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,
Library of Alexandria who had studied at the Library of Alexandria and their students continued to conduct research and write treatises, but most of them no longer did so in association with the Library of Alexandria. A diaspora of Alexandrian scholarship occurred, in which scholars dispersed first throughout the eastern Mediterranean and later throughout the western Mediterranean as well. Aristarchus's student Dionysius Thrax ( 170– 90 BC) established a school on the Greek island of Rhodes. Dionysius Thrax wrote the first book on Greek grammar, a succinct guide to speaking and writing clearly and effectively. This book remained the primary grammar textbook for