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 BC, however, Aristarchus became caught up in a dynastic struggle in which he supported Ptolemy VII Neos Philopator as the ruler of Egypt. Ptolemy VII was murdered and succeeded by Ptolemy VIII Physcon, who immediately set about punishing all those who had supported his predecessor, forcing Aristarchus to flee Egypt and take refuge on the island of Cyprus, where he died shortly thereafter. Ptolemy VIII expelled all foreign scholars from Alexandria, forcing them to disperse across the Eastern Mediterranean. Ptolemy VIII Physcon's expulsion of the scholars from Alexandria brought about a shift in the history of Hellenistic scholarship. The scholars