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
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