The theorems of Alhacen , Khayyam on quadrilaterals , were the first theorems on hyperbolic geometry . The theorems of Alhacen , Khayyam and al-Tusi on quadrilaterals , including the Ibn al-Haytham â `` Lambert quadrilateral and Khayyamâ `` Saccheri quadrilateral , were the first theorems on hyperbolic geometry .