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
Greek Orthodox Patriarchate of Alexandria and all Africa Greek Orthodox Patriarchate of Alexandria and all Africa The Greek Orthodox Patriarchate of Alexandria and all Africa (Greek: , "Patriarcheîon Alexandreías kaì pásēs Aphrikês") is an autocephalous Byzantine Rite jurisdiction of the Eastern Orthodox Church, having the African continent as its canonical territory. It is commonly called the "Greek" or "Eastern" Orthodox Patriarchate of Alexandria to distinguish it from the "Coptic" or "Oriental" Orthodox Patriarchate of Alexandria. Members of the Greek Orthodox Patriarchate were once known as Melkites, because they remained in communion with the Ecumenical Patriarchate of Constantinople after the schism that followed the Council of Chalcedon in 451.