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Preface to the English Edition
The Axioms of Elementary Geometry
The NonEuclidean Theory
7 other sections not shown
absolute conic affine space affine transformation assume automorphisms axioms of Groups axis Beltrami coordinates called Cartesian centre coefficients coincide common point condition congruent constant curvature coordinate system corresponding points cross ratio curve defined definition denote determined divides the pair elements elliptic geometry equal equation Euclidean geometry Euclidean plane Euclidean space Figure formulas function half line harmonically conjugate homogeneous coordinates horosphere hyperbolic hyperplane images implies inertial interior intrinsic geometry invariant inverse isotropic cone Lemma lies linear Lobachevskian geometry Lobachevskian plane lying manifold mapping matrix metric form Minkowski space motion non-Euclidean obtained one-to-one oricycle orthogonal pairs of points parallel Pasch's axiom pencil perpendicular point at infinity point of intersection points Mx projective geometry projective plane proof properties propositions proved pseudosphere rays real numbers Riemannian geometry satisfy set of points side sphere surface Theorem three points tions triangle vectors vertex