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,
Pappus of Alexandria Pappus of Alexandria Pappus of Alexandria (; ; ) was one of the last great Greek mathematicians of Antiquity, known for his "Synagoge" (Συναγωγή) or "Collection" (), and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than, (from his own writings) that he had a son named Hermodorus, and was a teacher in Alexandria. "Collection", his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics, including geometry, recreational mathematics, doubling the cube, polygons and polyhedra. Pappus was active in the 4th