Al-Kh?zin, Ab? Ja‘far Mu?ammad Ibn Al-H?asan Al-Khur?s?n?

(d 961/971)

astronomy, mathematics.

Al-Kh?zin, usually known as Ab? Ja?far al-Kh?zin, was a Sabaean of Persian origin. The Fihrist calls him al-Khur?n??, meaning from Khur?s?n, a province in eastern Iran. He should not be confused with A?bd al-Rahm?an al-Kh?zin? (ca. 1100), the probable author of Kit?b al-??t al?ajiba al-ra?diyya, on obsertvation instruments, often attributed to al-Kh?zin. (E. Wiedemann attributed this work, inconsistently, to al-Kh?zin in the Enzyklopaedie des Islam, II [Leiden-Leipzig, 1913], pp. 1005-1006, and to al-Kh?zini? in Beiträge, 9 [1906], 190. De Slane confounded these two astronomers in his translation of Ibn Khald?’s Prolegomena, I, 111.

Ab? Ja far al-Kh?zin, said to have been attached to the court of the Buwayhid ruler ruler al-Dawla (932-976) of Rayy, was well known among his contemporaries. In particular his Zij al-?saf?ih (“tables of the Disks [of the astrolabe]”0, which Ibn al-Qift? calls the best work in this field, if often cited. it may be related to manuscript “Liber de sphaera in plano describenda,” in the Laurentian library in Florence (Pal,-Med. 271).

Al-B??n?s Ris?la fi fihrist kutub Muhammad b. Zakariyy? al-R?zi (“Bibliography”) of 1036 lists several texts (written in cooperation with Ab? Na?r Man??r ibn ’Ir?aq), one of which is Fi tash?h m? waqa’a li Abi Ja?far al-Kh?zin min al-shaw fi zäj al-saf? ih (“On the Improvement of What Ab? Ja?far Neglected in His Tables of the Disks”). In Tamhid al-mustaqarr li-tahq?q man? al-mamarr, (“On Transits” ), al-B??n? criticizes Ab? Ja’ al-Kh?;zin for not having correctly handled two equations defining the location of a planet but remarks that the Z? al-saf?ih is correct on this matter. Ab? Ma’shar that. unlike manyolthers, he had fully determined the truth about the planets, which he had included in his Z?j. Ab? Jafar al-Kh?zin regarded this work as a mere compilation. Al-Bi?r?n? compared Ab? Ja?far al-Kh?zin very favorably with Ab? Ma’shar, and in his al-?th?r al-b?qiya min al-qu?n al-kh?liya (“Chronology of Ancient Nations”) he refers to Zij al saf? ih for a good explanation of the progressive and retrograde motion of the sphere.

An anonymous manuscript in Berlin (Staats-bibliothek, Ahlwardt Cat. No. 5857) contains two short chapters on astronomical instruments from a work by Ab? Jafar al-Kh?zin, probably the Zij al-saf? ih. The MS Or. 168 (4) in Leiden by Ab?’l-J?d quotes Ab? Ja?far al-Kh?zin’s remark in Zij al-saf? ih that he would be able to compute the chord of an angle of one degree if angle trisection were possible.

In Kit?b fi isi’?, dedaling with constructions of astrolabes, al-Bi?n? cites Ab? Ja‘far al-Kh?in’s work “Design of the Horizon of the Ascensions for the Signs of the Zodiac.” And in his Chronology he describes two methods for finding the Signum Muharrami (the day of the week on which al-Muharram, the first month of the Muslim year, begins) described by Ab? Ja?far al-Kh?zin in al-Madkhal al-kab?r f?ilm al-nuj?m (“Great Introduction to Astronomy”). Neither work is extant.

Also treated in al-B??n?’s Chronology is Ab? Ja?far al-Kh˜zin’s figure, different from the eccentric sphere and epicycle, in which the sun’s distance from the earth is always the same, independent of the rotation. This treatment gives two isothermal regions, one northern and one southern. Ibn Khald?n gives a precise exposition of Ab? Ja?far al-Kh?zin’s division of the earth into eight climatic girdles.

Al-Kharaq? (d. 1138/1139), in al-Muntah?, mentions Ab? Ja?far al-Kh?zin and Ibn al-Haytham as having the right understanding of the movement of the spheres. This theory was perhaps described in Ab? Ja?far al-Kh?zin’s Sirr al-’?lamin (not extant).

