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,
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