Axioms for Absolute Geometry
Axioms for Absolute Geometry
The axioms of Euclidean geometry may be divided into four groups: the axioms of order, the axioms of congruence, the axiom of continuity, and the Euclidean axiom of parallelism ( 6 ). If we omit this last axiom, the remaining axioms give either Euclidean or hyperbolic geometry. Many important theorems …