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
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