(; Abusahl Bijan-e Koohi) was a Persianal-Qūhī, Abu Sahl Wayjan ibn Rustam (c. 940-c. 1000) mathematician, physicist and astronomer. He was from Kuh (or Quh), an area in Tabaristan, Amol, and flourished in Baghdad in the 10th century. He is considered one of the greatest geometers, with many mathematical and astronomical writings ascribed to him.Suter, Die Mathematiker und Astronomen der Araber (75-76, 1900). In his treatise On Rising Times, he wrote that he had also investigated astronomy as well as centers of gravity and optics. His Perfect Compass, for example, represented a step beyond Ibn Sina’s pointwise constructions of conic sections and described an instrument al-Qūhī characterized as useful for drawing these sections on sundials and astrolabes. (PDF version)
Al-Qūhī was the leader of the astronomers working in 988 at the observatory built by the Buwayhid amir Sharaf al-Dawla in Badhdad. He wrote a treatise on the astrolabe in which he solves a number of difficult geometric problems.
In mathematics he devoted his attention to those Archimedean and Apollonian problems leading to equations higher than the second degree. He solved some of them and discussed the conditions of solvability. For example, he was able to solve the problem of inscribing an equilateral pentagon into a square, resulting in a fourth degree equation.Jan Hogendijk (1984) "al-Kuhi's construction of an equilateral pentagon in a given square", Zeitschrift für Gesch. Arab.-Islam. Wiss. 1: 100-144; correction and addendum Volume 4, 1986/87, p.267 He also wrote a treatise on the "perfect compass", a compass with one leg of variable length that allows users to draw any conic section: straight lines, circles, ellipses, parabolas and hyperbolas.Jan Hogendijk (2008) "Two beautiful geometrical theorems by Abu Sahl Kuhi in a 17th century Dutch translation", Ta'rikh-e Elm: Iranian Journal for the History of Science 6: 1-36 It is likely that al-Qūhī invented the device. Alt URL Reviews: Seyyed Hossein Nasr (1998) in Isis 89 (1) pp. 112-113 ; Charles Burnett (1998) in Bulletin of the School of Oriental and African Studies, University of London 61 (2) p. 406 .John Lennart Berggren, Hogendijk: The Fragments of Abu Sahl al-Kuhi's Lost Geometrical Works in the Writings of al-Sijzi, in: C. Burnett, J.P. Hogendijk, K. Plofker, M. Yano (eds): Studies in the History of the Exact Sciences in Honour of David Pingree, Leiden: Brill, 2003, pp. 605–665
al-Qūhī proposed that the weight of bodies varies with their distance from the center of the Earth.Mohammed Abattouy (2002), "The Arabic Science of weights: A Report on an Ongoing Research Project", The Bulletin of the Royal Institute for Inter-Faith Studies 4, p. 109-130 His theory of dynamics is essentially Aristotelian, though he disagreed with Aristotle in some important points.
The correspondence between al-Qūhī and Abu Ishaq al-Sabi, a high civil servant interested in mathematics, has been preserved.Berggren: "The correspondence of Abu Sahl al-Kuhi and Abu Ishaq al-Sabi: a translation with commentaries", J. Hist. Arabic Sci., volume 7, 1983, pp. 39-124.M. Steinschnieder, Lettere intorno ad Alcuhi a D. Bald. Boncompagni (Roma, 1863)
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