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