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 to the Capodimonte Palace by Gioacchino Murat and then in 1867 moved to the Palazzo Reale di Napoli, before being given to the Camera dei deputati in Palazzo Montecitorio in Rome. It later returned to Naples and since 1997 has hung in its original position in Room 31 of the Royal Apartments, also known as the Salone della Culla. 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