| From: Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, pp. 557-558 |
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Courtesy of 
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Ibn ʿIrāq: Abū Naṣr Manṣūr ibn ʿAlī ibn ʿIrāq
J. Len Berggren
Born Gīlān
(Iran), circa 950
Died Ghazna (Afghanistan),
circa 1036
Ibn
ʿIrāq was an astronomer
who also made important contributions to trigonometry. His name and contemporary
references to him as “prince” (al‐amīr) suggest that he
was a member of the Banū ʿIrāq dynasty,
which ruled Khwārizm until the Maʾmūnī dynasty conquered
it in 995.
Ibn
ʿIrāq was a pupil
of the famous scientist Abū al‐Wafāʾ
al‐Būzjānī, and he, in turn, had a pupil who
became one of medieval Islam's most famous scientists, Abū
al‐Rayḥān
al‐Bīrūnī. Among Abū Naṣr's works are a number of treatises answering questions
posed by Bīrūnī.
At some
point in the early 11th century – 1016 has been suggested – both Ibn ʿIrāq and Bīrūnī
joined the court of Maḥmūd
of Ghazna, Afghanistan, where Ibn ʿIrāq passed the
rest of his life.
Ibn
ʿIrāq was a capable
astronomer, and Bīrūnī praised his method for finding the solar
apogee as one that was as far beyond the methods of the modern astronomers
as theirs were beyond those of the ancients. However, his chief astronomical
work, the Royal Almagest (al‐Majisṭī
al‐shāhī), is lost, with only fragments surviving. The
same is true of his Book of Azimuths, on methods for finding the direction
of Mecca (the qibla). Of Ibn ʿIrāq's
surviving astronomical writings, a number of them deal with astrolabes, while
others correct errors or comment on astronomical writings of such predecessors
as Ḥabash al‐Ḥāsib and Abū
Jaʿfar al‐Khāzin.
In
another fragment of a lost writing, Abū Naṣr takes issue with a colleague
who suggested that the planetary orbits might be ellipses, rather than circles,
with a very slight difference between their major and minor axes. He also
discusses the possibility that the motions of the planets in their orbits
might be, not only apparently but in reality, nonuniform. Abū Naṣr comes down firmly for the prevailing ancient and medieval
view, however, that all heavenly bodies move with uniform motion on circles.
Among Ibn
ʿIrāq's
most famous contributions to mathematical astronomy are his discoveries of
both the Law of Sines (for plane and spherical triangles) and the polar triangle
(of a spherical triangle). Indeed, it appears he got into a controversy with
his teacher, Abū al‐Wafāʾ, over priority in the discovery
of the former. (It is quite possible, of course, that each discovered it independently
of the other since many important mathematical discoveries have been made
simultaneously by more than one person.) In any case, it is certain that Abū
Naṣr brought the Sine Law into the mathematical limelight with
his repeated use of the theorem and the several proofs he gave of it.
This
interest in spherical trigonometry is very much in line with Abū Naṣr's
preparing a reliable Arabic edition of the Spherica of Menelaus,
the first treatise to focus on the importance of the spherical triangle.
It is interesting
that the title of one of Ibn ʿIrāq's
treatises (On the reason for the followers of the Sindhind halving the
equation) shows that even in the late 10th or early 11th century astronomers
of the caliber of Abū Naṣr
were discussing seriously the contents of the then very ancient material of
the Indian tradition in the Sindhind.
Selected References
Goldstein, B. R. (1971). “Ibn ʿIrāḳ.”
In Encyclopaedia of Islam. 2nd ed. Vol. 3, p. 808. Leiden: E. J. Brill.
Samsó, Julio (1974). “Manṣūr
ibn ʿAlī
ibn ʿIrāq.” In
Dictionary of Scientific Biography, edited by Charles Coulston Gillispie.
Vol. 9, pp. 83–85. New York: Charles Scribner's Sons.
Sezgin, Fuat Geschichte des arabischen Schrifttums. Vol. 5, Mathematik (1974): 338–341: Vol. 6, Astronomie (1978): 242–245. Leiden: E. J. Brill.