ABŪ SAHL VĪJAN B. ROSTAM KŪHĪ (also QŪHĪ), mathematician and astronomer. He was born ca. 330/940 at Kūh, which, according to Ebn al-Nadīm (Fehrest, pp. 283-84), was in the mountains of Māzandarān. He was well enough known as an astronomer and expert on observational instruments to be chosen, along with Aḥmad b. Moḥammad Seǰzī, Naẓīf b. Yomn the Greek, and Abu’l-Qāsem Ḡolām Zoḥal, to assist ʿAbd-al-Raḥmān Ṣūfī: They observed the sun’s declinations at the winter solstices (December 16) of 359/969 and 360/970 and at the summer solstice (June 17) of 360/970. The observations were made in Shiraz for the Buyid ruler of Fārs, ʿAżod-al-dawla. (See Bīrūnī, Taḥdīd al-amāken, ed. P. Bulgakov, Cairo, 1964, pp. 99-100; tr. J. Ali, Beirut, 1967, pp. 69-70; comm. by E. S. Kennedy, Beirut, 1973, pp. 42-43. See also A. Sayili, The Observatory in Islam, Ankara, 1960, pp. 104-07.)
In 378/988-89 Šaraf-al-dawla, who had secured his power by expelling his brother Ṣamṣām-al-dawla from Baghdad, asked Kūhī to observe the seven planets for him. The latter built an observatory in the garden of the royal palace in Baghdad; there he observed the summer solstice (June 16) and autumnal equinox (September 18) of 379/988. At the latter observation were present many officials and several prominent astronomers, including Abu’l-Wafāʾ Būzǰānī and Abū Ḥāmed Aḥmad Ṣāḡānī (Bīrūnī, Taḥdīd, pp. 100-01/69-70/43; Ebn al-Qefṭī, Taʾrīḵ al-ḥokamāʾ, ed. J. Lippert, Leipzig, 1903, pp. 351-54; Ebn al-ʿEbrī, Taʾrīḵ moḵtaṣar al-dowal, Beirut, 1958, p. 176; Sayili, Observatory, pp. 112-17). Apparently the observatory did not survive Šaraf-al-dawla’s death (Jomādā II, 379/September-October, 989); and Kūhī could not have accomplished much of his original program of planetary observations.
Kūhī’s greatest fame derives from his highly competent work in geometry, which he based on the writings of Euclid, Apollonius, and Archimedes. Particularly elegant are his solutions utilizing conic sections and the related “conic compass.” His works were admired and sought after by Seǰzī, Abū Naṣr Manṣūr, Bīrūnī, Ebn al-Hayṯam, Ḵayyāmī, and Naṣīr-al-dīn Ṭūsī. Although many of these works survive, they provide no further details on his life.
Ebn al-Nadīm lists nine titles, most of which are repeated by Ebn al-Qefṭī: 1. Ketāb marākez al-okarr (“Book of the centers of spheres”), unfinished; lost. 2. Ketāb al-oṣūl ʿalā naḥw ketāb Oqlīdos waʾllaḏī ḵaraǰa minho (“Book of elements in the manner of the book of Euclid and what results from it”), lost. 3. Ketāb al-barkār al-tāmm (“Book of the perfect compass”); ed. in F. Woepcke, “Trois traités arabes sur le compas parfait,” Notices et extraits des manuscrits 22/1, 1874, pp. 145-74; tr., pp. 68-111. 4. Ketāb ṣaṇʿat al-asṭorlāb (“Book on constructing an astrolabe”); extant with a commentary by Abū Saʿd al-ʿAlāʾ b. Sahl; unpublished. 5. Ketāb eḥdāṯ al-noqaṭ ʿalā al-ḵoṭūṭ (“Book of producing points on lines”), lost; cited by Abū Naṣr Manṣūr b. ʿErāq in Resāla fi’l-ǰawāb ʿan baʿż masāʾel al-handasa (text no. 10 in his Rasāʾel, Hyderabad, 1947, p. 2). 6. Ketāb ʿalā monṭeqīyīn fī tawālā al-ḥarakatayn enteṣār ā le Ṯābet b. Qorra (“Book according to the logicians concerning the continuity of two motions in defense of Ṯābet b. Qorra”), lost. 7. Ketāb marākez al-dawāʾer al-motamāssa ʿala’l-ḵoṭūṭ men ṭarīq al-taḥlīl dūna al-tarkīb (“Book of the centers of circles situated on lines by the method of analysis without construction”), extant in a ms. copied by Seǰzī; not published. See F. Woepcke, L’Algèbred’Omar Alkhayyāmī, Paris, 1851, p. 55, n. 8. Ketāb al-zīādāt ʿalā Aršemīdes fi’l-maqālat al-ṯānīya (“Book of additions to Archemides in the second treatise”), in Woepcke, L’Algèbre, pp. 103-14; cf. Ṭūsī, Taḥrīr al-kora wa’l-osṭowāna, work no. 5 in his Rasāʾel II, Hyderabad, 1359/1940, p. 115. 9. Resāla fī esteḵrāǰ żeḷʿ al-mosabbaʿ fi’l-dāʾera (“Epistle on the derivation of the side of a heptagon in a circle”), addressed to ʿAżod-al-dawla. Facsimile of the Cairo ms. with tr. in Y. Samplonius, “Die Konstruktion des regelmässigen Siebenecks nach Abu Sahl al-Qūhī Waiğan ibn Rustam,” Janus 50, 1963, pp. 227-49.
