829-869 Ahmad ibn 'Abdallah Habash Hasib Marwazi
829 Ahmad ibn 'Abdallah Habash Hasib
Marwazi d. after 869 in Samarra, Iraq[1] ) was a Persian[2] astronomer,[3] geographer, and mathematician from Merv in Khorasan who described first time Trigonometric ratios: SIN, COS,
TAN & COT.
He flourished in Baghdad, and died a centenarian after 869. He worked under the Abbasid caliphs al-Ma'mun and al-Mu'tasim.
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.[4][5]
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:[6]
Earth
Moon
Moon's circumference: 5927.025 miles (9538.622 km)
Half-circumference of closest distance of Moon:
676,368;28,45,25,43 (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 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)
Merv produced one of the earliest and greatest scientists
of Islam Ahmad ibn 'Abdallah al-Marwazi (Marwazi means from Merv) best known as
Habash al-Hasib (the calculator) who flourished in Bagdad and died a
centenarian between 864 and 874. He was an astronomer under the Caliphs
al-Mamun and al-Muttasim. Habash made observations from 825 to 835 and
completed three astronomical tables, the best known being the mumtahin (tested)
tables, which may be a collective work of al-Ma'mun's astronomers, for there
was a whole team involved in observation at the court at the time. 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. He seems to have introduced the notion of
"shadow," umbra (versa), equivalent to our tangent, and he compiled a
table of such shadows which seems to be the earliest of its kind. One of
Habash’s son, called Djafar was also a distinguished astronomer and instrument
maker.
Died probably Samarra, (Iraq), 829 - 869
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 mumtaḥanobservations
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 ofḤabash.
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 thezīj 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 byḤabash 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.
Penggagas Pertama Kali Rasio
Trigonometri: Sinus (SIN), Cosinus (COS), Tangen (TAN) dan Cotangen (COT).
Sinus
Cosinus Tangen
Ahmad
ibn 'Abdallah Habash Hasib Marwazi adalah orang Persia yang
merupakan astronom, ahli geografi, dan matematikawan dari Merv, Khorasan yang
pertama kali menjelaskan tentang rasio trigonometri: Sinus (SIN), Cosinus
(COS), Tangen (TAN) dan Cotangen (COT).
Habash al-Hasib al-Marwazi lahir setelah tahun 869 di Samarra, Irak, Ia berkembang di Baghdad, dan meninggal di centenarian setelah tahun 869. Beliau hidup saah kekhalifahan Abbasiyah al-Ma'mun dan al-Mu'tasim.
Astronomi
Selama tahun 825-835, al-Marwazi membuat pengamatan dengan menyusun tiga tabel astronomi yakni:
Habash al-Hasib al-Marwazi lahir setelah tahun 869 di Samarra, Irak, Ia berkembang di Baghdad, dan meninggal di centenarian setelah tahun 869. Beliau hidup saah kekhalifahan Abbasiyah al-Ma'mun dan al-Mu'tasim.
Astronomi
Selama tahun 825-835, al-Marwazi membuat pengamatan dengan menyusun tiga tabel astronomi yakni:
1. Pertama masih dengan
cara Hindu
2. Kedua, disebut 'mengiuji
"tabel, tabel ini cenderung identik dengan "Ma'munic"atau
"tabel Arab" dan mungkin sebuah karya kolektif astronom al-Ma'mun,
3. Yang ketiga, yang
disebut tabel Shah, yang lebih kecil.
Pada
tahun 829 Ia melakukan penelitian yang berhubungan dengan gerhana
matahari, Habash memberi kita contoh pertama dari penentuan waktu dengan
ketinggian (dalam hal ini, matahari); metode yang umumnya diadopsi oleh para
astronom Muslim.
Matematika
Matematika
Pada
830, ia telah memperkenalkan konsep "bayangan," umbra (versa), setara
dengan singgung di trigonometri, dan ia menyusun tabel bayangan yang menjadi
awal dari jenisnya. Dia juga memperkenalkan kotangen, dan menghasilkan tabel
pertama untuk itu.
