Abu Nasr Mansur ibn Iraq

Abu Nasr Mansur ibn Ali ibn Iraq was born some time between about 960 and 970. Sources give his birthplace as either Gilan or Khwarazm, and the question has not been settled. He belonged to the Afrighid dynasty that ruled Khwarazm: a grandson of the Afrighid Iraq and a cousin of Abu Abdallah Muhammad, the last Khwarazmshah of that line. He is reported to have studied mathematics under Abu al-Wafa, and he lived at Kath (today the town of Beruniy).

From about 990 he taught the young al-Biruni. In 995 a coup toppled the Afrighids and the Ma’munids came to power in Khwarazm; some time later Ibn Iraq entered their service at Gurganj, first under Ali ibn Ma’mun and then under his successor Abu al-Abbas Ma’mun. Al-Biruni, who had left Khwarazm because of the civil strife, resumed working with his teacher from around 1004, and Ibn Iraq dedicated about a dozen of his treatises to him.

In 1017 Mahmud of Ghazna conquered Khwarazm, and both scholars followed the sultan to Ghazna. Ibn Iraq appears to have spent the rest of his life at Mahmud’s court.

He wrote roughly twenty-five works, seven on mathematics and eighteen on astronomy. His main contribution lies in spherical trigonometry: he wrote a commentary on Menelaus’ “Spherics”, improved its propositions and gave proofs of the spherical law of sines, and he used the polar triangle to find the sides of a triangle from its angles. He reduced the construction of a regular heptagon to a cubic equation and solved it with conic sections. His principal astronomical work, the “Shah’s Almagest”, is lost; several treatises on making and using the astrolabe survive.

The exact date of his death is unknown: in a treatise written in 427 AH (1035/36), al-Biruni already speaks of his teacher as deceased. His death is therefore usually placed around 1036, near Ghazna, in present-day Afghanistan.