| From: Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, pp. 652-563 |
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Ibn Muʿādh:
Abū ʿAbd Allāh Muḥammad ibn Muʿādh
al-Jayyānī
Emilia Calvo
Died probably (Spain),
after 1079
Ibn
Muʿādh al‐Jayyānī
was the author of several astronomical works, and yet very little is known
about him. Recent scholarship suggests that he was born in the early 11th
century. The only secure date we have for him is 1079, the year of a solar
eclipse he describes from first‐hand observation. “Jayyānī”
means from Jaen, the capital of the Andalusian province of the same name where
he served as a qāḍī (judge) for much
of his life. In fact, he belonged to a family of judges and jurists from that
province.
Among
Ibn Muʿādh's astronomical works was the Tabulae
Jahen, a set of astronomical tables probably translated into Latin by
Gerard of Cremona
with the title Liber tabularum Iahen cum regulis suis. A printed edition
of the canons, lacking the tables, appeared in 1549 at Nüremberg as Scriptum
antiquum saraceni cuiusdam de diversarum gentium Eris, annis ac mensibus et
de reliquis Astronomiae principiis. These tables were based on the tables
of Khwārizmī, and were adapted
to the geographical coordinates of Jaen for the epoch of midnight, 16 July
622 (the date of the hijra). But there are some modifications introduced
by Ibn Muʿādh,
such as the value of the geographical longitude of the city, which are in
accordance with the corrected values found in Andalusian astronomers from
the 10th century. In some points he seems to be independent of his sources,
as is the case in Chapter 19, devoted to the visibility of the new Moon, and
also in the trigonometric section. This work included a table of stars that
improved the one in Khwārizmī and was also independent of the Toledan
tradition. In Chapter 18 we find the first exact method used in Andalusia
to determine the azimuth of the qibla, the so‐called method
of the zījes, probably taken from a work by Bīrūnī.
In short, there is considerable new material as well as a personal vision;
in addition there is a possible influence from eastern astronomers such as
Bīrūnī, who until recently was thought not to have been known
in Andalusia.
Although
we do not have evidence of any astronomical observation made by Ibn Muʿādh,
there is a treatise on the solar eclipse already mentioned, which occurred
on 1 July 1079. The text of this treatise, “On the Total Solar Eclipse,” was
translated into Hebrew by Samuel ben Jehuda (flourished: circa 1335).
Another treatise by him, entitled “On the Dawn,” was also translated into
Hebrew. The Arabic texts of these two works are not known to be extant. A
Latin translation of the latter work was made by Gerard of Cremona as the
Liber de crepusculis. It deals with the phenomena of morning and evening
twilight, and in it Ibn Muʿādh gives an estimation of the angle
of depression of the Sun at the beginning of the morning twilight and at the
end of the evening twilight, obtaining the value of 18°. On the basis of this
and three other basic parameters (the mean distance between Earth and Sun
[1,110 in terrestrial radii], the relative size of Sun and Earth [5.5:1 in
terrestrial radii], and the circumference of the Earth [24,000 miles]), and
through the use of simple trigonometric functions, Ibn Muʿādh
calculates the height of the atmosphere to be around 52 miles. The work found
a wide interest in the Latin Middle Ages and in the Renaissance, and this
figure, 52 miles, remained canonical in the Latin West until the end of the
16th century, when the issue of atmospheric refraction was raised to prominence
by Tycho Brahe.
Consequently, this figure of 52 miles was drastically reduced by Johannes
Kepler and succeeding astronomers.
An
astrological work by Ibn Muʿādh is Maṭraḥ shuʿāʿāt al‐kawākib
(Projection of the rays of the stars) is preserved in an Arabic copy in the
Biblioteca Medicea Laurenziana Orientale 152. Although as yet not properly
studied, it seems to be the source of later works on the subject such as the
Libro del Ataçyr composed under the patronage of Alfonso
X the Wise in Toledo in the 13th century and included among the Libros
del Saber de Astronomía.