Kitab Badan dan Jarak
Al-Hasib melakukan berbagai pengamatan di observatorium Al-Shammisiyyah di Baghdad dan memperkirakan sejumlah nilai geografis dan astronomi. Dia mengumpulkan hasil dalam Kitab Badan dan Jarak, di mana beberapa dari hasil meliputi:
Bumi (Earth)
Kitab Badan dan Jarak
Al-Hasib melakukan berbagai pengamatan di observatorium Al-Shammisiyyah di Baghdad dan memperkirakan sejumlah nilai geografis dan astronomi. Dia mengumpulkan hasil dalam Kitab Badan dan Jarak, di mana beberapa dari hasil meliputi:
Bumi (Earth)
· Keliling
bumi (Earth's circumference): 20,160 mil (32,444 km)
· Diameter
bumi (Earth's diameter): 6414.54 mil (10323.201 km)
· Jari-jari
Bumi (Earth radius): 3207.275 mil (5161.609 km)
Bulan
(Moon)
· Diameter
Bulan (Moon's diameter): 1886.8 mil (3036.5 km)
· Keliling
Bulan (Moon's circumference): 5927.025 mil (9538.622 km)
· Radius
jarak terdekat dari Bulan (Radius of closest distance of Moon): 215,208;9,9
(sexagesimal)
miles
· Setengan-keliling
jarak terdekat dari Bulan (Half-circumference of closest distance of Moon):
676,368;28,45,25,43
(sexagesimal) mil
· Radius
jarak terjauh Bulan (Radius of furthest distance of Moon): 205,800;8,45
(sexagesimal)
mil
· Diameter
jarak terjauh Bulan (Diameter of furthest distance of Moon): 411,600.216 miles
(662,406.338
km)
· Keliling
jarak terjauh Moon (Circumference of furthest distance of Moon): 1,293,600.916
miles
(2,081,848.873 km)
Matahari
(Sun)
· Diameter
Matahari (Sun's diameter): 35,280;1,30 mil (56,777.6966 km)
· Keliling
Matahari (Sun's circumference): 110,880;4,43 mil (178,444.189 km)
· Diameter
orbit Matahari (Diameter of orbit of Sun): 7,761,605.5 mil (12,491,093.2 km)
· Kelilng
orbit Matahari (Circumference of orbit of Sun): 24,392,571.38 mil (39,256,038
km)
· Satu
derajat sepanjang orbit Matahari (One degree along orbit of Sun): 67,700.05 mil
(108,952.67 km)
· Satu
menit sepanjang orbit Matahari (One minute along orbit of Sun): 1129.283 mil
(1817.405
km)
- See more at: http://www.delapan6.com/read/2068-habash-al-hasib-al-marwazi-penggagas-pertama-kali-rasio-trigonometri-sinus-sin-cosinus-cos-tangen-tan-dan-cotangen-cot#sthash.ZLxNsaxF.dpuf
Selected References
Al‐Hāshimī, ʿAlī ibn
Sulaymān. The Book of
the Reasons Behind Astronomical Tables (Kitāb fī ʿilal al‐zījāt). (A
facsimile reproduction of the unique Arabic text contained in the Bodleian MS
Arch. Seld. A.11 with a translation by Fuad I. Haddad and E. S. Kennedy and a
commentary by David Pingree and E. S. Kennedy. Delmar, New York: Scholars'
Facsimiles and Reprints, 1981.)
Al‐Qifṭī,
Jamāl al‐Dīn (1903). Taʾrīkh al‐ḥukamāʾ, edited by J. Lippert. Leipzig: Theodor Weicher.
Ali, Jamil
(trans.) (1967). The
Determination of the Coordinates of Cities: Al‐Bīrūnī's Taḥdīd al‐Amākin. Beirut: American University of Beirut.
Berggren, J. L. (1980). “A Comparison of
Four Analemmas for Determining the Azimuth of the Qibla.” Journal for
the History of Arabic Science 4: 69–80
Selected References
Al‐Hāshimī, ʿAlī ibn
Sulaymān. The Book of
the Reasons Behind Astronomical Tables (Kitāb fī ʿilal al‐zījāt). (A
facsimile reproduction of the unique Arabic text contained in the Bodleian MS
Arch. Seld. A.11 with a translation by Fuad I. Haddad and E. S. Kennedy and a
commentary by David Pingree and E. S. Kennedy. Delmar, New York: Scholars'
Facsimiles and Reprints, 1981.)
Al‐Qifṭī,
Jamāl al‐Dīn (1903). Taʾrīkh al‐ḥukamāʾ, edited by J. Lippert. Leipzig: Theodor Weicher.
Ali, Jamil
(trans.) (1967). The
Determination of the Coordinates of Cities: Al‐Bīrūnī's Taḥdīd al‐Amākin. Beirut: American University of Beirut.
Berggren, J.
L. (1980). “A Comparison of Four Analemmas for Determining the Azimuth of the
Qibla.” Journal for
the History of Arabic Science 4: 69–80.
Penggagas Pertama Kali Rasio
Trigonometri: Sinus (SIN), Cosinus (COS), Tangen (TAN) dan Cotangen (COT).
Sinus
Cosinus Tangen
Ahmad ibn 'Abdallah Habash
Hasib Marwazi adalah
orang Persia yang merupakan astronom, ahli geografi, dan matematikawan dari
Merv, Khorasan yang pertama kali menjelaskan tentang rasio trigonometri: Sinus
(SIN), Cosinus (COS), Tangen (TAN) dan Cotangen (COT).
Habash al-Hasib al-Marwazi lahir setelah tahun 869 di Samarra, Irak, Ia berkembang di Baghdad, dan meninggal di centenarian setelah tahun 869. Beliau hidup saah kekhalifahan Abbasiyah al-Ma'mun dan al-Mu'tasim.
Astronomi
Selama tahun 825-835, al-Marwazi membuat pengamatan dengan menyusun tiga tabel astronomi yakni:
Habash al-Hasib al-Marwazi lahir setelah tahun 869 di Samarra, Irak, Ia berkembang di Baghdad, dan meninggal di centenarian setelah tahun 869. Beliau hidup saah kekhalifahan Abbasiyah al-Ma'mun dan al-Mu'tasim.
