Axiomatic Projective Geometry

List of SymbolsChapter I. Introduction. §1.1. The Axiomatic Method 1.2. Notions from Set Theory 1.3. Notions from Algebra 1.4. Analytic Projective Geometry 1.5. Analytic Solid Projective Geometry 1.6. Vector Spaces Over a Division RingChapter II. Incidence Propositions in the Plane. § 2.1. Trivial Axioms, Duality 2.2. Desargues' Proposition 2.3. Collineations 2.4. The First Quadrangle Proposition, Harmonic Pairs 2.5. Projectivities Between Lines 2.6. Pappos' PropositionChapter III. Coordinates in the Plane. §3.1. Ternary Fields Attached to a Given Projective Plane 3.2. Ternary Field and Axiom System 3.3. Some Complementary Results 3.4. The Geometry Over a Given Ternary Field 3.5. Independence Results 3.6. Homogeneous CoordinatesChapter IV. Incidence Propositions in Space. § 4.1. Trivial Axioms and Propositions 4.2. The Sixteen Points PropositionChapter V. Coordinates in Space. § 5.1. Coordinates of a Point 5.2. Equation of a Plane 5.3. Homogeneous Coordinates 5.4. The Geometry Over a Given Division RingChapter VI. The Fundamental Proposition of Projective Geometry. § 6.1. The Fundamental Proposition 6.2. Summary of ResultsChapter VII. Order. § 7.1. Cyclically Ordered Sets 7.2. Cyclical Order of a Projective Line 7.3. Order and Coordinates 7.4. The Geometry Over an Ordered Ternary Field 7.5. A Counterexample 7.6. The Axiom of Archimedes 7.7. The Axiom of ContinuityAppendicesIndex