GUŠYĀR (Arabicized Kušyār) GILĀNI, ABU’L-ḤASAN B. LABBĀN b. BĀŠAHRI, an astronomer and mathematician from Gilān, whence his nesba Jili/Gilāni (fl. late 4th/late 10th-early 11th cent.). Next to nothing is known of his life; even his dates can only be determined approximately. Though it has been stated (Sezgin, GAS V, p. 343) that he wrote his al-Zij al-jāmeʿ in 353/964, the catalogue of stars in it is for 1293 of the Era of Alexander/982 (Kennedy, 1956, p. 157), and the manuscript of the Zij at Alexandria was copied from a manuscript that Gušyār himself transcribed in 393/1002-3 (see Mazahéri, p. 41; Sezgin, GAS VI, p. 248). Since he is cited by Biruni (Ketāb fi efrād al-maqāl fi amr al-aẓlāl, see below) and by Neẓāmi ʿArużi (Čahār maqāla, ed. Qazvini, text, p. 89), Gušyār’s works must have become authoritative by the end of the first quarter of the 11th century.

Works. Mathematics (Sezgin, GAS V, pp. 343-45): Gušyār’s most significant contribution to mathematics was his Ketāb fi oṣul ḥesāb al-Hend. A manuscript (Meqāt 213) in the Dār al-kotob al-meṣriya in Cairo claims to contain the first chapter (maqāla) out of an original four, but the Istanbul manuscript (Aya Sofya 4857, fol. 263v-78; see Krause, pp. 472-73) says that the work contains only two maqālas. There is a facsimile of the Aya Sofya copy together with an English translation in Levey and Petruck (pp. 44-105) and a French translation in Aly Mazahéri. The first maqāla is on using “Hindu” numerals in performing the operations of adding, subtracting, multiplying, and dividing decimal numbers and in taking their square and cube roots, the second on the same operations using sexagesimal numbers. The first maqāla was translated into Hebrew and commented on by Shōlōm ben Joseph ʿAnābi in Istanbul in about 1450 or 1460. There also exists from Gušyār’s hand an ʿOyun al-oṣul fi’l-ḥesāb in a manuscript kept at the Central Library of the University of Tehran (Dānešgāh 2092, fols. 30-35, facs. reprod. in Qorbāni, pp. 184-94).

Astronomy (see Sezgin, GAS VI, pp. 246-49): Gušyār is the author of two astronomical tables (zij). The more important one is al-Zij al-Jāmeʿ in four chapters (maqā-lāt): the canons, the tables, theoretical astronomy, and proofs (Kennedy, 1956, p. 125, no. 9, with an abstract of the Berlin copy on pp. 156-57; King, p. 45). The preface was translated into German by Eilhard Wiedemann (Gesammelte Schriften II, pp. 894-95). A Resāla fi al-abʿād wa al-ajrām, apparently extracted from this zij, was published as text number four in the Rasāʾel al-motafarreqa fi’l-hayʾa (see Sezgin, GAS VI, p. 248), while Gušyār’s description of the chronological tables was discussed by Ludwig Ideler (II, pp. 623-33) and his two sine tables were described by Carl Schoy (pp. 395-96). Other technical aspects of Gušyār’s tables have been investigated by John Berggren (spherical trigonometry) and Glen van Brummelen (planetry tables). The true solar longitude table analyzed by Berno van Dalen is not with certainty attributed to Gušyār. Al-Zij al-Jāmeʿ is cited several times by Biruni in his Ketāb fi efrād al-maqāl fi amr al-aẓlāl (treatise number two in the Rasāʾel al-Biruni, p. 42 ll. 15-19, p. 52 ll. 8-11, p. 57 l. 13-p. 58, l. 1, and p. 62, ll. 13-16; for tr. and comm. see Kennedy, 1976). Aṯir-al-Din Mofażżal b ʿOmar Abahri wrote a compendium of astronomy which contains excerpts on cosmology from Gušyār (see Krause, p. 493); this is presumably based on “al-Bāb al-mofrad fi jawāmeʿ ʿelm al-hayʾa” from al-Zij al-jāmeʿ (see King, p. 45). This zij was translated into Persian by Moḥammad b. ʿOmar b. Abi Ṭāleb Tabrizi in 483/1090 during the reign of Sultan Malekšāh Sal-juqi (465-85/1072-92; Storey, II, p. 43; the sole known manuscript contains only the first maqāla). There may be a commentary on al-Zij al-jāmeʿ by Moḥammad b. ʿAbd-al-Karim Daḵāli in a manuscript in Tunis.

