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
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