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
Library of Alexandria scrolls in its collection, so, during the reign of Ptolemy III Euergetes, it opened a satellite collection in the Serapeum of Alexandria, a temple to the Greco-Egyptian god Serapis located near the royal palace. Aristophanes of Byzantium (lived 257– 180 BC) became the fourth head librarian sometime around 200 BC. According to a legend recorded by the Roman writer Vitruvius, Aristophanes was one of seven judges appointed for a poetry competition hosted by Ptolemy III Euergetes. All six of the other judges favored one competitor, but Aristophanes favored the one whom the audience had liked the least. Aristophanes declared that