Much less well known is al-Zij al-bāleḡ (see Kennedy, Survey, p. 125, no. 7). All that survives seems to be a fragment at Bombay (Sezgin, GAS VI, p. 248) and perhaps some tables mixed up in copies of Gušyār’s other zij.

There exist numerous copies of Gušyār’s Ketāb fi ṣanʿat al-asṭorlāb wa’l-ʿamal behe (Sezgin, GAS VI, pp. 248-49), but it has never been studied.

Finally, Ẓahir-al-Din ʿAli Bayhaqi (Tatemma ṣewān al-ḥekma, p. 43; Wiedemann, 1970, I, p. 650; Meyerhof, pp. 157-58) attributes to Gušyār a work called Eṣlāḥ taʿdil al-merriḵ, about which nothing more is known.

Astrology (see Sezgin, GAS VII, pp. 182-83): Gušyār’s principle treatise on astrology was his Ketāb al-modḵal fi ṣenāʿat aḥkām al-nojum, also known as the Ketāb al-mojmal fi oṣul ṣenāʿat al-nojum. It consists of four maqālas, modeled on and sometimes closely following the four books of Ptolemy’s Apotelesmatika. It was composed in about 361/992, the date for which the coordinates of the thirty significant fixed stars are given (Storey, II, p. 42; Yano, 1984, p. 67). Michio Yano has edited the Arabic text with an English translation (Tokyo, 1997); the first chapter of the first maqāla with an English translation has been published seperately (Yano, “Apology”). It is to be noted that in it Gušyār refers to his two zijes by name as separate works already completed. Yano has also edited the Chinese translation, which was made in 1383 by Wu Potsung. The Mojmal al-oṣul was commented on by Moḥammad b. Abi ʿAbd-Allāh Sanjar Kamāli in 703/1303-04 (see Storey, II, p. 65), and there exist both a Persian translation by Moḥammad b. Abi Ṭāleb Monajjem Tabrizi and a Turkish translation by Moḥammad b. Ḵosrow Miḵāliji (Storey, II, pp. 42-43; Sezgin, GAS VII, p. 183). Neẓāmi ʿArużi recommended the Mojmal al-oṣul to anyone aspiring to be an astrologer (Čahār maqāla, ed. Qazvini, text, p. 89, tr. p. 796).

Gušyār wrote three other tracts on astrology, namely Resālat dalālāt al-kawākeb, Ketāb al-qerānāt, and Ketāb al-eḵtiārāt on catarchic astrology (Sezgin, GAS VII, p. 183). None of these have been studied yet.



Ẓahir-al-Din ʿAli Bayhaqi, Tatemma ṣewān al-ḥekma, ed. M. Šafiʿ, Lahore, 1351/1932.

J. L. Berggren, “Spheric Trigonometry in Kushyār b. Labbān’s Jāmiʿ Zīj,” in From Deferent to Equant, New York, 1987, pp. 15-34.

Abu Rayḥān Biruni, Rasāʾel al-Biruni, Hyderabad, 1948.

Brockelmann, GAL I, pp. 222-23; Supp., I, pp. 397-98.

