Ahmad ibn 'Abdallah Habash Hasib
Marwazi (766 - d. after 869
in Samarra, Iraq) was
a Persian astronomer, geographer,
and mathematician from Merv in Khorasan who for
the first time described the trigonometric ratios: sine, cosine, tangent and cotangent.
He flourished in Baghdad, and died a centenarian after 869. He worked
under the Abbasid caliphs al-Ma'mun and al-Mu'tasim.
Work
He made observations from 825 to 835, and compiled three astronomical
tables: the first were still in the Hindu manner; the second, called the
'tested" tables, were the most important; they are likely identical with
the "Ma'munic" or "Arabic" tables and may be a collective
work of al-Ma'mun's astronomers; the third, called tables of the Shah, were
smaller.
Apropos of the solar eclipse of 829, Habash gives us the first instance of
a determination of time by an altitude (in this case, of the sun); a method which
was generally adopted by Muslim astronomers.
In 830, he seems to have introduced the notion of "shadow", umbra
(versa), equivalent to our tangent in trigonometry, and he
compiled a table of such shadows which seems to be the earliest of its kind. He
also introduced the cotangent, and produced the first tables of for it.
The
Book of Bodies and Distances
Al-Hasib conducted various observations at the Al-Shammisiyyah
observatory in Baghdad and estimated a number of geographic and
astronomical values. He compiled his results in The Book of Bodies and
Distances, in which some of his results included the following:
Earth
·
Earth's circumference: 20,160 miles (32,444 km)
·
Earth's diameter: 6414.54 miles (10323.201 km)
·
Earth radius: 3207.275 miles (5161.609 km)
Moon
·
Moon's diameter: 1886.8 miles (3036.5 km)
·
Moon's circumference: 5927.025 miles (9538.622 km)
·
Radius of closest distance of Moon: 215,208;9,9 (sexagesimal) miles
·
Half-circumference of closest distance of Moon: 676,368;28,45,25,43
(sexagesimal) miles
·
Radius of furthest distance of Moon: 205,800;8,45 (sexagesimal) miles
·
Diameter of furthest distance of Moon: 411,600.216 miles
(662,406.338 km)
·
Circumference of furthest distance of Moon: 1,293,600.916 miles
(2,081,848.873 km)
Sun
·
Sun's diameter: 35,280;1,30 miles (56,777.6966 km)
·
Sun's circumference: 110,880;4,43 miles (178,444.189 km)
·
Diameter of orbit of Sun: 7,761,605.5 miles (12,491,093.2 km)
·
Circumference of orbit of Sun: 24,392,571.38 miles (39,256,038 km)
·
One degree along orbit of Sun: 67,700.05 miles
(108,952.67 km)
·
One minute along orbit of Sun: 1129.283 miles (1817.405 km)
Ḥabash al‐Ḥāsib (literally,
“Ḥabash the calculator,” with the intended meaning of “mathematical
astronomer”) was one of the most original and most influential Muslim
astronomers of the formative period of Islamic astronomy. The dates of his
birth and death are not known, but according to the bibliographer Ibn al‐Nadīm he
died as a centenarian. Ḥabash was closely associated with
the ʿAbbāsid court; he was active in Baghdad during the reign of
Caliph Maʾmūn (813–833). Later, he lived and worked in
Samarra, which in 838, became the new administrative capital of
the ʿAbbāsid Empire.
Ḥabash's biography is yet to be definitively established. The bibliographer Ibn al‐Nadīm (died: 995) mentions Ḥabash as a scientist active at the time of Maʾmūn, and Ibn al‐Qifṭī (died: 1248) adds that he also lived under the reign of al‐Muʿtaṣim. In his own account of the achievements of the aṣḥāb al‐mumtaḥan – the group of scholars involved in the observational project sponsored by Caliph Maʾmūn whose objective was to check the parameters of Ptolemy's Almagest – Ḥabash does not present himself as one of their protagonists, although he was certainly in close contact with them. The earliest certain date associated with him is given by Ibn Yūnus, who reports an observation conducted by Ḥabash in Baghdad in the year 829/830 (i. e., 4 years before the death of Maʾmūn). This is also the date associated with many other mumtaḥan observations and with the mumtaḥan star‐table.
