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,
Library of Alexandria the "Letter of Aristeas" is very late and it contains information that is now known to be inaccurate. Other sources claim that the Library was instead created under the reign of Ptolemy I's son Ptolemy II Philadelphus (283–246 BC). Modern scholars agree that, while it is possible that Ptolemy I may have laid the groundwork for the Library, it probably did not come into being as a physical institution until the reign of Ptolemy II. By that time, Demetrius of Phalerum had fallen out of favor with the Ptolemaic court and could not, therefore, have had any role in establishing