Foundations of geometry—Euclidean and non-Euclidean geometry

Abstract

Euclidean geometry is the oldest and historically most important example of a deductive scientific discipline. Down to modern times it has been a model of an exact science and it became the starting point for a systematic development of the foundations of geometry. This development began at the turn of the 19th century with the discovery of non-Euclidean geometry, reached its zenith in the investigations of Hilbert, and now covers a wide field of inquiry.