The term Euclidean refers to everything that can historically or logically be referred to Euclid's monumental treatise The Thirteen Books of the Elements, written around the year 300 B.C. The Euclidean geometry of the plane (Books I-IV) and of the three-dimensional space (Books XI-XIII) is based on five postulates, the first four of which are about the basic objects of plane geometry (point, straight line, circle, and right angle), which can be drawn by straightedge and compass (the so-called Euclidean tools of geometric construction). Euclid's fifth postulate, also known as the parallel postulate, is modified in so-called non-Euclidean geometry.

compass | constructible number | elements | Euclidean algorithm | Euclidean geometry | Euclidean metric | Euclidean motion | Euclidean number | Euclidean plane | Euclidean ring | Euclidean space | Euclidean topology | geometric congruence | geometric construction | non-Euclidean geometry | parallel postulate | straightedge

Euclid