IMI/Publicaţii/BASM/Ediţii/BASM n.4 (10), 1992/

Construction of quasi-affine axiomatics of Lobachevskij geometry. (Russian)

Authors: Zamorzaev A. M.


The new axiomatics of Lobachevsky planimetry is constructed by analogy with the axiomatics of affine geometry. Namely, from Hilbert axiomatics of Euclidean (or non-Euclidean) geometry the group of axioms of congruence is removed, Dedekind principle is used as axiom of continuity, and some other axioms such as strengthened Lobachevsky postulate, the existence of a straight line inside any angle are strengthened.