دانلود کتاب Introduction to Non-Euclidean Geometry

فهرست مطالب :

Content: Cover
Title Page
Copyright Page
Preface
Contents
1 The Foundation of Euclidean Geometry
1. Introduction
2. The Definitions
3. The Common Notions
4. The Postulates
5. Tacit Assumptions Made by Euclid. Superposition
6. The Infinitude of the Line
7. Pasch's Axiom
8. The Principle of Continuity
9. The Postulate System of Hilbert
2 The Fifth Postulate
10. Introduction
11. Substitutes for the Fifth Postulate
12. Playfair's Axiom
13. The Angle-Sum of a Triangle
14. The Existence of Similar Figures
15. Equidistant Straight Lines
16. Other Substitutes. 17. Attempts to Prove the Fifth Postulate18. Ptolemy
19. Proclus
20. Nasiraddin
21. Wallis
22. Saccheri
23. Lambert
24. Legendre
25. Some Fallacies in Attempts to Prove the Postulate
26. The Rotation Proof
27. Comparison of Infinite Areas
3 The Discovery of Non-Euclidean Geometry
28. Introduction
29. Gauss
30. Bolyai
31. Lobachewsky
32. Wachter, Schweikart and Taurinus
33. Riemann
34. Further Developments
35. Conclusion
4 Hyperbolic Plane Geometry
36. Introduction
37. The Characteristic Postulate of Hyperbolic Geometry and Its Immediate Consequences. 38. Elementary Properties of Parallels39. Ideal Points
40. Some Properties of an Important Figure
41. The Angle of Parallelism
42. The Saccheri Quadrilateral
43. The Lambert Quadrilateral
44. The Sum of the Angles of a Triangle
45. The Common Perpendicular of Two Non-Intersecting Lines
46. Ultra-Ideal Points
47. The Variation in the Distance between Two Lines
48. The Perpendicular Bisectors of the Sides of a Triangle
49. The Construction of the Parallels to a Line through a Point
50. The Construction of a Common Parallel to Two Intersecting Lines. 51. The Construction of a Line Perpendicular to One of Two Intersecting Lines and Parallel to the Other52. Units of Length and Angle
53. Associated Right Triangles
54. The Construction of a Triangle when Its Angles are Given
55. The Absolute
56. Circles
57. Corresponding Points
58. Limiting Curves and Their Properties
59. Equidistant Curves and Their Properties
60. The Limiting Curve as Related to Circles and Equidistant Curves
61. Area
62. Equivalence of Polygons and Triangles
63. Measure of Area
64. The Triangle with Maximum Area
5 Hyperbolic Plane Trigonometry. 65. Introduction66. The Ratio of Corresponding Arcs of Concentric Limiting Curves
67. Relations between the Parts of an Important Figure
68. A Coördinate System and Another Important Figure
69. The Relations between Complementary Segments
70. Relations among the Parts of a Right Triangle
71. Relations among the Parts of the General Triangle
72. The Relation between a Segment and Its Angle of Parallelism
73. Simplified Formulas for the Right Triangle and the General Triangle
74. The Parameter
6 Applications of Calculus to the Solutions of Some Problems in Hyperbolic Geometry.