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
Ptolemy (name) Ptolemy (name) The name Ptolemy or Ptolemaeus may refer to: Ptolemy, or Ptolemaeus, or Tolomeo (Italian spelling) may also refer to: According to Georg Autenrieth, the English name Ptolemy comes from the Ancient Greek name Πτολεμαῖος ("Ptolemaios"), "warlike" or "son of war". Autienrieth renders the meaning of the name to be an adjective from πτόλεμος ("ptólemos"), explained as a Homeric Greek form of πόλεμος ("pólemos"), "war". A nephew of Antigonus I Monophthalmus was called "Polemaeus", the normal form of the adjective. "Ptolemaios" is first attested in Homer's Iliad and is the name of an Achaean warrior, son of Piraeus, father