AbūTorāb's Treatise on Trisection of Angles

Trisection of an angle is one of the famous problems in the history of mathematics. The impossibility of trisecting an angle with a straightedge andcompasses was known. Therefore finding an accurate approximation of irrational quantity of the Sine of degree- which was important for setting up sine tables in Zījes, and also for astronomical calculations- is very difficult. So, many scientists devoted their attempts to find a solution to this problem. MīrzāAbūTorābNatanzī, a scholar of theQajarid era, in a Persian treatise entitled Darma‘rifat-i watar-i thulth-i qaws-i ma‘lūmat al-watar (on the knowledge of the chord of one-third of an arc with a known chord), presented a geometrical method for trisecting an angle which turns out to be mathematically equivalent to the algebraic method of JamshīdKāshānī (al-Kāshī) for finding the Sine of one degree. Surveying different approximate methods of trisecting an angle in ancient Greek and Islamic periods, this paper presents a critical edition and a commentary of MīrzāAbūTorāb’s treatise.