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
Ptolemy II Philadelphus and dissolute, intellectual and artificial, has been compared with the Palace of Versailles of Louis XIV of France. Ptolemy deified his parents and his sister-wife after their deaths. Ptolemy II began his reign as co-regent with his father, Ptolemy Soter, from c. 285 to c. 283 BCE, and maintained a splendid court in Alexandria. Egypt was involved in several wars during his reign. His maternal half-brother Magas had declared himself king of Cyrene in 276 and began a war against Ptolemy's government in 274 BCE. Magas managed to keep Cyrenaica independent of the Ptolemies until his death in 250 BCE.