Ancient Arabic manuscript. Extract from Tanqih al-Manazir, written by Kamal al-Din al-Farisi (1267-1319). Kamal al-Din Hasan ibn Ali ibn Hasan al-Farisi, or Abu Hasan Muhammad ibn Hasan, was a prominent Persian scientist born in Tabriz, Iran. He is best known for giving the first mathematically satisfactory explanation of the rainbow and a number of important contributions to number theory. His most notable being on amicable numbers. Farisi was a pupil of the great astronomer and mathematician Qutb al-Din al-Shirazi, who in turn was a pupil of Nasir al-Din Tusi.