目录

●Author's note to the English-language edition
●1 Desarguesian geometry and the Desarguesian number system
● 1.1 Hilbert's 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 Hilbert's 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 Hilbert's mechanization theorem about pure point of intersection theorems in Pascalian geometry......