Non-Euclidean geometry that are both perpendicular to a third line: Euclidean geometry, named after the Greek mathematician Euclid, includes some of the oldest known mathematics, and geometries that deviated from this were not widely accepted as legitimate until the 19th century. The debate that eventually led to the discovery of the non-Euclidean geometries began almost as soon as Euclid's work "Elements" was written. In the "Elements", Euclid began with a limited number of assumptions (23 definitions, five common notions, and five postulates) and sought to prove all the other results (propositions) in the work. The most notorious of the postulates is often
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