Foundations of geometry different sets of axioms for Euclidean geometry, any of these can replace the Euclidean parallel postulate. The following partial list indicates some of these theorems that are of historical interest. Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. The term was introduced by János Bolyai in 1832. It is sometimes referred to as neutral geometry, as it is neutral with respect to the parallel postulate. In Euclid's "Elements", the first 28 propositions and Proposition I.31 avoid using the parallel postulate,
Cosmas I of Alexandria Cosmas I of Alexandria Cosmas I or Kosmas I () served as Greek Patriarch of Alexandria between ca. 727 and his death in 768. Cosmas was the first residential Chalcedonian (Melkite) patriarch to be established in Alexandria following the Muslim conquest of Egypt in the 640s. The see had remained vacant since, but Cosmas was appointed with the consent of both the Umayyad Caliph and the Byzantine Emperor. The chronicler Theophanes the Confessor reports that in 742/3, he abjured Monotheletism, the dominant doctrine among Alexandrian Melkites since it had been promulgated by Emperor Heraclius. As Cosmas himself was most likely