Several
mathematical works by Ibn Muʿādh are
also extant in Arabic. His treatise Kitāb Majhūlāt qisī
al‐kura (Determination of the magnitudes of the arcs on the surface
of a sphere), which is also cited in his Tabulae Jahen, is a work on
spherical trigonometry, probably the most ancient treatise on this topic in
the medieval west. It is also a text in which this discipline is entirely
independent from astronomy, and in which the author shows that he was aware
of the main novelties introduced by Eastern Islamic mathematicians at the
end of the previous century. Ibn Muʿādh probably
had access to Eastern literature on spherical trigonometry, but he was also
capable of dealing with this subject in an independent way.
The Maqāla
fī sharḥ al‐nisba (On ratio)
is a defense of Euclid. It falls into a tradition of geometric research documented
in the works of earlier Andalusian mathematicians such as Muʾtaman ibn
Hūd and Ibn Sayyid. Ibn Muʿādh says
in his preface that this treatise is intended “to explain what may not be
clear in the fifth book of Euclid's writing.” There was a general dissatisfaction
among Arabic mathematicians with Euclid V, definition 5. As a consequence
of the abstract form in which the Euclidean doctrine of proportions was presented,
the Arabs, from the ninth century on, tried either to obtain equivalent results
more in accord with their own views, or to find a relation between their views
and the unsatisfying theory. The most successful among them was Ibn Muʿādh, who showed an understanding comparable
with that of Isaac Barrow, who is customarily regarded as the first to have
really understood Euclid's Book V.
Selected References
Hermelink, Heinrich (1964). “Tabulae Jahen.” Archive for
History of Exact Sciences 2: 108–112.
Plooij, Edward B. (1950). Euclid's Conception of Ratio and
His Definition of Proportional Magnitudes as Criticized by Arabian Commentators.
Rotterdam: W. J. van Hengel.
Sabra,
A. I. (1967). “The Authorship of the Liber de crepusculis,
an Eleventh‐Century Work on Atmospheric Refraction.” Isis 58:
77–85.
Saliba, George (1987). “The Height of the Atmosphere According
to Muʾayyad al‐Dīn al‐ʿUrḍī,
Quṭb al‐Dīn Al‐Shirāzī, and Ibn Muʿādh.” In From Deferent to Equant:
A Volume of Studies in the History of Science in the Ancient and Medieval
Near East in Honor of E. S. Kennedy, edited by David A. King and George
A. Saliba, pp. 445–465. New York: New York Academy of Sciences.
Samsó,
Julio (1992). Las ciencias de los antiguos en al‐Andalus. Madrid:
Mapfre.
——— (1996). “‘Al‐Bīrūnī’
in al‐Andalus.” In From Baghdad to Barcelona: Essays on the History
of the Islamic Exact Sciences in Honour of Prof. Juan Vernet, edited by
Josep Casulleras and Julio Samsó, vol. 2, pp. 583–612. Barcelona: Instituto “Millás Vallicrosa”
de Historia de la Ciencia árabe.
Samsó, Julio and Honorino, Mielgo (1994). “Ibn Isḥāq
al‐Tūnisī and Ibn Muʿādh
al‐Jayyānī on the Qibla.” In Islamic Astronomy and Medieval
Spain, edited by Julio Samsó, VI. Aldershot: Variorum.
Smith, A. Mark (1992). “The Latin Version of Ibn Muʿādh's
Treatise ‘On Twilight and the Rising of Clouds.’” Arabic Sciences and Philosophy
2: 83–132.
Smith, A. Mark and Bernard, R. Goldstein (1993). “The Medieval
Hebrew and Italian Versions of Ibn Muʿādh's
‘On Twilight and the Rising of Clouds.’” Nuncius 8: 611–643.
Suter, Heinrich (1900). “Die Mathematiker und Astronomen der
Araber und ihre Werke.” Abhandlungen zur Geschichte der mathematischen
Wissenschaften 10: 96 and 214, n. 44; and Suter, “Nachträge und Berichtigungen.”
Abhandlungen zur Geschichte der mathematischen Wissenschaften 14: 170.
Villuendas,
M. V. (1979). La trigonometría europea en el siglo XI: Estudio de la obra
de Ibn Muʿād, El Kitāb mayhūlāt. Barcelona: Instituto de Historia de la Ciencia de la
Real Academia de Buenas Letras.