Projective geometry
著者
書誌事項
Projective geometry
Springer-Verlag, 1987
2nd ed
- : us
- : gw
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注記
Reprint, slightly revised, of 2nd ed. originally published by University of Toronto Press, 1974
Includes index
Bibliography: p. 157-158
First softcover printing, 2003
内容説明・目次
内容説明
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, repectively. 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 shows the connections among projective, Euclidean, and analytic geometry.
目次
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.
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