FAZ˜LNAYRÈZÈ, ABU'L ¿ABBAÚS b. H®a@tem, mathematician and astronomer (fl. 900 C.E.). His family originated from Nayr^z/N^r^z, a small town near Shiraz. Almost nothing is known of his personal life. The fact that he dedicated several works to the caliphs al-Mo¿tazµed (279-89/892-902) and al-Moktaf^ (289-95/902-8) and also the dedication notice to a vizier in his Resa@la f^ aháda@t¯ al-jaww, suggest that he, already a mature scholar, spent some time at the caliphal court in Baghdad around the turn of the 10th century (Sezgin, GAS VII, p. 330).

Nayr^z^'s most important work on mathematics is his ˆarhá keta@b Oql^des fi'l-osáu@l, a commentary on Euclid's Elements (Sezgin, GAS V, p. 284), in which he quotes extensively from Simplicius' commentary on the definitions and postulates and from Heron's commentary on the propositions. Unfortunately, only the commentary on books 1-6 survive in Arabic; some lacunae are filled in the Latin translation by Gerard of Cremona of the commentary on books 1-10. One of Nayr^z^'s most interesting contributions to the study of Euclid was his citation of the discussions of the fifth postulate, i.e., that on parallel lines, by Ag@a@n^s (convincingly identified with Agapius by Sabra, 1974, X, p. 6) and Simplicius (see Sabra, 1969). Nayr^z^, basing himself on Ag@a@n^s, also wrote an independent treatise called Resa@la f^ baya@n al-mosáa@dara al-maæhu@ra (Sezgin, GAS V, pp. 284-85).

Ebn al-Nad^m (ed. Flügel, p. 279) ascribes to Nayr^z^ two sets of astronomical tables, a Keta@b al-z^j al-kab^r and a Keta@b al-z^j al-sáag@^r (Kennedy, p. 131, no. 46 and p. 135, no. 75; see Sezgin, GAS VI, p. 192). Ebn al-Qeftá^ (p. 254) informs us that the former follows the Sendhend—that is, the Islamic adaptation of Indian astronomy best known in the 9th century through the Keta@b al-z^j al-Sendhend of Moháammad b. Mu@sa@ K¨úa@razm^. The Keta@b al-z^j al-kab^r, then must be the work referred to by S®a@¿ed Andalos^ (tr. p. 112) and by Abu@ Rayháa@n B^ru@n^ (q.v.) in his Keta@b f^ efra@d al-maqa@l f^ amr al-záela@l (B^ru@n^, Rasa@÷el, pp. 39, 51-53, 94), where Nayr^z^ is associated in his treatment of gnomonics with such followers of the Sendhend as Ebra@h^m b. H®ab^b Faza@r^, Ya¿qu@b b. T®a@req, Moháammad K¨úa@razm^, Ahámad b. ¿Abd-Alla@h H®abaæ Marvaz^, and Abu@ Ma¿æar Balkò^ (q.v.). If this Z^j al-kab^r is the one consistently referred to by B^ru@n^, as seems plausible, then it was dedicated to al-Mo¿tazµed, since once in al-Qa@nu@n al-mas¿u@d^ (II, pp. 675-76) B^ru@n^ refers to the motion of the solar apogee expounded by Nayr^z^ in the third maqa@la of his al-Z^j al-mo¿tazµed^ (for other references to Nayr^z^'s Z^j by B^ru@n^, see B^ru@n^'s al-Qa@nu@n al-mas¿u@d^ II, pp. 581-85, 591, 595, 604, 952-54; Keta@b tahád^d, p. 196; and Keta@b maqa@l^d, pp. 132-33). Also Ebn Yu@nos (pp. 60-65, 68-75, 118-21, 160-61, 164-65) frequently criticizes Nayr^z^ for mostly minor errors, especially those consequent on his blindly accepting the results of Yaháya@ b. Ab^ Mansáu@r T®abar^ and his al-Z^j al-momtaháan al-rasáad^ al-ma÷mu@n^. Perhaps in al-Z^j al-sáag@^r Nayr^z^ became a partisan of al-Z^j al-momtaháan. It is not clear to which z^j might be attributed Nayr^z^'s adoption under the name al-jadwal al-ja@me¿ of H®abaæ's jadwal al-taqw^m and his use of them in the solution of problems in spherical trigonometry described at length by Abu@ Nasár b. ¿Era@q (pp. 30-58). Like the two z^jes, Nayr^z^'s Tafs^r al-keta@b al-majestÂ^, a commentary on Ptolemy's Almagest, is lost (Ebn al-Nad^m, ed. Flügel, p. 268; Ebn al-Qeftá^, p. 254; Sezgin, GAS VI, p. 192). It is, however, often referred to by B^ru@n^ (AÚtòa@r, tr. Sachau, pp. 139-40; idem, Tahád^d, p. 95; idem, Qa@nu@n II, pp. 779-80; idem, Keta@b maqa@l^d, pp. 148-51), and is mentioned by Nezáa@m^ ¿Aru@zµ^ (Ùaha@r maqa@la, ed. Qazv^n^, text, p. 88) as the best commentary on the Almagest.

