them. Its essential role was discovered by Moritz Pasch in 1882. The axiom states that, Pasch's axiom — Let A, B, C be three points that do not lie on...

Pasch may refer to: Passover Easter Pasch (surname), German and Swedish surname Pasch configuration Pasch's axiom Pasch's theorem Pasch egg, easter eggs...

statement, is also included and remains an axiom in Hilbert's treatment. Ordered geometry Pasch's axiom Pasch 1912 Coxeter (1969, p. 179) states the result...

a line, there is no more than one which lies between the other two. Pasch's Axiom: Let A, B, C be three points not lying in the same line and let a be...

thinking about the foundations of Euclidean geometry. Pasch is perhaps best remembered for Pasch's axiom: Given three noncollinear points a, b, c and a line...

Society in 1902. Hilbert moved the axiom to Theorem 5 and renumbered the axioms accordingly (old axiom II-5 (Pasch's axiom) now became II-4). While not as...

can lead to deeper insights into a subject (e.g., the introduction of Pasch's axiom of Euclidean geometry, the five colour theorem of graph theory). Pseudaria...

Tarski's axioms are an axiom system for Euclidean geometry, specifically for that portion of Euclidean geometry that is formulable in first-order logic...

positive, the case where DEF crosses two sides of the triangle. (See Pasch's axiom.) To check the magnitude, construct perpendiculars from A, B, C to the...

real line forms the Cayley absolute of the Poincaré half-plane model. Pasch's axiom and the exterior angle theorem still hold for an omega triangle, defined...