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
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.