Kushyar Gilani was born c. 971. Little is known about his life. The word “Gilani” added to his name refers to Gilan, a region of northern Iran south of the Caspian Sea. The works attributed to Kushyar have survived, but of these only three have received scholarly attention, two zijes and arithmetic. The two zijes are al-Jamd, “The Comprehensive,” and al-Baligh, “The Far-reaching.” Each is in four sections: introductory notes, tables, explanations, and proofs. Of the al-Baligh only the first two sections are extant in the Berlin manuscript.
Kushyar’s arithmetic is Usui Hisab al-Hind, “Elements of Hindu Reckoning.” There is a Hebrew commentary to this work written by ‘Anabi in the fifteenth century.
Kushyar is, however, credited with having developed the study of trigonometric functions started by Abu’l- Wafa and al-Battani. Abu’l-Wafa gives sine tables, and al-Battani gives sines and cotangents; but Kushyar’s zljes contain sines, cotangents, tangents, and versed sines, together with tables of differences. In most of these tables the functions are calculated to three sexagesimal places and the angles increase in steps of one degree.
The importance of Kushyar’s Usui Jisab al-Hind lies in his having written it to introduce the Hindu methods into astronomical calculations. Abu Hanifa al-Dinawari, a lawyer, wrote on arithmetic to introduce these methods into business. ‘All ibn Ahmad al-Nasawi, known to have been Kushyar’s student, commented sarcastically on these two works because Abu Hanifa’s was lengthy and Kushyar’s was compact; he said that the former proved to be for astronomers and the latter for businessmen.
Abu Jafar Al Khazin the Mathematician and the Astronomer
