| From: Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, pp. 188-189 |
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Būzjānī: Abū al‐Wafāʾ Muḥammad ibn Muḥammad ibn Yaḥyā al‐Būzjānī
Behnaz Hashemipour
Born Būzjān
(Būzhgān, Khurāsān, Iran), 10 June 940
Died Baghdad, (Iraq),
997 or 998
Būzjānī
was one of the leading astronomers and mathematicians of the Middle Ages,
with significant contributions in observational astronomy. His achievements
in trigonometry paved the way for more precise astronomical calculations.
Būzjānī
was born in Būzjān, in the region of Nīshāpūr. The
town is now a deserted land in the vicinity of the small town of Torbat‐i
Jām, located today in the Iranian province of Khurāsān. He
was from an educated and well‐established family. He is said to have
studied arithmetic under both his paternal and maternal uncles.
Būzjānī
flourished in an age of great political upheavals. The Būyids (945 to
1055), a family originally from the highlands of Daylam in northern Iran,
had built a new dynasty that soon extended its rule over Iraq, the heart of
the ʿAbbāsid
caliphate, reducing the caliph's rule to a mere formality. Under the Būyids,
who were great patrons of science and the arts, many scientists and scholars
were attracted to Baghdad to enjoy the benefits of the new rulers' patronage.
The change in the political climate had brought with it a great cultural revival
in the eastern Islamic lands promoting literary, scientific, and philosophical
activities on a grand scale.
At the age of 20, Būzjānī moved to Baghdad, the capital
of the ʿAbbāsid caliphate,
where he soon rose to prominence as a leading astronomer and mathematician
at the Būyid court, conducting observations and research in the Bāb
al‐Tibn observatory. The decade following 975 seems to have been
his most active years in astronomy, during which he is said to have conducted
most of his observations. Later, to comply with the wishes of Sharaf al‐Dawla,
the Būyid Amīr (Regent), who was himself a learned man with keen
interest in astronomy, Būzjānī became actively involved in
the construction of a new observatory in Baghdad. His collaborator was Kūhī,
another celebrated astronomer from the northern part of Iran who at the time
was unrivaled in making astronomical instruments. The astronomical work of
Būzjānī and his colleagues in Baghdad mark the revival of the
“Baghdad school,” a tradition with much vitality in the preceding century.
Bīrūnī, the renowned astronomer
and scientist living in Kath (in central Asia), tells us of his correspondence
with Būzjānī, who was in Baghdad. This correspondence, and
the exchange of astronomical data and measurements between them, signifies
not only their mutual recognition as the leading astronomers of the time,
but also the vigor with which astronomical observations were carried out in
those days. According to Bīrūnī, in 997 the two astronomers
prearranged to make a joint astronomical observation of a lunar eclipse to
establish the difference in local time between their respective localities.
The result showed a difference of approximately 1 hour between the two longitudes
– very close to present‐day calculations. In addition to this, Bīrūnī
makes numerous references to Būzjānī's measurements in his
various works.
Būzjānī's
principal astronomical work, and his sole extant writing on the subject, is
Kitāb al‐Majisṭī.
The book consists of three chapters: trigonometry, application of spherical
trigonometry to astronomy, and planetary theory. An incomplete manuscript
of this work exists in the Bibliothèque nationale, Paris.
A
misinterpretation of a part of this book led Louis A. Sedillot (the French
scientist) to claim that credit for discovering the variation (the third inequality)
of the Moon's motion belonged to Būzjānī, and not to Tycho
Brahe. This gave rise to a long‐lived debate in the French Academy
of Science from 1837 to 1872. The case was finally resolved by Carra de Vaux,
the prominent historian of science in Islam, who, after a thorough study of
the manuscript in 1893, reasserted Brahe's right to this discovery.
Although
Būzjānī's al‐Majisṭī – at least judging
from the extant portion – did not introduce considerable theoretical novelties,
it did contain observational data that were used by many later astronomers.
More importantly, its section on trigonometry was a comprehensive study of
the subject, introducing proofs in a masterly way for the most important relations
in both plane and spherical trigonometry. Būzjānī's approach,
at least in some instances, bears a striking resemblance to modern presentations.
In al‐Majisṭī,
Būzjānī introduced for the first time the tangent function
and hence facilitated the solutions to problems of the spherical right‐angled
triangle in his astronomical calculations. He also devised a new method for
constructing the sine tables, which made his tables for sin 30′ more precise than those
of his predecessors. This was an important advance, since the precision of
astronomical calculations depends upon the precision of the sine tables. The
sine table in Būzjānī's Almagest was compiled at 15' intervals and given to
four sexagesimal places. In the sixth chapter of al‐Majisṭī,
Būzjānī defines the terms tangent, cotangent, sine, sine of
the complement (cosine), secant and cosecant, establishing all the elementary
relations between them. Then assuming the radius of the (trigonometric) circle
R = 1, he deduces that the tangent will be equal to the ratio of the sine
to the sine of complement, and the inverse for the cotangent (identical to
our present terminology). Later, Bīrūnī, inspired by Būzjānī
and for simplification, uses this norm of R = 1 instead of R = 60 which was
up until then commonly used in compiling the tables.
