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Projective geometry

Author: H S M Coxeter
Publisher: [Toronto], [Buffalo] : University of Toronto Press, 1974.
Edition/Format:   Print book : English : 2d edView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Additional Physical Format: Online version:
Coxeter, H.S.M. (Harold Scott Macdonald), 1907-
Projective geometry.
[Toronto, Buffalo] University of Toronto Press [1974]
(OCoLC)625732002
Document Type: Book
All Authors / Contributors: H S M Coxeter
OCLC Number: 977732
Description: xii, 162 pages : illustrations ; 24 cm
Contents: Triangles and quadrangles --
The principle of duality --
The fundamental theorem and Pappu's theorem --
One-dimensional projectivities --
Two-dimensional projectivities --
Polarities --
The conic --
A finite projective plane --
Parallelism --
Coordinates.
Responsibility: H.S.M. Coxeter.

Abstract:

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.

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