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
Political and military events in Scotland during the reign of David I Political and military events in Scotland during the reign of David I Political and military events in Scotland during the reign of David I are the events which took place in Scotland during David I of Scotland's reign as King of Scots, from 1124 to 1153. When his brother Alexander I of Scotland died in 1124, David chose, with the backing of Henry I of England, to take the Kingdom of Alba for himself. David was forced to engage in warfare against his rival and nephew, Máel Coluim mac Alaxandair. Subduing the latter took David ten years, and involved the