目录 Authors note to the English-language edition 1 Desarguesian geometry and the Desarguesian number system 1.1 Hilberts axiom system of ordinary geometry 1.2 The axiom of infinity and Desargues axioms 1.3 Rational points in a Desarguesian plane 1.4 The Desarguesian number system and rational number subsystem 1.5 The Desarguesian number system on a line 1.6 The Desarguesian number system associated with a Desarguesian plane 1.7 The coordinate system of Desarguesian plane geometry 20rthogonal geometry, metric geometry and ordinary geometry 2.1 The Pascalian axiom and commutative axiom of multiplication- (unordered) Pascalian geometry 2.20 rthogonal axioms and (unordered) orthogonal geometry 2.3 The orthogonal coordinate system of (unordered) orthogonal geometry 2.4 (Unordered) metric geometry 2.5 The axioms of order and ordered metric geometry 2.6 Ordinary geometry and its subordinate geometries 3 Mechanization of theorem proving in geometry and Hilberts mechanization theorem 3.1 Comments on Euclidean proof method 3.2 The standardization of coordinate representation of geometric concepts 3.3 The mechanization of theorem proving and Hilberts mechanization theorem about pure point of intersection theorems in Pascalian geometry 3.4 Examples for Hilberts mechanical method 3.5 Proof of Hilberts mechanization theorem 4 The mechanization theorem of (ordinary) unordered geometry 4.1 Introduction 4.2 Factorization of polynomials 4.3 Well-ordering of polynomial sets 4.4 A constructive theory of algebraic varieties -irreducible ascending sets and irreducible algebraic varieties 4.5 A constructive theory of algebraic varieties -irreducible decomposition of algebraic varieties 4.6 A constructive theory of algebraic varieties -the notion of dimension and the dimension theorem 4.7 Proof of the mechanization theorem of unordered geometry 4.8 Examples for the mechanical method of unordered geometry 5 Mechanization theorems of (ordinary) ordered geometries 5.1 Introduction 5.2 Tarskis theorem and Seidenbergs method 5.3 Examples for the mechanical method of ordered geometries 6 Mechanization theorems of various geometries 6.1 Introduction 6.2 The mechanization of theorem proving in projective geometry 6.3 The mechanization of theorem proving in Bolyai-Lobachevskys hyperbolic non-Euclidean geometry 6.4 The mechanization of theorem proving in Riemanns elliptic non-Euclidean geometry 6.5 The mechanization of theorem proving in two circle geometries 6.6 The mechanization of formula proving with transcendental functions References Subject index
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