Čahār maqāla, ed. Qazvini, comm., pp. 261-73; tr. E. G. Browne as “The Chahár Maqála (Four Discourses) of Nidhámí-i ʿArúḏi-i-Samarqandi,” JRAS, 1899, pp. 613-63, 757-845; rev. ed. with abridged tr. of M. Qazvini’s notes, London, 1921.

ʿA. Eqbāl, “Yak ḥekāyat-e ḥakimāna rājeʿ ba Gušyār Monajjem,” Āmuzeš o parvareš 14, 1323 Š./1944, pp. 169-71.

L. Ideler, Handbuch der mathematischen und technischen Chronologie, 2 vols., Berlin, 1826.

E. S. Kennedy, The Exhaustive Treatise on Shadows, 2 vols., Aleppo 1976.

Idem, A Survey of Islamic Astronomical Tables, Philadelphia, 1956.

D. A. King, A Survey of the Scientific Manuscripts in the Egyptian National Library, Winona Lake, Ind., 1986.

M. Krause, “Stambuler Handschriften islamischer Mathematiker,” Quellen und Studien, B 3, 1936, pp. 437-532.

M. Levey and M. Petruck, Kushyār ibn Labbān: Principles of Hindu Reckoning, Madison and Milwaukee, 1965.

A. Mazahéri, Les origines persanes de l’arithmétique, Nice, 1975.

M. Meyerhof, “ʿAli al-Bayhaqī’s Tatimmat Ṣiwān al-Ḥikma,” Osiris 8 1948, pp. 122-217.

M. Moʿin, “Gušyār Deylami,” Nāma-ye Farhang 1, 1330 Š./1952, pp. 201-4 (comm. by I. Afšār, Mehr 8, 1331 Š./1952, p. 309); repr. in idem, Majmuʿa-ye maqālāt, ed., M. Moʿin, 2 vols., Tehran, 1364-67 Š./1985-87, II, pp. 419-26.

M.-R. Naṣiri, ed., Hezāra-ye Gušyār Gili, Rašt, 1367 Š./1988.

A. Qor-bāni, Riāżidānān-e irāni az-Ḵᵛārazmi tā Ebn-e Sinā, Tehran, 1350 Š./1971, pp. 169-94.

Rasāʾel al-motafarreqa fi al-hayʾa, Hyderabad, 1948.

A. S. Saidan, “Kushyār ibn Labbān,” in Ch. C. Gillispie, ed., Dictionary of Scientific Biography, 14 vols., New York, 1970-76, VII, pp. 531-33.

C. Schoy, “Beiträge zur arabischen Trigonometrie,” Isis 5, 1923, pp. 364-99.

H. Suter, Die Mathematiker und Astronomen der Araber und ihre Werke, Leipzig, 1900, pp. 83-84, no. 192.

G. Van Brummelen, “Mathematical Methods in the Tables of Planetry Motion in Kušyār ibn Labbān’s Jāmiʿ Zīj,” Historia Mathematica 25, 1998, pp. 265-80.

B. Van Dalen, “A Table for the True Solar Longitude in the Jāmiʿ Zīj,” in Ad Radices, Stuttgart, 1994, pp. 171-90.

E. Wiedemann, Aufsätze zur arabischen Wissenschaftsgeschichte, 2 vols., Hildesheim and New York, 1970. Idem, Gesammelte Schriften, 3 vols., Frankfurt, 1984.

M. Yano, “Kushyār ibn Labbān’s Book on Astrology,” Bulletin of the International Institute for Linguistic Sciences 5/2, 1984, pp. 67-89.

Idem, “Apology for Astrology by Kušyār ibn Labbān,” Bulletin of the International Institute for Linguistic Sciences 17/2, 1996, pp. 221-34.

Idem, Kušyār Ibn Labbān’s Introduction to Astrology, Tokyo, 1997.

(David Pingree)

Originally Published: December 15, 2002

Last Updated: February 24, 2012

This article is available in print.
Vol. XI, Fasc. 4, pp. 407-408