Foundations of geometry

mathematical treatise by Euclid

axiom in Euclidean geometry

formal system

statement in plane geometry, used implicitly by Euclid, which cannot be derived from the postulates as Euclid gave them

statement equivalent to Euclid's parallel postulate, that given a line and a point not on it, there is at most one line parallel to the given line through the point

one of twenty-three, asking to construct all metric spaces where lines resemble those on a sphere

postulates of Euclidean geometry

theorem

study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries

first-order axiomatization of a fragment of Euclidean geometry