Ebn al-Qefṭī adds: 10. Ketāb eḵrāǰ al-ḵaṭṭayn ʿalā nesba (“Book of the discovery of two lines in a [given] ratio”), extant, not published. A number of other works are not listed by either bibliographer: 11. Resāla fī ʿamal moḵammas motasāwī al-ażlāʿ fī morabbaʿ maʿlūm (“Epistle on constructing an equilateral pentagon in a given quadrilateral”), unpublished. 12. Resāla fī esteḵrāǰ mešāḥat al-moǰassam al-mokāfī (“Epistle on the derivation of the area of a paraboloid”), printed as work no. 6 in the Rasāʾel al-motafarreqa fi’l-hayʾa, Hyderabad, 1948; tr. in H. Suter, “Die Abhandlungen Thābit b. Ḳurras und Abū Sahl al-Kūhīs über die Ausmessung der Paraboloide,” Sitzungsberichte der Physikalisch-medizinischen Sozietät in Erlangen 48-49, 1916-17, pp. 213-21. 13. Resāla fī qesmat al-zāwīat al-mostaqīmat al-ḵaṭṭayn be ṯalāṯ a aqsām motasāwīa (“Epistle on the division of an angle into three equal parts”); ed. and tr. in A. Sayili, “Ebū Sahl el Kūhī’nin bir açiyi ūç eşit kisma bölme problemi için bulduğu çōzūm,” Belleten 26, 1962, pp. 693-700. See also idem, “The Trisection of the Angle by Abu Sahl Wayjan ibn Rustam al Kūhī (fl. 970-988),” Actes du Xe Congrès International d’Histoire des Sciences, Paris, 1964, I, pp. 545-46. This epistle is cited by Seǰzī; see Woepcke, L’Algèbre, pp. 117-19. 14. Resāla fī nesbat mā yaqaʿa bayn ṯalāṯ a ḵoṭūṭ men ḵaṭṭ wāḥed (“Epistle on the proportion between three lines from one line”), addressed to Šaraf-al-dawla; unpublished. 15. Ketāb eḵrāǰ al-ḵaṭṭayn men noqṭa ʿalā al-zāwīat al-maʿlūma be ṭarīq al-taḥlīl (“Book of discovering two lines from a point at a given angle by means of analysis”); unpublished, but see Woepcke, L’Algèbre, pp. 55-56, n. 16. Resāla fī maʿref a meqdār al-boʿd men markaz al-arż wa makān al-kawākeb allaḏī yanqażż be’l-layl (“Epistle on knowing the radius of the earth and the place at which a star falls in the night”), unpublished. 17. Ketāb al-masāʾel al-handasīya (“Book of geometrical questions”), unpublished. 18. Maqāla fī anna nesbat al-qoṭr elā al-moḥīṭ nesbat al-wāḥed elā ṯalāṯa wa sobʿ (“Treatise on the fact that the ratio of the diameter to the circumference is the ratio of one to 31/7”), unpublished. 19. Ketāb taqsīm al-kora be soṭūḥ mostawīya (“Book of the division of a sphere into equal surfaces”), unpublished. 20. Ketāb esteḵrāǰ samt al-qebla (“Book of the derivation of the azimuth of the qibla”), unpublished. 21. Resāla fī maʿref a mā yorā men al-samāʾ wa’l-baḥr (“Epistle on knowing what is seen of the sky and the sea”), unpublished. 22. Qawl ʿalā anna fi’l-zamān al-motanāhī ḥaraka ḡayr motanāhīya (“Report on the fact that [there can be] an unlimited motion in a limited time”); ed. and tr. A. Sayili, “Kūhī’nin sinirli zamanda sonsuz hareket hakkindaki yazisi,” Belleten 21, 1957, pp. 489-94; cf. idem, “A Short Article of Abū Sahl Waijan ibn Rustam al Qūhī on the Possibility of Infinite Motion in Finite Time,” Actes du VIIIe Congrès International d’Histoire des Sciences, Florence and Paris, 1958, I, pp. 248-49.
Abū Sahl also wrote various notes on Euclid (cf. above, no. 2) which survive; they are on the pseudo-Archimedean Lemmata. (See H. L. L. Busard, “Der Codex Orientalis 162 der Leidener Universitätsbibliothek,” Actes du XIIe Congrès International d’Histoire des Sciences, Paris, 1971, pp. 25-31.) He also wrote letters to Abū Esḥāq Ṣābeʾ (314-84/925-94).
See also Sezgin, GAS V, pp. 314-21.
Y. Dold-Samplonius in Dictionary of Scientific Biography XI, New York, 1975, pp. 239-41.
Originally Published: December 15, 1983
Last Updated: July 21, 2011
This article is available in print.
Vol. I, Fasc. 4, pp. 370-371
David Pingree, “ABŪ SAHL KŪHĪ,” Encyclopædia Iranica, I/4, pp. 370-371; an updated version is available online at http://www.iranicaonline.org/articles/abu-sahl-vijan-b (accessed on 31 January 2014).