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
Reign of Cleopatra conflicting evidence that he publicly denied fathering him but privately accepted him as his son. Cleopatra, on the other hand, made repeated official declarations about Caesarion's parentage, with Caesar as the father. She also built a Caesareum temple near the harbor of Alexandria dedicated to his worship. Cleopatra VII and her nominal joint ruler Ptolemy XIV visited Rome sometime in late 46 BC, presumably without Caesarion. They were given lodging in Caesar's Villa within the Horti Caesaris. Like he did with their father Ptolemy XII, Julius Caesar awarded both Cleopatra VII and Ptolemy XIV with the legal status of 'friend