A number of geometers made attempts to prove the parallel postulate , including Omar KhayyÃ m , and later Giovanni Gerolamo Saccheri , John Wallis , Lambert , and Legendre . A number of geometers made attempts to prove the parallel postulate by assuming its negation and trying to derive a contradiction , including Proclus , Ibn al-Haytham ( Alhacen ) , Omar KhayyÃ m , Nasir al-Din al-Tusi , Witelo , Gersonides , Alfonso , and later Giovanni Gerolamo Saccheri , John Wallis , Johann Heinrich Lambert , and Legendre .