Parallel (geometry) as a pair of straight lines in a plane which do not meet appears as Definition 23 in Book I of Euclid's Elements. Alternative definitions were discussed by other Greeks, often as part of an attempt to prove the parallel postulate. Proclus attributes a definition of parallel lines as equidistant lines to Posidonius and quotes Geminus in a similar vein. Simplicius also mentions Posidonius' definition as well as its modification by the philosopher Aganis. At the end of the nineteenth century, in England, Euclid's Elements was still the standard textbook in secondary schools. The traditional treatment of geometry was being
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