Euclidean geometry is described in a scientific and numerical treatise.
 A broad vision of the subject of geometry was then expressed  by Riemann in his 1867 inauguration lecture ber die Hypothesen, welche der Geometrie zu Grunde liegen (On the hypotheses on which geometry is based), published only after his death
  The theorems of Ibn al-Haytham (Alhazen), Omar Khayyam and Nasir al-Din al-Tusi on quadrilaterals, including the Lambert quadrilateral and Saccheri quadrilateral, were early results in hyperbolic geometry, and along with their alternative postulates, such as Playfair's axiom, these works had a considerable influence on the development of non-Euclidean geometry among later European geometers, including Vitello (c