Ibn al‐Qifṭī attributes a zīj
(astronomical handbook) to Ḥabash. This was compiled when he was a young man in
the tradition of the Indian Sindhind, and was based upon the zīj of Khwārizmī.
Also ascribed to him is another smaller work, the Zīj al‐Shāh, probably
following the same Pahlavi tradition as the eponym work by Fazārī. The
composition of those two non‐Ptolemaic zījes must have occurred before 829/830,
the year when the mumtaḥan observational program was inaugurated. But Ḥabash is
best known to his contemporaries and successors for his authorship of a third
zīj, whose content is almost entirely Ptolemaic, and which became known as
“the” zīj of Ḥabash.
Ḥabash al‐Ḥāsib (literally, “Ḥabash the calculator,” with the intended meaning of “mathematical astronomer”) was one of the most original and most influential Muslim astronomers of the formative period of Islamic astronomy. The dates of his birth and death are not known, but according to the bibliographer Ibn al‐Nadīm he died as a centenarian. Ḥabash was closely associated with the ʿAbbāsid court; he was active in Baghdad during the reign of Caliph Maʾmūn (813–833). Later, he lived and worked in Samarra, which in 838, became the new administrative capital of the ʿAbbāsid Empire.
Ḥabash's biography is yet to be
definitively established. The bibliographer Ibn al‐Nadīm (died: 995) mentions
Ḥabash as a scientist active at the time of Maʾmūn, and Ibn al‐Qifṭī (died:
1248) adds that he also lived under the reign of al‐Muʿtaṣim. In his own
account of the achievements of the aṣḥāb al‐mumtaḥan – the group of scholars
involved in the observational project sponsored by Caliph Maʾmūn whose
objective was to check the parameters of Ptolemy's Almagest – Ḥabash does not
present himself as one of their protagonists, although he was certainly in
close contact with them. The earliest certain date associated with him is given
by Ibn Yūnus, who reports an observation conducted by Ḥabash in Baghdad in the
year 829/830 (i. e., 4 years before the death of Maʾmūn). This is also the date
associated with many other mumtaḥan observations and with the mumtaḥan
star‐table.
Ibn al‐Qifṭī attributes a zīj
(astronomical handbook) to Ḥabash. This was compiled when he was a young man in
the tradition of the Indian Sindhind, and was based upon the zīj of Khwārizmī.
Also ascribed to him is another smaller work, the Zīj al‐Shāh, probably
following the same Pahlavi tradition as the eponym work by Fazārī. The
composition of those two non‐Ptolemaic zījes must have occurred before 829/830,
the year when the mumtaḥan observational program was inaugurated. But Ḥabash is
best known to his contemporaries and successors for his authorship of a third
zīj, whose content is almost entirely Ptolemaic, and which became known as
“the” zīj of Ḥabash.
In the introduction to this
latter zīj, Ḥabash informs his readers that after Maʾmūn's death he took upon
himself the task of revising the observational data gathered by the “mumtaḥan
astronomers.” Hence, inspired by Ptolemy's methodology, he conducted his own
observations of the Sun and Moon, and also made repeated observations of the
remaining planets at specific times. The latest dates associated with Ḥabash
are recorded in his zīj – 22 April 849, 17 November 860, and 15 September 868.
These dates coincide with the reigns of Caliph al‐Mutawakkil (reigned: 847–861)
and of his third short‐lived successor al‐Muʿtazz (reigned: 866–869). We can
assume that the zīj was finalized after the year 869 and represented Ḥabash's
ultimate achievement. A further indication of this is the fact that Ḥabash uses
an obliquity of the ecliptic of 23° 35′, a value observed by the Banū Mūsā in
Samarra in the year 868/869. He could not have been more than circa 75 years
old at that time, which would then imply that he was not born before circa 796.
The period 796–894, in fact, seems to be the most reasonable estimate for his
life span, and this would make him belong to the same generation as Abū Maʿshar
and Kindī. The usual modern references to him as flourishing circa 830 would
seem to correspond in actuality to the earliest period of his life.
To summarize, we can
divide Ḥabash's scientific career into the following four distinct
periods:
1.
|
The early, formative period in Baghdad (circa 815–829),
during which he became acquainted with the Indian and Persian astronomical
systems through the works of Fazārī and Khwārizmī, and composed two zījes
based upon these systems.
|
2.
|
The mumtaḥan period (829–834), during which he presumably
had close contacts with the mumtaḥan group of astronomers in
Baghdad and Damascus, and benefited from their new observations and insights.
