From: Thomas Hockey et al. (eds.). The Biographical Encyclopedia of Astronomers, Springer Reference. New York: Springer, 2007, pp. 581582 
Courtesy of

Jābir ibn Aflaḥ: Abū Muḥammad
Jābir ibn Aflaḥ
Emilia Calvo
Flourished probably Seville, (Spain), 12th century
Jābir ibn Aflaḥ was
a mathematician and astronomer in 12thcentury Andalusia, who wrote a treatise
entitled Iṣlāḥ alMajisṭi (Correction
of the Almagest) in which, as the title suggests, the author
made a long series of criticisms and corrections of Ptolemy’s main astronomical treatise.
Little
is known of Jābir’s life. It seems that he was from Seville, since he
is referred to in several sources as alIshbīlī. One of these sources
is Maimonides; in his Guide for the Perplexed, he claims to have met Jābir’s son.
This reference suggests that Jābir was alive sometime between the end
of the 11th century and the first half of the 12th century.
Jābir’s main work is
a commentary on Ptolemy’s Almagest, a treatise that he had seen in two translations from
the Greek. The Almagest
is both the great synthesis
and the culmination of mathematical astronomy of the ancient world, composed
in Alexandria in the second century. It was translated into Arabic at least
five times, and, from the late ninth century onward, constituted the basis
of the mathematical astronomy carried out in the Islamic world.
In
one of the preserved manuscripts (Berlin MS 5653), Jābir’s work appears
under the title Iṣlāḥ alMajisṭi (Correction
of the Almagest); in fact, it is a reworking of Ptolemy’s
work. Mathematical precision and proof seem to be Jābir’s maximum aspiration
in his Iṣlāḥ. It is divided into nine books. In the foreword,
the author outlines the main differences between the Iṣlāḥ and
the Almagest. The theorem of Menelaus
that Ptolemy used is systematically replaced
by theorems related to spherical triangles. These theorems were probably taken
from mathematicians such as Abū alWafāʾ
alBūzjānī and
Abū Naṣr Manṣūr ʿAlī ibn ʿIrāq, who were responsible for what has been
called the “trigonometric revolution” in eastern Islam around the year 1000.
In Andalusia, these theorems were formulated for the first time by Ibn Muʿādh at the beginning of the 11th century. Somewhat
surprisingly, Jābir does not mention any Arab authors in his treatise—not
even Ibn Muʿādh
despite the fact that both authors were Andalusians.
Jābir’s most notable divergence
from Ptolemy concerns the model of the inferior planets, Venus and Mercury.
Ptolemy placed them between the Moon and the Sun. He had to explain the fact
that these two planets do not pass in front of the Sun by arguing that they
are never on the line between the Sun and the view of the observer. Jābir
affirmed that this argument was mistaken, and he placed these planets above
the Sun.
Jābir criticizes Ptolemy
harshly. He says that the mathematical basis of the Almagest
should be improved, though
both the parameters and some planetary models had already been modified by
previous Arab astronomers.
Jābir’s work is the first
criticism of the Almagest in the Islamic West. Its focus is original,
far removed from that of the Aristotelian philosophers who launched the “Andalusian
Revolt” against Ptolemy or from the criticisms of the astronomers at the Marāgha
Observatory in the 13th century.
Jābir’s criticisms of Ptolemy
bear witness to his great mathematical ability but also suggest that his grasp
of more practical matters was limited. It would have been extremely difficult
to obtain the observations of planets required to apply his alternative methods.
The
Iṣlāḥ is,
clearly, the work of a theoretical author. The demonstrations include neither
numerical examples nor tables. However, the work describes an instrument,
which the author claims, can replace the four instruments described by Ptolemy
for astronomical determinations. With the exception of Zarqālī’s armillary
sphere, this is the first description in an Andalusian text of an instrument
designed for astronomical observation. It is extremely large and has been
considered a forerunner of the torquetum, an instrument of European tradition
described for the first time in a 13thcentury Latin text.
The
text of the Iṣlāḥ was
probably revised by the author himself—if not all, at least the section on
trigonometry. It was later introduced in Egypt by Maimonides who, with one
of his pupils, revised the text around 1185. In Andalusia, Ibn Rushd and Biṭrūjī were
clearly influenced by this author.
During
the 13th century the text spread in the East: a manuscript of this work, preserved
in Berlin, was copied in Damascus in 1229. A summary of the text was also
compiled by Quṭb alDīn alShīrāzī, a Persian astronomer and physicist.
Jābir’s work seems to have had considerable
influence upon Hebrew astronomy. There are two Hebrew translations of this
work, one dating from 1274, by Moshe ben Tibbon, and the second
by his nephew Jacob
ben Makhir, revised in 1335 by Samuel ben Yehuda of Marseilles.
Thanks to these Hebrew translations and the Latin translation, due to Gerard
of Cremona, the text reached
a wide readership in Europe.
In the Latin world,
Jābir was considered a vigorous critic of Ptolemy’s astronomy. His treatise
helped to spread trigonometry in Europe; in the 13th century, the trigonometric
theorems were used by the astronomers who compiled the Libro del Cuadrante Sennero (Book of the sine
quadrant) working under the patronage of King Alfonso X the Wise. In the
14th century, Richard
of Wallingford used the theorems
in his work on the Albion. Jābir is probably the source of much of Johann
Müller’s (Regiomontanus’s)
trigonometric work entitled De triangulis (On the triangles) although he is not mentioned. Finally,
he may also be the source of the trigonometric section in Nicolaus Copernicus’s De Revolutionibus (On the revolutions [of the celestial spheres]).
HugonnardRoche,
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S. Shukla, pp. 207–208. Cambridge: Cambridge University Press.
Lorch, Richard
P. (1975). “The Astronomy of Jābir ibn Aflaḥ.”
Centaurus 19: 85–107.
——— (1976). “The Astronomical
Instruments of Jābir ibn Aflaḥ
and the Torquetum.” Centaurus 20: 11–34.
——— (1995). “Jābir ibn
Aflaḥ and
the Establishment of Trigonometry in the West.” In Lorch, Arabic Mathematical Sciences:
lnstruments, Texts, Transmission, VIII. Aldershot: Variorum.
Samsó, Julio
(1992). Las ciencias
de los antiguos en alAndalus. Madrid:
Mapfre, pp. 317–320 and 326–330.
——— (2001). “Ibn alHaytham
and Jābir b. Aflaḥ’s criticism of Ptolemy’s
determination of the parameters of Mercury.” Suhayl 2: 199–225.
Swerdlow,
Noel M (1987). “Jābir ibn Aflaḥ’s
Interesting Method for Finding the Eccentricities and Direction of the Apsidal
Line of a Superior Planet.” In From Deferent to Equant: A Volume of Studies
in the History of Science in the Ancient and Medieval Near East in Honor of
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