Coxeter, H.S.M. Projective Geometry

# Projective Geometry

## Coxeter, H.S.M.

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From the Publisher:

In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.

From the Back Cover:

In Euclidean geometry, constructions are made with a ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity.

This classic book introduces the important concepts of the subject and provides the logical foundations, including the famous theorems of Desargues and Pappus and a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in this account is then utilized to deal with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The book concludes by demonstrating the connections among projective, Euclidean, and analytic geometry.

From the reviews of Projective Geometry:

...The book is written with all the grace and lucidity that characterize the author's other writings. ...

-T. G. Room, Mathematical Reviews

This is an elementary introduction to projective geometry based on the intuitive notions of perspectivity and projectivity and, formally, on axioms essentially the same as the classical ones of Vebber and Young...This book is an excellent introduction.

- T. G. Ostrom, Zentralblatt

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## 1.Projective Geometry

ISBN 10: 0387406239 ISBN 13: 9780387406237
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(Mannheim, Alemania)
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Descripción Estado de conservación: New. Publisher/Verlag: Springer, Berlin | 1 Introduction.- 1.1 What is projective geometry?.- 1.2 Historical remarks.- 1.3 Definitions.- 1.4 The simplest geometric objects.- 1.5 Projectivities.- 1.6 Perspectivities.- 2 Triangles and Quadrangles.- 2.1 Axioms.- 2.2 Simple consequences of the axioms.- 2.3 Perspective triangles.- 2.4 Quadrangular sets.- 2.5 Harmonic sets.- 3 The Principle of Duality.- 3.1 The axiomatic basis of the principle of duality.- 3.2 The Desargues configuration.- 3.3 The invariance of the harmonic relation.- 3.4 Trilinear polarity.- 3.5 Harmonic nets.- 4 The Fundamental Theorem and Pappus&apos;s Theorem.- 4.1 How three pairs determine a projectivity.- 4.2 Some special projectivities.- 4.3 The axis of a projectivity.- 4.4 Pappus and Desargues.- 5 One-dimensional Projectivities.- 5.1 Superposed ranges.- 5.2 Parabolic projectivities.- 5.3 Involutions.- 5.4 Hyperbolic involutions.- 6 Two-dimensional Projectivities.- 6.1 Projective collineations.- 6.2 Perspective collineations.- 6.3 Involutory collineations.- 6.4 Projective correlations.- 7 Polarities.- 7.1 Conjugate points and conjugate lines.- 7.2 The use of a self-polar triangle.- 7.3 Polar triangles.- 7.4 A construction for the polar of a point.- 7.5 The use of a self-polar pentagon.- 7.6 A self-conjugate quadrilateral.- 7.7 The product of two polarities.- 7.8 The self-polarity of the Desargues configuration.- 8 The Conic.- 8.1 How a hyperbolic polarity determines a conic.- 8.2 The polarity induced by a conic.- 8.3 Projectively related pencils.- 8.4 Conics touching two lines at given points.- 8.5 Steiner&apos;s definition for a conic.- 9 The Conic, Continued.- 9.1 The conic touching five given lines.- 9.2 The conic through five given points.- 9.3 Conics through four given points.- 9.4 Two self-polar triangles.- 9.5 Degenerate conies.- 10 A Finite Projective Plane.- 10.1 The idea of a finite geometry.- 10.2 A combinatorial scheme for PG(2, 5).- 10.3 Verifying the axioms.- 10.4 Involutions.- 10.5 Collineations and correlations.- 10.6 Conies.- 11 Parallelism.- 11.1 Is the circle a conic?.- 11.2 Affine space.- 11.3 How two coplanar lines determine a flat pencil and a bundle.- 11.4 How two planes determine an axial pencil.- 11.5 The language of pencils and bundles.- 11.6 The plane at infinity.- 11.7 Euclidean space.- 12 Coordinates.- 12.1 The idea of analytic geometry.- 12.2 Definitions.- 12.3 Verifying the axioms for the projective plane.- 12.4 Projective collineations.- 12.5 Polarities.- 12.6 Conics.- 12.7 The analytic geometry of PG(2, 5).- 12.8 Cartesian coordinates.- 12.9 Planes of characteristic two.- Answers to Exercises.- References. | Format: Paperback | Language/Sprache: english | 305 gr | 235x155x9 mm | 162 pp. Nº de ref. de la librería K9780387406237

