absolute geometry

Etymology
From 1832; introduced by Hungarian mathematician (1802—1860).

Noun

 * 1)  The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative.
 * 2) * 1993 [Princeton University Press], Donald M. Davis, The Nature and Power of Mathematics, 2004, Dover, page 85,
 * Recall that absolute geometry is the set of statements that can be deduced from Euclid's first four postulates. Then existence of parallel lines is certainly a theorem of absolute geometry, while the question being addressed by most of the mathematicians discussed in this section is whether uniqueness of parallels is also a theorem of absolute geometry.
 * 1)  Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate.
 * 2) * 1970, J. F. Rigby, Axioms for Absolute Geometry, III, , Vol. XXII, No. 1,, , page 185,
 * A discussion of one-dimensional absolute geometries, with examples, will be given in a separate paper.

Translations

 * Japanese: 絶対幾何学
 * Russian: абсолю́тная геоме́трия