| From: Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, pp. 630-631 |
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Khujandī: Abū
Maḥmūd
Ḥāmid ibn al‐Khiḍr al‐Khujandī
Glen Van Brummelen
Born Khujand, (Tajikstan),
circa 945
Died 1000
Khujandī
was an astronomer of some repute who constructed a variety of instruments
and contributed to the mathematics supporting astronomical work. He is best
known for the first very large mural quadrant that was intended to make solar
observations of unprecedented accuracy. Only a few details are known of his
life; he was likely one of the khans of Khujanda in Transoxania and was supported
by the Būyid ruler Fakhr al‐Dawla.
Khujandī's
towering achievement, the giant mural sextant near Rayy, was perhaps the most
ambitious instrument of its time. Named al‐suds al‐Fakhrī
(after its sponsor Fakhr al‐Dawla), it consisted of 60° of a meridian
arc about 43 m in diameter, built at and below ground level. A small aperture
in the roof of the building that housed the instrument allowed a cone of the
Sun's rays to shine through. A circle with crosshatch lines was placed on
the rays that fell onto the scale in order to determine their center. The
scale was marked to 10', making it the first
instrument capable of measuring with a precision better than minutes.
In 994 Khujandī used the suds al‐Fakhrī to measure
meridian transits near solstices; from this he obtained the value ε
= 23;32,19° for the obliquity of the ecliptic, and a value of 35;34,38.45°
for the latitude of Rayy (accurate to within one').
On the basis of earlier determinations of ε, Khujandī decided
that ε is a variable quantity, a conclusion with which Bīrūnī
disagreed. In his Taḥdīd
al‐amākin, Bīrūnī discusses Khujandī's
work in detail. He argues that the measurements failed to produce the expected
accuracy because the building settled between the summer and winter solstices,
causing the height of the aperture in the roof to drop. After the failure
of the suds al‐Fakhrī, the observational program probably
continued with armillary spheres and other instruments, and Khujandī
eventually produced the Zīj al‐Fakhrī (an astronomical
handbook) on the basis of his results. (A partially extant Persian zīj
written 200 years later may also derive from Khujandī's observations.)
Although the large instrument was an immediate failure, it was a model for
similar instruments at the observatories in Marāgha and Samarqand in
the 13th and 15th centuries, respectively. These avoided the problem of settling
by using different construction materials.
Astronomical
instruments are a recurring interest in Khujandī's other works. A treatise
entitled The Comprehensive Instrument describes an invention called
a shāmila designed to replace the astrolabe or a quadrant. It
was not universal in the sense that it was restricted for use in a particular
range of terrestrial latitudes.
Two
geometric methods of drawing azimuth circles on an astrolabe are credited
to Khujandī by other medieval authors. He constructed an astrolabe in
984/985, which is one of the earliest still extant. It is considered to be
one of the most important surviving astronomical instruments.
Khujandī
composed several mathematical works, among them a text on geometry and a flawed
proof of Fermat's last theorem for n = 3. He is also one of several
competing claimants to the rule of four quantities, a theorem in spherical
trigonometry that was simpler than Menelaus' theorem and, for many Muslim
astronomers, replaced it as the basic tool of spherical astronomy.
Selected References
Al‐Bīrūnī, Abū Rayḥān (1985). Kitāb Maqālīd ʿilm al‐hayʾa: La trigonométrie sphérique chez
les arabes de l'est à la fin du Xesiècle, edited and translated by Marie‐Thérèse Debarnot. Damascus: Institut
français de Damas.
Ali, Jamil (trans.)
(1967). The Determination of the Coordinates of Cities: Al‐Bīrūnī's
Taḥdīd al‐Amākin. Beirut: American University of Beirut.
Berggren, J. L. (1991). “Medieval Islamic Methods for Drawing
Azimuth Circles on the Astrolabe.” Centaurus 34: 309–344.
Cheikho, Louis (1908). “Risālat al‐Khujandī
fī al‐mayl wa ʿard al‐balad.”
Al‐Machriq 11: 60–69.
Frank, Josef (1921).
“Über zwei astronomische arabische Instrumente.” Zeitschrift für Instrumentenkunde
41: 193–200.
Kennedy, E. S. (1973).
A Commentary Upon Bīrūnī's Kitāb Taḥdīd
al‐Amākin. Beirut: American University of Beirut.
Samsó,
Julio (1969). Estudios sobre Abū Naṣr
Manṣūr
b. ʿAlī b. ʿIrāq. Barcelona:
Asociación para la Historia de la Ciencia Española.
——— (1986). “Al‐Khudjandī.”
In Encyclopaedia of Islam. 2nd ed. Vol. 5, pp. 46–47. Leiden: E. J.
Brill.
Sayılı, Aydin (1960). The Observatory in Islam.
Ankara: Turkish Historical Society.
Schirmer,
Oskar (1926/1927). “Studien zur Astronomie der Araber.” Sitzungsberichte
der Physikalisch‐Medizinische Sozietät in Erlangen 58–59: 33–88.
Tekeli, Sevim (1973). “Al‐Khujandī.” In Dictionary
of Scientific Biography, edited by Charles Coulston Gillispie. Vol. 7,
pp. 352–354. New York: Charles Scribner's Sons.
Wiedemann,
E. (1919). “Über den Sextant des al‐Chogendi.” Archiv
für die Geschichte der Naturwissenschaften und der Technik 2: 148–151.