Unlike these three major works, Nayr^z^'s minor works on astronomy (Sezgin, GAS VI, p. 192) for the most part are extant. His Keta@b le'l-¿amal be'l-astáorla@b al-koraw^, said to be the best on the subject, and Resa@la f^ samt al-qebla have been translated into German.

Nayr^z^ composed a number of works on astrology. His commentary on Ptolemy's Quadripartitum (Keta@b al-arba¿a; Ebn al-Nad^m, ed. Flügel, p. 279; Ebn al-Qeftá^, p. 98; Sezgin, GAS VII, p. 44) is lost, nor is it at all certain that B^ru@n^'s quotation from Nayr^z^ in his Maqa@la f^ sayr sahmay al-sa¿a@da (pp. 24-27) is, as Sezgin states, from this commentary. B^ru@n^'s other citation of an astrological opinion held by Nayr^z^ (Tafh^m, sec. 389, pp. 236-37) is from his equally non-extant Keta@b al-mawa@l^d. There does survive from Nayr^z^'s pen an unpublished Maqa@la f^ hawa@det¯ al-qera@na@t wa'l-kosu@fa@t al-da@lla ¿ala'l-fetan wa'l-háoru@b. . . (Sezgin, GAS VII, p. 156).

Nayr^z^ is also the author of two works dealing more or less with meteorology. The first is philosophical and mathematical, entitled Keta@b f^ ma¿refat a@la@t to¿lamo beha@ ab¿a@d al-aæya@÷ al-æa@kòesáa fi'l-hawa@÷ wa'llat^ ¿ala@ bas^tá al-¿arzµ wa ajwa@r al-awd^a wa'l-a@ba@r wa ¿oru@zµ al-anha@r (Sezgin, GAS VII, pp. 268-69); the other work, entitled Resa@la f^ aháda@tò al-jaww, is more astrological. According to Ebn al-Nad^m (p. 279) and Ebn al-Qeftá^ (p. 254), the latter was dedicated to al-Mo¿tazµed, but the Istanbul manuscript examined by Sezgin (GAS VII, p. 330) refers only to an unnamed vizier.

Bibliography (for cited works not given in detail, see "Short References"): Editions and translations of Nayr^z^'s works: (1) Fasál f^ takòtá^tá al-sa@¿a@t al-zama@n^ya f^ koll qobba wa f^ qobba yosta¿mal laha@, published in al-Rasa@÷el al-motafarreqa fi'l-hay÷a le'l-motaqaddem^n wa mo¿a@sáer^n al-B^ru@n^, Hyderabad, 1948. (2) Keta@b le'l-¿amal be'l-astáorla@b al-koraw^, tr. H. Seemann as Das kugelformige Astrolab nach den Mitteilungen von Alfons X von Kastilien und den vorhandenen arabischen Quellen, Abh. zur Geschichte der Naturwissenschaften und der Medizin 8, Erlangen, 1925, pp. 32-40; reprod. in F. Sezgin, ed., Arabische Instrumente in orientalistischen Studien IV, Frankfurt, 1991, pp. 359-431 (Seemann's tr. pp. 394-402). (3) Resa@la f^ samt al-qebla, tr. C. Schoy as "Abhandlung von al-Fadál b. H®a@tim an-Nair^z^. Über die Richtung der Qibla," Sitzungsberichte der Bayerischen Akademie der Wissenschaften, Math.-phys. Kl., 1922, pp. 55-68. (4) ˆarhá keta@b Oql^des fi'l-osáu@l, first six books ed. with Latin translation by R. O. Besthorn and J. L. Heiberg as Codex Leidensis 399 1, 3 parts in six fascicles (fasc. 1-3/1, Leiden, 1893-1910; 3/2, ed. G. Junge, J. Raeder, and W. Thomson, Leiden, 1932); books 1-10 in Gerard of Cremona@'s Latin translations, publ. by M. Curtze as Anaritii in decem libros priores elementorum Euclidis commentaria, Leipzig, 1899; new ed. of books 1-4 by P. M. J. E. Tummers, Nijmegen, 1994.