In Tahd? nih?y?t al-am?kin. . ., al-B??ni criticizes the verbosity of Ab? Ja‘far al-Kh?zin’s commentary on the Almagest and objects to Ibr?h?m ibn S?n?n and Ab? Jafar al-Kh?zin’s theory of the variation of the obliquity of the ecliptic; al-B??n? himself considered it to be constant. The obliquity was measured by al Harawi and Ab? Jafar al-Kh?zin at Rayy (near modern Teheran) in 959/960, on the order of Abu’l Fa?l ibn al-’Amid, the vizier of Rukn al-Dawla. The determination of this quantity by “al-Kh?zin and his collaborators using a ring about 4 meters” is recorded by al-Nasawi.

Ab? Ja?far al-Kh?zin was, according to Ibn al Qif?i, an expert in arithmetic, geometry, and tasy?r (astrological computastions based on planetary trajectoris). According to al-Khayy?mi, he used conic sections to give the first solution of the cubic equation by which al-M?h?n? represented Archimedes’ problem of dividing a sphere by a plane into two parts whose volumes are in a given ratio (Sphere and Cylinder II, 4) and also gave a defective proof of Euclid’s fifth postulate.

Ab? Ja?far al-Kh?zin wrote a commentary on Book X of the Elements, a work on numerical problems (not extant), and another (also not extant) on spherical trigonometry, Ma??lib juziyya mail almuy?l al-juz iyya wa ‘l-ma??li’ fi’l0kura al-mustaqima From the latter, al-??s?, in Kit?b šakl al-qa??? (“On the Transversal Figure”), quotes a proof of the sine theorem for right spherical triangles. Al-T?s? also added another proof of Hero’s formula to the Verba filiorum of the Banu? M?s? (in Majm? al-rasa?il, II [Hyderabad, 1940]), attributing it to one al-Kh?zin. This proof, closer to that of Hero than the proof by the Ban? M?sã, and in which the same figure and letters are used as in Hero’s Dioptra, is not found in the Latin editions of the Verbafiliorum.

BIBLIOGRAPHY

I. Original Works. Not many of al-Kh?zin’ writings are extant. The available MSS are listed in C. Brockelmann, Geschichte der arabischen Literatur, Supplementband, I (Leiden, 1943), 387. The commentary on Book X of the Elements is discussed by G. P. Matvievskaya in Uchenie o chisle na srednevekovom Blizhnem i Srednem Vostgoke (“Studies About Number in the Medieval Near and Middle East”; Tashkent, 1967), ch. 6.

II. Secondary Literature. Biographical and bibliographgical references can be found in Ya’qub al-Nadim, al-Fihrist, G. Glügel, ed. (Leipzig, 1871-1872), pp. 266, 282; Ibn al-Qif??, Ta‘rikh-al-hukam?, J. Lippert, ed. (Leipzig, 1903), 396; H?jj? Khalifa, Lexicon bibliographicum (repr. New York, 1964), I. 382, II, 584, 585, III, 595, VI, 170; H. Suter, Die Mathematiker und Astronomen der Araber ubd ihre Werke (Leipzig, 1900), p. 58, and Nachträge, p. 165; and A. Sayili, The Observatory in Islam (Ankara, 1960), pp. 103-104, 123, 126, which emphasizes the observations at Rayy. For Ab? Ja‘far al-Khaldün, Prolegomena I, M. de Slane, trans. (repr. Paris, 1938), p. 111; and al-Bi?n?, Chronology of Ancient Nations, C. E. Sachau, ed. (London, 1879), pp. 183, 249; On Transits, M. Saffouri and A. Ifram, trans. with a commentary by E. S. Kennedy (Beirut, 1959), pp. 85-87, and Tahd?d nih?y?t al-am?kin (Cairo, 1962), pp. 57, 95, 98, 101, 119.

M. Clagett, Archimedes in the Middle Ages, I, The Arabo-Latin Tradition (Madison, Wis., 1964), p. 353; and H. Suter, “über die Geometrie der Söhne des M?s? ben Sch?kir,” in Bibliotheca mathematica, 3rd ser., 3, no. 1 9190-20, p. 271, mention the proof of Hero’ formula. For the cubic equation of al-M?h?ni, see F. Woepcke, L’, algé du quadrilatére, A. Carathéodory, ed. (Constantino;le, 1891), pp. 148-151; for the fifth postulate, see G. Jacob and E. Wiedemann, “Zu ‘Omer-i-Chajjâm,” in Der Islam, 3 (1912), p. 56. Other articles by E. Wiedemann containing information on Ab? Ja?far al-Kh?zin are in Beiträge 60 (1920-1921) and 70 (1926-1927), of Sitzungsberichte der Physikalisch-Medizinischen Sozietät zu Erlangen. Now available in E. Wiedemann, Aufsätze zur arabischen Wissenchaftsgeschichte, II (Hidesheim, 1970), pp. 498, 503, 633.

Yvonne Dold-Samplonius