During this crucial period, the superiority of Ptolemy's system became
gradually obvious to most specialists. With the resulting consensus in favor
of Ptolemaic astronomy and the consequent abandonment of Persian and Indian
theories, Islamic astronomy reached a new, stable phase of its development.
|
3.
|
The post‐mumtaḥan period, beginning after the death of Maʾmūn
in August 833, and possibly based in Damascus, during which Ḥabash
pursued his own observational program following the mumtaḥan tradition.
|
4.
|
The Samarra period, covering the last half of his career, during which he
finalized his Ptolemaic zīj and composed most of his
astronomical works that are now extant.
|
The Ptolemaic zīj of Ḥabash, the
only one that is extant, is known under four different names – al‐Zīj
al‐Mumtaḥan and al‐Zīj al‐Maʾmūnī (because it is based on the observational
program of the mumtaḥan group under the sponsorship of Maʾmūn), al‐Zīj
al‐Dimashqī (presumably because it was also based on observations conducted by
Ḥabash in Damascus), and al‐Zīj al‐ʿArabī (because it is based on the Arabic
Hijra calendar).
There is absolutely no evidence
to support the contention that the above appellations might refer to more than
a single work. Every reference to “the zīj of Ḥabash” encountered in later
sources (notably Bīrūnī and Ibn Yūnus) is in accord with the single version of
the zīj by this author that is preserved for us. There is an instance where
Bīrūnī mentions the zīj of Ḥabash in general terms, and later characterizes the
same work with the epithet al‐mumtaḥan. This zīj is the earliest independently
compiled Ptolemaic astronomical handbook in the Arabic language that is
preserved in its entirety. Undoubtedly, it was also one of the most influential
zījes of its generation.
Indeed, Bīrūnī, in the early (Khwārizmian) period of his life, utilized it for his own astronomical practice. Although Ḥabash follows Ptolemy's models and procedures very closely, he does introduce several new, improved parameters as well as an impressive amount of original computational methods, some of them undoubtedly of Indian origin or inspiration.
His zīj also contains a set of
auxiliary trigonometric tables, called jadwal al‐taqwīm, which are of singular
importance in the history of trigonometry.
Two copies of this zīj are
available, one preserved in Istanbul, which preserves fairly well the original
text, and a second one in Berlin. The latter is a recension of the original,
mixed with materials due to various later astronomers. (A table of concordance
with the Istanbul MS is appended to M. Debarnot's survey of the Istanbul MS.)
Unfortunately, Ḥabash's zīj is yet to be published.
Another work of Ḥabash, his Book
of Bodies and Distances, is in fact devoted to five different topics of
scientific activity conducted under the patronage of Maʾmūn, including an
interesting report on the geodetic expedition to determine the radius of the
Earth (or equivalently the length of 1° of the meridian). Ḥabash also devoted
several works to the topic of astronomical instrumentation. An important
treatise on the construction of the melon astrolabe, which he probably invented
and whose principle is based on an “azimuthal equidistant” mapping, has been
published by E. Kennedy et al. (1999). An anonymous treatise on the
construction of a highly original but still unexplained universal instrument
for timekeeping with the stars, preserved in a unique and incomplete copy, has
been published lately, and Ḥabash's authorship has been established. D. King
recently suggested that this instrument could be a companion to the medieval
European universal dial known as navicula de venetiis, which he hypothesizes to
be, ultimately, of Islamic origin. Ḥabash also composed treatises on the use of
the celestial globe, the spherical astrolabe, and the armillary sphere.
Ḥabash's graphical procedure (a
so–called analemma construction) for determining the direction of Mecca (qibla)
is preserved in a letter of Bīrūnī to an Abū Saʿīd (most probably Sijzī), in
which the contents of Ḥabash's treatise – not extant in its original form but
incorporated in his zīj – are summarized. Among several works of his that have
not survived are treatises on the construction of the standard planispheric
astrolabe, on the prediction of lunar crescent visibility, on the construction
of sundials, and on some geometrical problem; also lost are his two critical
reports on the observations conducted by the mumtaḥan group in Baghdad and
Damascus.
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