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
Attic Greek used for the language of later writers following conventionally the accession in 285 BC of Greek-speaking Ptolemy II to the throne of the Kingdom of Egypt. Ruling from Alexandria, Ptolemy launched the Alexandrian period, during which the city of Alexandria and its expatriate Greek-medium scholars flourished. The original range of the spoken Attic dialect included Attica and a number of the central Cyclades islands; the closely related Ionic was also spoken along the western and northwestern coasts of Asia Minor in modern Turkey, in Chalcidice, Thrace, Euboea, and in some colonies of Magna Graecia. Eventually, the texts of literary Attic