# Abū Sahl al-Qūhī

Abū Sahl Wayjan ibn Rustam al-Qūhī (al-Kūhī; Persian: ابوسهل بیژن کوهیAbusahl Bijan-e Koohi) was a Persian[1] 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 Muslim geometers, with many mathematical and astronomical writings ascribed to him.

Engraving of al-Quhi's perfect compass to draw conic sections

He was the leader of the astronomers working in 988 AD at the observatory built by the Buwayhid 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 a regular pentagon into a square, resulting in an equation of fourth degree.[2] He alse wrote a treatise on the "perfect compass", a compass with one leg of variable length that allows to draw any conic section: straight lines, circles, ellipses, parabolas and hyperbolas. It is likely that al-Quhi invented the device.[3]

Like Aristotle, al-Quhi proposed that the heaviness of bodies vary with their distance from the center of the Earth.[4]

The correspondence between al-Quhi and Abu Ishaq al-Sabi, a high civil servant interested in mathematics, has been preserved.[5]

## Notes

1. ^ al-Quhi, Abu Sahl Wayjan ibn Rustam (c. 940-c. 1000)
2. ^ Hogendijk: "al-Kuhi's construction of an equilateral pentagon in a given square", Zeitschrift für Gesch. Arab.-Islam. Wiss., Volume 1, 1984, pp. 100-144; correction and addendum Volume 4, 1986/87, p.267
3. ^
4. ^ 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
5. ^ 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.

## References

• Rashed, Roshdi (1996). Les Mathématiques Infinitésimales du IXe au XIe Siècle 1: Fondateurs et commentateurs: Banū Mūsā, Ibn Qurra, Ibn Sīnān, al-Khāzin, al-Qūhī, Ibn al-Samḥ, Ibn Hūd. London. 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.
• M. Steinschnieder, Lettere intorno ad Alcuhi a D. Bald. Boncompagni (Roma, 1863)
• Suter, Die Mathematiker und Astronomen der Araber (75-76, 1900).
• Jan Hogendijk: 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 (2008), 1-36
• 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