Flourished Seville, (Spain),
addition to his own astronomical accomplishments, Ibn al‐Hāʾim
provides important historical information on earlier astronomers in al‐Andalus.
All we know of his life is that he came from Seville, and that he probably
worked in North Africa under the Almohad dynasty.
At the beginning of the 13th century (1204–1205), Ibn al‐Hāʾim
composed a single work entitled al‐Zīj al‐kāmil
which he dedicated to the caliph Abū ʿAbd Allāh Muḥammad
who reigned from 1195 to 1213. It is a relatively long text, consisting
of an introduction and seven books (maqālāt). The text
can be considered a zīj (astronomical handbook) on the basis
of its structure and contents, even though it does not include numerical
tables; it contains only the canons giving calculating procedures together
with geometrical proofs. Ibn al‐Hāʾim was a good mathematician
and was familiar with the new trigonometry introduced in al‐Andalus
by Ibn Muʿādh
(11th century) and extended by Jābir
ibn Aflaḥ (12th century).
Al‐Zīj al‐kāmil is important because
it describes the astronomy practiced in al‐Andalus and the Maghreb
at the beginning of the 13th century and informs us of the Toledan observations
al‐Ṭulayṭuliyya) and the activities of
the Toledan astronomers (al‐jamāʿa
al‐Ṭulayṭuliyya) working under the patronage
of Ṣāʿid al‐Andalusī in the 11th century.
The work also gives us historical data on the Andalusian astronomer Zarqālī,
who seems to have had a considerable influence on Ibn al‐Hāʾim's
theories and models. In the introduction to his book, Ibn al‐Hāʾim
criticizes two books by Zarqālī's student Ibn
al‐Kammād: al‐Kawr ʿalā
al‐Zīj al‐kāmil, Ibn al‐Hāʾim
seems to describe all he knows about the trepidation and obliquity of the
ecliptic models developed in al‐Andalus, especially Zarqālī's
third model, in which variable precession becomes independent of the oscillation
of the obliquity of the ecliptic. Trepidation has to be taken into account
in most of the calculations and procedures presented in the book. He provides
a description and a geometrical demonstration, explains how to use the tables,
and also presents the spherical trigonometrical formulae involved. Ibn al‐Hāʾim
attributes the Risālat al‐iqbāl wa‐ʾl‐ibdār
(Epistle on accession and recession) to the 11th century astrologer Abū
Marwān al‐Istijjī, and preserves some data from that book.
treatise on the Sun (Fī sanat al‐shams, On the solar year)
is only known through secondary works, Ibn al‐Hāʾim's text
is a useful additional source. Ibn al‐Hāʾim follows Zarqālī
in establishing and calculating the basic elements of solar theory. He gives
a longitude of the solar apogee of 85° 49′, which coincides
with the value determined by Zarqālī in his observations performed
in 1074/1075, as documented in the Latin tradition of Bernard of Verdun.
To calculate the solar equation and the true longitude of the Sun, Ibn al‐Hāʾim
follows Zarqālī's solar model of variable eccentricity. Ibn al‐Hāʾim
describes three different types of year: tropical, sidereal, and anomalistic.
His classification is practically identical to the one given by Zarqālī
himself. Ibn al‐Hāʾim devotes great attention to the computation
of the anomalistic year which, in his opinion, is the basis for obtaining
the other two types of year; since its value is fixed, it is the one that
should be used to obtain mean motions and to carry out astronomical calculations.
As for lunar theory, the zīj deals with two aspects of
the theory of the Moon: the computation of its longitude, and the computation
of its latitude. Ibn al‐Hāʾim proposes two corrections to
the standard Ptolemaic lunar theory. The first is an attempt to correct
the theory of lunar longitude. The correction is ascribed to a lost astronomical
work of Zarqālī, which Ibn al‐Hāʾim had read in
a manuscript written by the Toledan astronomer himself. It seems to imply
the existence of a lunar equant point that rotates with the motion of the
solar apogee. We do not know to what extent the generalization of the correction
of the Ptolemaic lunar model is due to Zarqālī himself or is the
result of Ibn al‐Hāʾim's interpretation of his work. In
any case, this model met with some success, for we find the same correction
in later zījes although restricted to the calculation of eclipses
and the New Moon. The second correction is a peculiar one: It is a correction
of the computation of the lunar latitude that is directly related to a practice
in the calculation of longitudes that had been standard among Muslim astronomers
since the Mumtaḥan zīj of Yaḥyā
ibn Abī Manṣūr,
though with Ibn al‐Hāʾim there is a change of approach.
He believes that his lunar model gives ecliptic longitudes, that Yaḥyā's
reduction to the ecliptic is unnecessary for the computation of longitudes,
and that an inverse reduction to the lunar orbit should be operated to calculate
latitudes. The results of Ibn al‐Hāʾim's model are different
and also from those obtained by Yaḥyā ibn Abī Manṣūr and his followers.
Abdulrahman, Muhammad (1996). “Ḥisāb
al‐kawākib fī al‐Zīj al‐shāmil fī
tahdhīb al‐kāmil li‐Ibn al‐Raqqām” (in
Arabic). Ph.D. diss., University of Barcelona.
Calvo, Emilia (1998). “Astronomical Theories Related to the
Sun in Ibn al‐Hāʾim's al‐Zīj al‐kāmil
fī‐l‐taʿālīm.” Zeitschrift für Geschichte
der Arabisch‐Islamischen Wissenschaften 12: 51–111.
Comes, Mercè (2001). “Ibn al‐Hāʾim's Trepidation
Model.” Suhayl 2: 291–408.
Puig, Roser (2000). “The Theory of the Moon in the Al‐Zīj
al‐kāmil fī‐l‐taʿālīm of Ibn al‐Hāʾim
(circa. 1205).” Suhayl 1: 71–99.