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 of Mauretania by an Athenian inscription, but her name has not been preserved. She may have been called Drusilla of Mauretania. His father Juba II was the son of King Juba I of Numidia, who was descended from the Berbers of North Africa and was an ally to the Roman Triumvir Pompey. His mother Cleopatra Selene II was the daughter of the Ptolemaic Greek Queen Cleopatra VII of Egypt and the Roman Triumvir Mark Antony. Ptolemy was of Berber, Greek and Roman ancestry. Ptolemy and his sister were the only known children of Juba II and Cleopatra Selene II to reach maturity