America
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781451000085
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Librería: PBShop.store UK, Fairford, GLOS, Reino Unido
PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781451000085
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Librería: Revaluation Books, Exeter, Reino Unido
Paperback. Condición: Brand New. 368 pages. 9.00x6.00x0.83 inches. This item is printed on demand. Nº de ref. del artículo: zk1451000081
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