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 in the Library of Alexandria Ptolemy II Philadelphus in the Library of Alexandria Ptolemy Philadelphus in the Library of Alexandria is an 1813 oil on canvas painting by Vincenzo Camuccini. It is now in the National Museum of Capodimonte in Naples. The work was commissioned by Napoleon I along with "Charlemagne Ordering Italian Scholars to Found the University of Paris", both for the central hall of Rome's Palazzo del Quirinale. It shows Ptolemy II Philadelphus in red robes among several philosophers in the Library of Alexandria. The artist had recently returned to Italy from Paris and decided to accept the commission. "Ptolemy" was then moved