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 |