In an İstanbul manuscript which is more than nine hundred years old (Ayasofya Museum Library, No. 4832) there is a short tract giving a method found by Al Kûhî for the trisection of the angle. It is on page 147b of this sizeable volume which is a collection of a large number of articles and short treatises. The present text occupies only part of a single page. For the trisection of the angle Al Kûhî utilizes here a problem of the construction, in a giyen plane, of a hyperbola in which the angle between a diameter and the corresponding ordinates, called the angle of arrangement by Al Kûhî, equals a giyen angle and whose parameter corresponding to the particular diameter and the diameter itself have giyen values. Al Kûhî’s method of trisection calls for the construction of such a hyperbola whose angle of arrangement is equal to the angle to be trisected and in which the parameter and the diameter are equal to each other.