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 Ptolemy II Philadelphus Ptolemy II Philadelphus (, "Ptolemaîos Philádelphos" "Ptolemy, lover of his sister"; 308/9–246 BCE) was the king of Ptolemaic Egypt from 283 to 246 BCE. He was the son of Ptolemy I Soter, the Macedonian Greek general of Alexander the Great who founded the Ptolemaic Kingdom after the death of Alexander, and queen Berenice I, originally from Macedon in northern Greece. During Ptolemy II's reign, the material and literary splendour of the Alexandrian court was at its height. He promoted the Museum and Library of Alexandria. He erected a commemorative stele, the Great Mendes Stela. He also led