Noneuclidean Geometry |
Contents
On Proofs and Definitions | 1 |
Hilberts System of Axioms | 8 |
From the History of the Parallel | 21 |
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Common terms and phrases
A₁ absolute geometry angle of parallelism angle sum antipodal points assertion axiom of parallels axioms in groups B₁ bisector Bolyai bounding parallel common perpendicular congruence theorem construction cos˛ cosh cosh cosh cosh2 cot˛ cross ratio definition e-ray el-line g El-point elliptic geometry elliptic pencil determined equal equator equidistant Euclid euclidean geometry follows formulas g₁ and g₂ given point h-circle h-length h-plane h-points h-segment h₁ halfplane Hence Hilbert hyperbolic geometry hyperbolic pencil hyperparallels implies interior midpoints noneuclidean geometry orthogonal P₁ pair of antipodal parallel axiom parallel lines parallel postulate perpendicular to g plane Poincaré model point of intersection possible PP₁ proof proving Theorem radical axis reader reflection right angles right left right triangle Saccheri quadrilateral segment sin˛ sinh sinh2 sphere stereographic projection straight line subtriangles system of axioms tangents tanh Theorem 19 Theorem 23 triangle ABC trigonometry unit circle x-axis