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 I Soter Ptolemy I Soter Ptolemy I Soter (; , "Ptolemaĩos Sōtḗr" "Ptolemy the Savior"; c. 367 BC – January 282 BC) was a companion and historian of Alexander the Great who succeeded to his empire. Ptolemy became ruler of Egypt (323–282 BC) and founded the Ptolemaic dynasty which ruled it for the next three centuries, turning Egypt into a Hellenistic kingdom and Alexandria into a center of Greek culture. Ptolemy was the son of Arsinoe of Macedon by either her husband Lagus or Philip II of Macedon, the father of Alexander. Ptolemy was one of Alexander's most trusted companions and military