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 II Philadelphus Ptolemy II Philadelphus Ptolemy II Philadelphus (, "Ptolemaîos Philádelphos" "Ptolemy, lover of his sister"; 308/9–246 BCE) was the king of Ptolemaic Egypt from 283 to 246 BCE. He was the son of Ptolemy I Soter, the Macedonian Greek general of Alexander the Great who founded the Ptolemaic Kingdom after the death of Alexander, and queen Berenice I, originally from Macedon in northern Greece. During Ptolemy II's reign, the material and literary splendour of the Alexandrian court was at its height. He promoted the Museum and Library of Alexandria. He erected a commemorative stele, the Great Mendes Stela. He also led