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 I Soter Ptolemy I Soter Ptolemy I Soter (; , "Ptolemaĩos Sōtḗr" "Ptolemy the Savior"; c. 367 BC – January 282 BC) was a companion and historian of Alexander the Great who succeeded to his empire. Ptolemy became ruler of Egypt (323–282 BC) and founded the Ptolemaic dynasty which ruled it for the next three centuries, turning Egypt into a Hellenistic kingdom and Alexandria into a center of Greek culture. Ptolemy was the son of Arsinoe of Macedon by either her husband Lagus or Philip II of Macedon, the father of Alexander. Ptolemy was one of Alexander's most trusted companions and military