A model for Smarandache's anti-geometry.

From: Smarandache Notions Journal | Date: January 1, 2001| Author: | Copyright information

David Hilbert's Foundations of Geometry (1899) contain nineteen statements, labelled axioms, from which every theorem in Euclid's Elements can be derived by deductive inference, according to the classical rules of logic. The axioms use three property words--'point', 'straight' and 'plane'--and three relation words --'incident', 'between' and 'congruent'--for which no definition is given. These words have, of course, a so-called intuitive meaning in English (as the German equivalents actually used by Hilbert have in his language). But Hilbert believed they ought to be understood ...

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