Al-Khāzin, Abū Ja‘far Muḥammad Ibn Al-Ḥasan Al-Khurāsānī
Al-Khāzin, usually known as Abũ Jaʿfar al-Khāzin, was a Sabaean of Persian origin. The Fihrist calls him al-Khurānāā, meaning from Khurāsān, a province in eastern Iran. He should not be confused with Aʿbd al-Rahmāan al-Khāzinī (ca. 1100), the probable author of Kitāb al-āāt alʿajiba al-raādiyya, on obsertvation instruments, often attributed to al-Khāzin. (E. Wiedemann attributed this work, inconsistently, to al-Khāzin in the Enzyklopaedie des Islam, II [Leiden-Leipzig, 1913], pp. 1005-1006, and to al-Khāziniī in Beiträge, 9 , 190. De Slane confounded these two astronomers in his translation of Ibn Khaldũ’s Prolegomena, I, 111.
Abũ Ja far al-Khāzin, 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-āsafāih (“tables of the Disks [of the astrolabe]”0, which Ibn al-Qiftī 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-Bīũnīs Risāla fi fihrist kutub Muhammad b. Zakariyyā al-Rāzi (“Bibliography”) of 1036 lists several texts (written in cooperation with Abũ Naşr Manşũr ibn ’Irāaq), one of which is Fi tashīh mā waqa’a li Abi Jaʿfar al-Khāzin min al-shaw fi zäj al-safā ih (“On the Improvement of What Abũ Jaʿfar Neglected in His Tables of the Disks”). In Tamhid al-mustaqarr li-tahqīq manā al-mamarr, (“On Transits” ), al-Bīũnī criticizes Abũ Ja’ al-Khā;zin for not having correctly handled two equations defining the location of a planet but remarks that the Zī al-safāih is correct on this matter. Abũ Ma’shar that. unlike manyolthers, he had fully determined the truth about the planets, which he had included in his Zīj. Abũ Jafar al-Khāzin regarded this work as a mere compilation. Al-BiũrŪnī compared Abũ Jaʿfar al-Khāzin very favorably with Abũ Ma’shar, and in his al-āthār al-bāqiya min al-quũn al-khāliya (“Chronology of Ancient Nations”) he refers to Zij al safā 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 Abũ Jafar al-Khāzin, probably the Zij al-safā ih. The MS Or. 168 (4) in Leiden by Abũ’l-Jũd quotes Abũ Jaʿfar al-Khāzin’s remark in Zij al-safā ih that he would be able to compute the chord of an angle of one degree if angle trisection were possible.
In Kitāb fi isi’ā, dedaling with constructions of astrolabes, al-Biũnī cites Abũ Ja‘far al-Khāin’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 Abũ Jaʿfar al-Khāzin in al-Madkhal al-kabīr fīilm al-nujũm (“Great Introduction to Astronomy”). Neither work is extant.
Also treated in al-Bīũnī’s Chronology is Abũ Jaʿfar 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 Khaldũn gives a precise exposition of Abũ Jaʿfar al-Khāzin’s division of the earth into eight climatic girdles.
Al-Kharaqī (d. 1138/1139), in al-Muntahā, mentions Abũ Jaʿfar al-Khāzin and Ibn al-Haytham as having the right understanding of the movement of the spheres. This theory was perhaps described in Abũ Jaʿfar al-Khāzin’s Sirr al-’ālamin (not extant).
In Tahdī nihāyāt al-amākin. . ., al-Bīũni criticizes the verbosity of Abũ Ja‘far al-Khāzin’s commentary on the Almagest and objects to Ibrāhīm ibn Sānān and Abũ Jafar al-Khāzin’s theory of the variation of the obliquity of the ecliptic; al-Bīũnī himself considered it to be constant. The obliquity was measured by al Harawi and Abũ Jafar al-Khāzin at Rayy (near modern Teheran) in 959/960, on the order of Abu’l Faḍl ibn al-’Amid, the vizier of Rukn al-Dawla. The determination of this quantity by “al-Khāzin and his collaborators using a ring about 4 meters” is recorded by al-Nasawi.
Abũ Jaʿfar al-Khāzin was, according to Ibn al Qifţi, an expert in arithmetic, geometry, and tasyīr (astrological computastions based on planetary trajectoris). According to al-Khayyāmi, he used conic sections to give the first solution of the cubic equation by which al-Māhānī 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.
Abũ Jaʿfar al-Khāzin wrote a commentary on Book X of the Elements, a work on numerical problems (not extant), and another (also not extant) on spherical trigonometry, Maţālib juziyya mail almuyũl al-juz iyya wa ‘l-maţāli’ fi’l0kura al-mustaqima From the latter, al-Ţũsī, in Kitāb šakl al-qaţţā (“On the Transversal Figure”), quotes a proof of the sine theorem for right spherical triangles. Al-Tũsī also added another proof of Hero’s formula to the Verba filiorum of the Banuũ Mũsũ (in Majmũ al-rasaāil, II [Hyderabad, 1940]), attributing it to one al-Khāzin. This proof, closer to that of Hero than the proof by the Banũ Mũsã, 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.
I. Original Works. Not many of al-Khāzin’ 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-Qifţī, Ta‘rikh-al-hukamā, J. Lippert, ed. (Leipzig, 1903), 396; Hājjī 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 Abũ Ja‘far al-Khaldün, Prolegomena I, M. de Slane, trans. (repr. Paris, 1938), p. 111; and al-Biũnī, 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 Tahdīd nihāyāt al-amākin (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 Mũsā ben Schākir,” in Bibliotheca mathematica, 3rd ser., 3, no. 1 9190-20, p. 271, mention the proof of Hero’ formula. For the cubic equation of al-Māhāni, 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 Abũ Jaʿfar al-Khāzin 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.