Būzjānī's
contributions to mathematics cover both theoretical and practical aspects
of the science. His practical textbook on geometry, A Book on Those Geometric
Constructions Which Are Necessary for a Craftsman, is unparalleled among
the geometrical works of its kind written in the Islamic world. Būzjānī
wrote a practical textbook on arithmetic as well. The book is entitled Book
on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen.
This is apparently the first and only place where negative numbers have been
employed in medieval Islamic texts.
On
the basis of works attributed to him, Būzjānī seems to have
been a prolific scholar. He is said to have written 22 books and treatises.
These include works on astronomy, arithmetic, and geometry, as well as translations
and commentaries on the algebraic works of past masters like Diophantus and
Khwārizmī, and a commentary
on Euclid's Elements. Of all these works, however, only eight (as far
as we know) have survived. Of his astronomical works, references were made
to a Zīj al‐wāḍiḥ, an influential work that
is no longer extant.
Historical
evidence, as well as the judgments of Būzjānī's colleagues
and generations of scholars who came after him, all attest to the fact that
he was one of the greatest astronomers of his age. He was also said to have
been a man with great moral virtues who dedicated his life to astronomy and
mathematics. His endeavors in the domain of science did not die with him.
In fact, the data Būzjānī had gathered from his observations
were used by astronomers centuries after him. Furthermore, the science of
trigonometry as it is today is much indebted to him for his work. In his honor
and to his memory, a crater on the Moon has been named for Būzjānī.
Selected References
al‐Qifṭī,
Jamāl al‐Dīn (1903). Taʾrīkh al‐ḥukamāʾ, edited
by J. Lippert. Leipzig: Theodor Weicher.
Carra
de Vaux (May–June 1892). “L'Almageste d'Abū ʾl Wéfā
Alboūzdjānī.” Journal asiatique, 8th ser., 19: 408–471.
Debarnot, Marie‐Thérèse (1996). “Trigonometry.” In Encyclopedia
of the History of Arabic Science, edited by Roshdi Rashed. Vol. 2, pp.
495–538. London: Routledge.
Ghorbani, A. and M. A. Sheykhan (1992). Buzdjānī
Nāmeh: The Biography and a Survey of Buzdjānī's Mathematical
Works. Tehran: Enqelab‐e Eslami Publishing and Educational Organization.
Gupta, R. C. (1992).
“Abū al‐Wafāʾ and His Indian Rule about Regular Polygons.”
Gaṇita Bhāratī 14:
57–61.
Ibn al‐Nadīm (1970). The Fihrist of al‐Nadīm:
A Tenth‐Century Survey of Muslim Culture, edited and translated
by Bayard Dodge. 2 Vols., Vol. 1, p. 83. New York: Columbia University Press.
Kennedy, E. S. (1984). “Applied Mathematics in the Tenth Century:
Abu ʾl‐Wafāʾ Calculates the Distance Baghdad–Mecca.”
Historia Mathematica 11: 193–206.
Kennedy, E. S. and Mustafa Mawaldi (1979). “Abū al‐Wafāʾ
and the Heron Theorems.” Journal of the History of Arabic Science 3:
19–30.
Kraemer, Joel L. (1992).
Humanism in the Renaissance of Islam: The Cultural Revival During the Buyid
Age. 2nd rev. ed. Leiden: E. J. Brill.
Medovoi, M. I. (1960). “On the Arithmetic Treatise of Abū
ʾl‐Wafāʾ.” Studies in the History of Mathematics
13: 253–324.
Pingree, David (1983). “Abu ʾl‐ Wafāʾ.”
In Encyclopaedia Iranica, edited by Ehsan Yarshater. Vol. 1, pp. 392–394.
London: Routledge and Kegan Paul.
Saidan,
Ahmad S. (1974). “The Arithmetic of Abū ʾl‐Wafāʾ.”
Isis 65: 367–375.
Sesiano,
Jacques (1998). “Le traité d'Abū ʾl‐Wafāʾ sur les
carrés magiques.” Geschichte der Arabisch‐Islamischen Wissenschaften
12: 121–244.
Suter,
H. (1960). “Abu ʾl‐Wafāʾ al‐Būzadjānī.”
In
Encyclopaedia of Islam. 2nd ed. Vol. 1, p. 159. Leiden: E. J. Brill.
Youschkevitch, A. P. (1970). “Abū ʾl‐Wafāʾ
al‐Būzjānī.” In Dictionary of Scientific Biography,
edited by Charles Coulston Gillispie. Vol. 1, pp. 39–43. New York: Charles
Scribner's Sons.