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## 2.Projective Geometry (Paperback)

Editorial: Springer-Verlag New York Inc., United States (2003)
ISBN 10: 0387406239 ISBN 13: 9780387406237
Librería
The Book Depository
(London, Reino Unido)
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Descripción Springer-Verlag New York Inc., United States, 2003. Paperback. Estado de conservación: New. 2nd ed. 1974. 2nd printing 2003. 234 x 155 mm. Language: English . Brand New Book. In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt s approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry. Nº de ref. de la librería KNV9780387406237

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## 3.Projective Geometry (Paperback)

Editorial: Springer-Verlag New York Inc., United States (2003)
ISBN 10: 0387406239 ISBN 13: 9780387406237
Librería
The Book Depository US
(London, Reino Unido)
Valoración

Descripción Springer-Verlag New York Inc., United States, 2003. Paperback. Estado de conservación: New. 2nd ed. 1974. 2nd printing 2003. 234 x 155 mm. Language: English . Brand New Book. In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt s approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry. Nº de ref. de la librería KNV9780387406237

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## 4.Projective Geometry

Editorial: Springer-Verlag Gmbh Okt 2003 (2003)
ISBN 10: 0387406239 ISBN 13: 9780387406237
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Descripción Springer-Verlag Gmbh Okt 2003, 2003. Taschenbuch. Estado de conservación: Neu. 236x154x15 mm. Neuware - In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry. 162 pp. Englisch. Nº de ref. de la librería 9780387406237

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## 5.Projective Geometry 2nd Edition

ISBN 10: 0387406239 ISBN 13: 9780387406237
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Descripción Estado de conservación: New. This item is printed on demand. Nº de ref. de la librería 1997442-n

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## 6.Projective Geometry

Editorial: Springer (2003)
ISBN 10: 0387406239 ISBN 13: 9780387406237
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Book Deals
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Descripción Springer, 2003. Estado de conservación: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: 1. Introduction.- 2. Triangles and Quadrangles.- 3. The Principle of Duality.- 4. The Fundamental Theorem and Pappus's Theorem.- 5. One-dimensional Projectivities.- 6. Two-dimensional Projectivities.- 7. Polarities.- 8. The Conic.- 9. The Conic, Continued.- 10. A Finite Projective Plane.- 11. Parallelism.- 12. Coordinates. Nº de ref. de la librería ABE_book_new_0387406239

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## 7.Projective Geometry

Editorial: Springer (2003)
ISBN 10: 0387406239 ISBN 13: 9780387406237
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Descripción Springer, 2003. Paperback. Estado de conservación: New. 2nd. This item is printed on demand. Nº de ref. de la librería DADAX0387406239

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## 8.Projective Geometry

Editorial: Springer (2003)
ISBN 10: 0387406239 ISBN 13: 9780387406237
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Descripción Springer, 2003. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0387406239

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## 9.Projective Geometry

Editorial: Springer-Verlag New York Inc. (2003)
ISBN 10: 0387406239 ISBN 13: 9780387406237
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Descripción Springer-Verlag New York Inc., 2003. PAP. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería I2-9780387406237

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## 10.Projective Geometry

Editorial: Springer Verlag (2003)
ISBN 10: 0387406239 ISBN 13: 9780387406237
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Revaluation Books
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Descripción Springer Verlag, 2003. Paperback. Estado de conservación: Brand New. 2nd edition. 162 pages. 9.00x6.00x0.50 inches. In Stock. Nº de ref. de la librería __0387406239

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