The Trisection of the Angle by Abû Sahl Wayjan ibn Rustam al Kûhî

Year 1962, Volume: 26 Issue: 104, 696 - 700, 20.10.1962

Aydın Sayılı

Abstract

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.

Keywords

Ebû Sehl el Kûhî, Math, Science, Astronomy, Islamic History of Science, Apollonios