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 of Antipater. Ptolemy II was born and raised in Telmessos in Lycia at an unknown date during his father’s reign of Telmessos. His father Lysimachus ruled as the Ptolemaic Client King of Telmessos from February 240 BC until his death in 206 BC. Little is known on his early life prior to succeeding his father. When his father died in 206 BC, Ptolemy II became the fourth and final ruler from the Lysimachid dynasty, which is also known as the Ptolemaic/Lysimachid dynasty in Lycia to rule the city. Ptolemy II also, was the third and final Ptolemaic Client King of