Sources and studies. Abu@ Nasár Mansáu@r b. ¿Al^ b. ¿Era@q, Resa@la f^ bara@h^ a¿ma@l jadwal al-taqw^m f^ z^j H®abaæ al-háa@seb, in idem, Rasa@÷el Ab^ Nasár Mansáu@r b. ¿Era@q ela@ al-B^ru@n^, Hyderabad, 1948, treatise iv. Abu@ Rayh®a@n B^ru@n^, al-Tafh^m le awa@÷el sáena@¿at al-tanj^m, ed. and tr. R. R. Wright as The Book of Instruction in the Elements of the Art of Astrology, London, 1934. Idem, al-Qa@nu@n al-mas¿u@d^ fi'l-hay÷a wa'l-noju@m, ed. S. H. Baran^, 3 vols., Hyderabad, 1945-56. Idem, Rasa@÷el al-B^ru@n^, Hyderabad, 1948. Idem, Keta@b tahád^d neha@yat al-ama@ken, ed. P. G. Bulgakov, Cairo, 1964. Idem, Maqa@la f^ sayr sahmay al-sa¿a@da wa'l-g@ayb, ed. and tr. with commentary, F. I. Haddad, D. Pingree, and E. S. Kennedy as "Al-B^ru@n^'s Treatise on Astrological Lots," Zeitschrift for Geschichte der Arabisch-Islamischen Wissenschaft 1, 1984, pp. 9-54. Idem, Keta@b maqa@l^d ¿elm al-hay÷a, ed. M. T. Debarnot, Damascus, 1985. Ebn al-Qeftá^, Ta÷r^kò al-háokama@÷, ed. J. Lippert, Leipzig, 1903. Abu'l-H®asan ¿Al^ Ebn Yu@nos, Z^j al-kab^r al-háa@kem^, ed. and tr. C. Caussin as "Le livre de la grande table Hake‚mite," Notices et extraits des manuscrits de le Bibliotheàque nationale 7, 1804, pp. 16-240. T. Heath, A History of Greek Mathematics, 2 vols., Oxford, 1921, II, pp. 228-30 (Ag@a@n^s, whom Heath identifies with Geminus) and pp. 309-14 (Heron). Kh. Jouiche, La the‚orie des paralle‚les en pays d'Islam, Paris, 1986, pp. 127-37. E. S. Kennedy, "A Survey of Islamic Astronomical Tables," Transactions of the American Philosophical Society, N.S. 46, 1956, pp. 121-77. A. Qorba@n^, R^a@zµ^da@na@n-e ^ra@n^ az K¨úa@razm^ ta@ Ebn S^na@, Tehran, 1350 ˆ./1971, pp. 73-85. A. I. Sabra, "Simplicius's Proof of Euclid's Parallels Postulate," Journal of the Warburg and Courtauld Institutes 32, 1969, pp. 1-24. Idem, Dictionary of Scientific Biography, New York, 1974, X, pp. 5-7. Qa@zµ^ Abu'l-Qa@sem S®a@¿ed b. Ahámad Andalos^, Keta@b tÂabaqa@t al-omam, ed. H. Bu@ ¿Alwa@n, Beirut, 1985; tr. R. Blacheàres, as Cate‚gories des nations, Paris,1935.

(DAVID PINGREE)