From: Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, pp. 625-626 |
Courtesy of |
Khalīlī: Shams al‐Dīn Abū ʿAbdallāh Muḥammad ibn Muḥammad al‐Khalīlī
David A. King
Flourished Damascus, (Syria),
circa 1365
Khalīlī
was an astronomer associated with the Umayyad Mosque in the center of Damascus.
A colleague of the astronomer Ibn al‐Shāṭir,
he was also a muwaqqit – i. e., an astronomer concerned with
ʿilm
al‐mīqāt, the science of timekeeping by the
Sun and stars and regulating the astronomically defined times of Muslim prayer.
Khalīlī's major work, which represents the culmination of the medieval
Islamic achievement in the mathematical solution of the problems of spherical
astronomy, was a set of tables for astronomical timekeeping. Some of these
tables were used in Damascus until the 19th century, and they were also used
in Cairo and Istanbul for several centuries. The main sets of tables survive
in numerous manuscripts, but they were not investigated until the 1970s.
Khalīlī's tables can be categorized as follows:
(1) |
tables for reckoning time by the Sun, for the latitude
of Damascus; |
(2) |
tables for regulating the times of Muslim prayer, for
the latitude of Damascus; |
(3) |
tables of auxiliary mathematical functions for timekeeping
by the Sun for all latitudes; |
(4) |
tables of auxiliary functions for finding the solar
azimuth from the solar altitude for any latitude; |
(5) |
tables of auxiliary functions for solving the problems
of spherical astronomy for all latitudes; |
(6) |
a table displaying the qibla, i. e., the direction
of Mecca, as a function of terrestrial latitude and longitude for each
degree of both arguments; and |
(7) |
tables for converting
lunar ecliptic coordinates to equatorial coordinates. |
(Paris,
Bibliothèque Nationale MS ar. 2558, copied in 1408, contains all of the tables
in Khalīlī's major set [1, 2, 5 and 6]. Dublin, Chester Beatty MS
4091 and Bursa, Haraççioğlu MS 1177,4 are unique copies of the minor
auxiliary tables [3] and [4], respectively.)
The
first two sets of tables correspond to those in the large corpus of spherical
astronomical tables computed for Cairo that are generally attributed to the
10th‐century Egyptian astronomer Ibn
Yūnus.
Khalīlī's fifth set of tables was designed to solve all the standard problems of spherical astronomy, and they are particularly useful for those problems that, in modern terms, involve the use of the cosine rule for spherical triangles. Khalīlī tabulated three functions and gave detailed instructions for their application. The functions are the following:
f_{ϕ} = sin θ/ cos ϕ and g_{ϕ} = sin θ tan ϕ,
K(x,y) = arc cos {x/cos y},
and it is not difficult to show the equivalence of Khalīlī's rule to the modern formula
t = arc cos {[sin h – sin δ sin ϕ ] / [ cos δ cos ϕ ]} .
Khalīlī's computational ability is best revealed by his qibla table. The determination of the qibla for a given locality is one of the most complicated problems of medieval Islamic trigonometry. If (L,φ) and (LM,φ_{M}) represent the longitude and latitude of a given locality and of Mecca, respectively, and ΔL = |L−LM|, then the modern formula for q(L,φ), the direction of Mecca for the locality, measured from the south, is
q = arc cot {[ sin ϕ cos ΔL – cos ϕ tan ϕ_{M} ] / sin ΔL}.
King, David A. (1973). “Al‐Khalīlī's Auxiliary
Tables for Solving Problems of Spherical Astronomy.” Journal for the History
of Astronomy 4: 99–110. (Reprinted in King, Islamic Mathematical Astronomy,
XI. London: Variorum Reprints, 1986; 2nd rev. ed., Aldershot: Variorum, 1993.)
——— (1975). “Al‐Khalīlī's
Qibla Table.” Journal of Near Eastern Studies 34: 81–122. (Reprinted
in King, Islamic Mathematical Astronomy, XIII. London: Variorum Reprints,
1986; 2nd rev. ed., Aldershot: Variorum, 1993.)
——— (1978). “Al‐Khalīlī.”
In Dictionary of Scientific Biography, edited by Charles Coulston Gillispie.
Vol. 15, pp. 259–261. New York: Charles Scribner's Sons.
——— (1983). “The Astronomy
of the Mamluks.” Isis 74: 531–555. (Reprinted in King, Islamic Mathematical
Astronomy, III. London: Variorum Reprints, 1986; 2nd rev. ed., Aldershot:
Variorum, 1993.)
———
(1993). “L'astronomie en Syrie à l'époque islamique.” In Syrie, mémoire
et civilization, [exhibition catalogue] edited by Sophie Cluzan, Eric
Delpont and Jeanne Mouliérac, pp. 392–394, 440. Paris: Institut du monde arabe
and Flammarion.
——— (2004). In
Synchrony with the Heavens: Studies in Astronomical Timekeeping and Instrumentation
in Medieval Islamic Civilization. Vol. 1, The Call of the Muezzin
(Studies I–IX). Leiden: Brill, II–10.
Van Brummelen, Glen
(1991). “The Numerical Structure of al‐Khalīlī's Auxiliary
Tables.” Physis, n.s., 28: 667–697.