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 IV Philopator major antagonist of the apocryphal 3 Maccabees, which describes events following the Battle of Raphia, in both Jerusalem and Alexandria. Ptolemy IV's reign was also marked by trade with other contemporaneous polities. In the 1930s, excavations by Mattingly at a fortress close to Port Dunford (the likely Nikon of antiquity) in present-day southern Somalia yielded a number of Ptolemaic coins. Among these pieces were 17 copper mints from the reigns of Ptolemy III, Ptolemy IV and Ptolemy V, as well as late Imperial Rome and Mamluk Sultanate coins. Ptolemy IV Philopator Ptolemy IV Philopator (, "Ptolemaĩos Philopátōr" "Ptolemy, lover of