最 低 价：￥121.60
定 价：￥135.15
作 者：A. Seidenberg 著 著
出 版 社：Oversea Publishing House
出版时间：2006-1-1
I S B N：9780486446189
| CHAPTER 1 PROJECTIVE GEOMETRY AS AN EXTENSION OF HIGH SCHOOL GEOMETRY 1. Two approaches to projective geometry 2. An initial question 3. Projective invariants 4. Vanishing points 5. Vanishing lines 6. Some projective nouinvariants 7. Betweenness 8. Division of a segment in a ratio 9. Desargues' Theorem 10. Perspectivity; projectivity 11. Harmonic tetrads; fourth harmonic 12. Further theorems on harmonic tetrads 13. The cross-ratio 14. Fundamental Theorem of Projective Geometry 15. Further remarks on the cross-ratio 16. Construction of the projective plane 17. Previous results in the constructed plane 18. Analytic construction of the projective plane 19. Elements of linear equations CHAPTER 2 THE AXIOMATIC FOUNDATION 1. Unproved propositions and undefined terms 2. Requirements on the axioms and undefined terms 3. Undefined terms and axioms for a projective plane 4. Initial development of the system; the Principle of Duality 5. Consistency of the axioms 6. Other models 7. Independence of the axioms 8. Isomorphism 9. Further axioms 10. Consequences of Desargues' Theorem 11. Free planes CHAPTER 3 ESTABLISHING COORDINATES IN A PLANE 1. Definition of a field 2. Consistency of the field axioms 3. The analytic model 4. Geometric description of the operations plus and times 5. Setting up coordinates in the projective plane 6. The noncommutative case CHAPTER 4 RELATIONS BETWEEN THE BASIC THEOREMS CHAPTER 5 AXIOMATIC INTRODUCTION OF HIGHER-DIMENSIONAL SPACE 1. Higher-dimensional, especially 3-dimensional projective space 2. Desarguesian planes and higher-dimensional space CHAPTER 6 CONICS 1. Study of the conic on the basis of high school geometry 2. The conic, axiomatically treated 3. The polar 4. The polar, axiomatically treated 5. Polarities CHAPTER 7 HIGHER-DIMENSIONAL SPACES RESUMED 1. Theory of dependence 2. Application of the dependency theory to geometry 3. Hyperplanes 4. The dual space 5. The analytic case CHAPTER 8 COORDINATE SYSTEMS AND LINEAR TRANSFORMATIONS CHAPTER 9 COORDINATE SYSTEMS ABSTRACTLY CONSIDERED CHAPTER 10 CONIC SECTIONS ANALYTICALLY TREATED APPENDIX TO CHAPTER X CHAPTER 11 COORDINATES ON A CONIC CHAPTER 12 PAIRS OF CONICS CHAPTER 13 QUADRIC SURFACES CHAPTER 14 THE JORDAN CANONICAL FORM BIBLIOGRAPHICAL NOTE INDEX |
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