Higher Geometry |
Contents
A Short Review of Investigations | 12 |
The Axioms of Elementary Geometry | 42 |
The NonEuclidean Theory | 85 |
Copyright | |
8 other sections not shown
Common terms and phrases
a₁ affine assume Axiom III.1 axioms of Groups axis belonging Beltrami coordinates called centre coincide common point condition congruent conic coordinate system corresponding points cross ratio curve defined definition denote determined divides the pair elementary geometry elements equal equation Euclidean geometry Euclidean plane Euclidean space fifth postulate Figure formulas four points half line half plane harmonically conjugate Hilbert's axioms homogeneous coordinates horosphere images implies inverse Lemma lies linear Lobachevskian geometry Lobachevskian plane lying M₁ M₂ manifold mapping motion non-Euclidean obtained oricycle orthogonal pairs of points parallel Pasch's axiom pencil perpendicular point at infinity point of intersection points M1 projective geometry projective line proof properties proposition proved pseudosphere rays real numbers Riemannian geometry right angles satisfy segment set of points side sphere surface tangent Theorem three points tion transformation triangle u₁ vectors vertex x₁