Ancestral to the modern concept of a manifold were several important results of 18th and 19th century mathematics. The oldest of these was Non-Euclidean geometry, which considers spaces where Euclid's parallel postulate fails. Saccheri first studied this geometry in 1733. Lobachevsky, Bolyai, and Riemann developed the subject further 100 years later. Their research uncovered two types of spaces whose geometric structures differ from that of classical Euclidean space; these are called hyperbolic geometry and elliptic geometry. In the modern theory of manifolds, these notions correspond to manifolds with constant, negative and positive curvature, respectively.