A geometry based on the axioms of Euclidean geometry, except for the axiom on parallel straight lines (postulate V). The assumptions underlying absolute geometry are common to Euclidean geometry and to Lobachevskii geometry. The term "absolute geometry" was introduced by J. Bolyai in 1832.
Absolute geometry. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Absolute_geometry&oldid=13268