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 largest and most significant libraries of the ancient world, but details about it are a mixture of history and legend. The earliest known surviving source of information on the founding of the Library of Alexandria is the pseudepigraphic "Letter of Aristeas", which was composed between 180 and 145 BC. The "Letter of Aristeas" claims that the Library was founded during the reign of Ptolemy I Soter ( 323– 283 BC) and that it was initially organized by Demetrius of Phalerum, a student of Aristotle who had been exiled from Athens and taken refuge in Alexandria within the Ptolemaic court. Nonetheless,