几何基础（英文版）

样章

作者：

David Hilbert, Authorized Translation by E. J. Townsend

定价：

69.00 元

版面字数：

150千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2025年

ISBN：

978-7-04-060492-4

物料号：

60492-00

出版时间：

2023-06-28

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

几何学

暂无

目录
- 前辅文
- INTRODUCTION
- CHAPTER I THE FIVE GROUPS OF AXIOMS
  - §1. The elements of geometry and the five groups of axioms
  - §2. Group I. Axioms of connection
  - §3. Group II. Axioms of order
  - §4. Consequences of the axioms of connection and order
  - §5. Group III. Axiom of parallels (Euclid’s axiom)
  - §6. Group IV. Axioms of congruence
  - §7. Consequences of the axioms of congruence
  - §8. Group V. Axiom of continuity (Archimedes’s axiom)
- CHAPTER II COMPATIBILITY AND MUTUAL INDEPENDENCE OF THE AXIOMS
  - §9. Compatibility of the axioms
  - §10. Independence of the axioms of parallels (Non-euclidean geometry)
  - §11. Independence of the axioms of congruence
  - §12. Independence of the axiom of continuity (Non-archimedean geometry)
- CHAPTER III THE THEORY OF PROPORTION
  - §13. Complex number systems
  - §14. Demonstration of Pascal’s theorem
  - §15. An algebra of segments, based upon Pascal’s theorem
  - §16. Proportion and the theorems of similitude
  - §17. Equations of straight lines and of planes
- CHAPTER IV THE THEORY OF PLANE AREAS
  - §18. Equal area and equal content of polygons
  - §19. Parallelograms and triangles having equal bases and equal altitudes
  - §20. The measure of area of triangles and polygons
  - §21. Equality of content and the measure of area
- CHAPTER V DESARGUES’S THEOREM
  - §22. Desargues’s theorem and its demonstration for plane geometry by aid of the axioms of congruence
  - §23. The impossibility of demonstrating Desargues’s theorem for the plane without the help of the axioms of congruence
  - §24. Introduction of an algebra of segments based upon Desargues’s theorem and independent of the axioms of congruence
  - §25. The commutative and the associative law of addition for our new algebra of segments
  - §26. The associative law of multiplication and the two distributive laws for the new algebra of segments
  - §27. Equation of the straight line, based upon the new algebra of segments
  - §28. The totality of segments, regarded as a complex number system
  - §29. Construction of a geometry of space by aid of a desarguesian number system
  - §30. Significance of Desargues’s theorem
- CHAPTER VI PASCAL’S THEOREM
  - §31. Two theorems concerning the possibility of proving Pascal’s theorem
  - §32. The commutative law of multiplication for an Archimedean number system
  - §33. The commutative law of multiplication for a non-archimedean number system
  - §34. Proof of the two propositions concerning Pascal’s theorem (Non-pascalian geometry)
  - §35. The demonstration, by means of the theorems of Pascal and Desargues, of any theorem relating to points of intersection
- CHAPTER VII GEOMETRICAL CONSTRUCTIONS BASED UPON THE AXIOMS I–V
  - §36. Geometrical constructions by means of a straight-edge and a transferer of segments
  - §37. Analytical representation of the co-ordinates of points which can be so constructed
  - §38. The representation of algebraic numbers and of integral rational functions as sums of squares
  - §39. Criterion for the possibility of a geometrical construction by means of a straight-edge and a transferer of segments
- CONCLUSION
- APPENDIX