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
Ptolemaic cult of Alexander the Great who had succeeded to temporarily evict her son from Alexandria. As women could not occupy a supreme priesthood in the Greek world, she had to content herself with placing one of her supporters in the post, as a public sign of her new dominance. After Artemidorus, however, the name of Ptolemy IX was subsequently added in the papyrus, which means that he managed to return to Alexandria in the same year. In 107 BC, Cleopatra III managed to expel Ptolemy IX for good from Alexandria, and raised her second son, Ptolemy X, to the throne as her co-ruler and priest