CHAPTER 1. FOUNDATIONS OF GEOMETRY |
1-1 Logical systems |
1-2 Logical notations |
1-3 Inductive and deductive reasoning |
1-4 Postulates |
1-5 Independent postulates |
1-6 Categorical sets of postulates |
1-7 A geometry of number triples |
1-8 Geometric invariants |
CHAPTER 2. SYNTHETIC PROJECTIVE GEOMETRY |
2-1 Postulates of incidence and existence |
2-2 Properties of a projective plane |
2-3 Figures |
2-4 Duality |
2-5 Perspective figures |
2-6 Projective transformations |
2-7 Postulate of Projectivity |
2-8 Quadrangles |
2-9 Complete and simple n-points |
2-10 Theorem of Desargues |
2-11 Theorem of Pappus |
2-12 Conics |
2-13 Theorem of Pascal |
2-14 Survey |
CHAPTER 3. COORDINATE SYSTEMS |
3-1 Quadrangular sets |
3-2 Properties of quadrangular sets |
3-3 Harmonic sets |
3-4 Postulates of Separation |
3-5 Nets of rationality |
3-6 Real projective geometry |
3-7 Nonhomogeneous coordinates |
3-8 Homogeneous coordinates |
3-9 Survey |
CHAPTER 4. ANALYTIC PROJECTIVE GEOMETRY |
4-1 Representations in space |
4-2 Representations on a plane |
4-3 Representations on a line |
4-4 Matrices |
4-5 Cross ratio |
4-6 Analytic and synthetic geometries |
4-7 Groups |
4-8 Classification of projective transformations |
4-9 Polarities and conics |
4-10 Conics |
4-11 Involutions on a line |
4-12 Survey |
CHAPTER 5. AFFINE GEOMETRY |
5-1 Ideal points |
5-2 Parallels |
5-3 Mid-point |
5-4 Classification of conics |
5-5 Affine transformations |
5-6 Homothetic transformations |
5-7 Translations |
5-8 Dilations |
5-9 Line reflections |
5-10 Equiaffine and equiareal transformations |
5-11 Survey |
CHAPTER 6. EUCLIDEAN PLANE GEOMETRY |
6-1 Perpendicluar lines |
6-2 Similarity transformations |
6-3 Orthogonal line reflections |
6-4 Euclidean transformations |
6-5 Distances |
6-6 Directed angles |
6-7 Angles |
6-8 Common figures |
6-9 Survey |
CHAPTER 7. THE EVOLUTION OF GEOMETRY |
7-1 Early measurements |
7-2 Early Greek influence |
7-3 Euclid |
7-4 Early euclidean geometry |
7-5 The awakening in Europe |
7-6 Constructions |
7-7 Descriptive geometry |
7-8 Seventeenth ce |
7-9 Eighteenth century |
7-10 Euclid's fifth postulate |
7-11 Nineteenth and twentieth centuries |
7-12 Survey |
CHAPTER 8. NONEUCLIDEAN GEOMETRY |
8-1 The absolute polarity |
8-2 Points and lines |
8-3 Hyperbolic geometry |
8-4 Elliptic and spherical geometries |
8-5 Comparisons |
CHAPTER 9. TOPOLOGY |
9-1 Topology |
9-2 Homeomorphic figures |
9-3 Jordan Curve Theorem |
9-4 Surfaces |
9-5 Euler's Formula |
9-6 Tranversable networks |
9-7 Four-color problem |
9-8 Fixed-point theorems |
9-9 Moebius strip |
9-10 Survey |
BIBLIOGRAPHY |
INDEX |