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,
Aristobulus of Alexandria quoted by Anatolius. He is incorrectly named "Aristobulus of Paneas" in Rufinus' Latin translation of Eusebius' "Historia Ecclesiastica" (7, 32, 16). It is a wrong translation of the Greek ὁ πάνυ, "the Great". In addition, the author here quoted by Eusebius, Anatolius of Laodicea (270 CE), was mistaken in believing that Aristobulus was one of the 70 priests who translated the Torah into Greek (the "Septuagint") during the reign of Ptolemy II Philadelphus (3rd century BC). Anatolius of Laodicea incorrectly said that he lived in the time of Ptolemy Philadelphus. A further mistake in Rufinus' Latin translation of the Anatolius