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 of Telmessos a paternal first cousin called Antipater Epigonos and likely he had a paternal second cousin called Epigonos. Through his father, Ptolemy II was a direct descendant of Lysimachus who was one of the Diadochi of the Greek King Alexander the Great who was King of Thrace, Asia Minor and Macedonia and Ptolemy I Soter another of the Diadochi of the Greek King Alexander the Great who was the founder of the Ptolemaic dynasty of Ancient Egypt and his wife, Berenice I of Egypt. Berenice I was the great-niece of the powerful Regent Antipater, through her maternal grandfather Cassander, the brother