Non-Euclidean geometry that are both perpendicular to a third line: Euclidean geometry, named after the Greek mathematician Euclid, includes some of the oldest known mathematics, and geometries that deviated from this were not widely accepted as legitimate until the 19th century. The debate that eventually led to the discovery of the non-Euclidean geometries began almost as soon as Euclid's work "Elements" was written. In the "Elements", Euclid began with a limited number of assumptions (23 definitions, five common notions, and five postulates) and sought to prove all the other results (propositions) in the work. The most notorious of the postulates is often
Menelaus of Alexandria great circle arcs, which he named "trilaterals") and proves Menelaus' theorem on collinearity of points on the edges of a triangle (which may have been previously known) and its analog for spherical triangles. It was later translated by the sixteenth century astronomer and mathematician Francesco Maurolico. The lunar crater Menelaus is named after him. The titles of a few books by Menelaus have been preserved: Menelaus of Alexandria Menelaus of Alexandria (; , "Menelaos ho Alexandreus"; c. 70 – 140 CE) was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of