Astronomi
Selama tahun 825-835, al-Marwazi membuat pengamatan dengan menyusun tiga tabel astronomi yakni:
1.
Pertama masih dengan cara Hindu
2.
Kedua, disebut 'mengiuji "tabel, tabel ini cenderung
identik dengan "Ma'munic"atau "tabel
3.
Arab" dan mungkin sebuah karya kolektif astronom
al-Ma'mun,
4.
Yang ketiga, yang disebut tabel Shah, yang lebih kecil.
Pada tahun 829 Ia melakukan
penelitian yang berhubungan dengan gerhana matahari, Habash memberi kita contoh
pertama dari penentuan waktu dengan ketinggian (dalam hal ini, matahari);
metode yang umumnya diadopsi oleh para astronom Muslim.
Matematika
Matematika
Pada 830, ia telah memperkenalkan konsep
"bayangan," umbra (versa), setara dengan singgung di trigonometri,
dan ia menyusun tabel bayangan yang menjadi awal dari jenisnya. Dia juga memperkenalkan
kotangen, dan menghasilkan tabel pertama untuk itu.
Kitab Badan dan Jarak
Al-Hasib melakukan berbagai pengamatan di observatorium Al-Shammisiyyah di Baghdad dan memperkirakan sejumlah nilai geografis dan astronomi. Dia mengumpulkan hasil dalam Kitab Badan dan Jarak, di mana beberapa dari hasil meliputi:
Bumi (Earth)
Kitab Badan dan Jarak
Al-Hasib melakukan berbagai pengamatan di observatorium Al-Shammisiyyah di Baghdad dan memperkirakan sejumlah nilai geografis dan astronomi. Dia mengumpulkan hasil dalam Kitab Badan dan Jarak, di mana beberapa dari hasil meliputi:
Bumi (Earth)
· Keliling
bumi (Earth's circumference): 20,160 mil (32,444 km)
· Diameter
bumi (Earth's diameter): 6414.54 mil (10323.201 km)
· Jari-jari
Bumi (Earth radius): 3207.275 mil (5161.609 km)
Bulan (Moon)
· Diameter
Bulan (Moon's diameter): 1886.8 mil (3036.5 km)
· Keliling
Bulan (Moon's circumference): 5927.025 mil (9538.622 km)
· Radius
jarak terdekat dari Bulan (Radius of closest distance of Moon): 215,208;9,9
· (sexagesimal)
miles
· Setengan-keliling
jarak terdekat dari Bulan (Half-circumference of closest distance of
· Moon):
676,368;28,45,25,43 (sexagesimal) mil
· Radius
jarak terjauh Bulan (Radius of furthest distance of Moon): 205,800;8,45
· (sexagesimal)
mil
· Diameter
jarak terjauh Bulan (Diameter of furthest distance of Moon): 411,600.216 miles
· (662,406.338
km)
· Keliling
jarak terjauh Moon (Circumference of furthest distance of Moon): 1,293,600.916
· miles
(2,081,848.873 km)
Matahari (Sun)
· Diameter
Matahari (Sun's diameter): 35,280;1,30 mil (56,777.6966 km)
· Keliling
Matahari (Sun's circumference): 110,880;4,43 mil (178,444.189 km)
· Diameter
orbit Matahari (Diameter of orbit of Sun): 7,761,605.5 mil (12,491,093.2 km)
· Kelilng
orbit Matahari (Circumference of orbit of Sun): 24,392,571.38 mil (39,256,038
km)
· Satu
derajat sepanjang orbit Matahari (One degree along orbit of Sun): 67,700.05 mil
· (108,952.67
km)
· Satu
menit sepanjang orbit Matahari (One minute along orbit of Sun): 1129.283 mil
· (1817.405
km)
- See more at: http://www.delapan6.com/read/2068-habash-al-hasib-al-marwazi-penggagas-pertama-kali-rasio-trigonometri-sinus-sin-cosinus-cos-tangen-tan-dan-cotangen-cot#sthash.ZLxNsaxF.dpuf
Selected
References
Al‐Hāshimī, ʿAlī ibn Sulaymān. The Book of the Reasons Behind
Astronomical Tables (Kitāb fī ʿilal al‐zījāt). (A facsimile reproduction of the unique
Arabic text contained in the Bodleian MS Arch. Seld. A.11 with a translation by
Fuad I. Haddad and E. S. Kennedy and a commentary by David Pingree and E. S.
Kennedy. Delmar, New York: Scholars' Facsimiles and Reprints, 1981.)
Al‐Qifṭī,
Jamāl al‐Dīn (1903). Taʾrīkh al‐ḥukamāʾ, edited by J. Lippert. Leipzig: Theodor Weicher.
Ali, Jamil (trans.) (1967). The Determination of the Coordinates of
Cities: Al‐Bīrūnī's Taḥdīd al‐Amākin. Beirut: American University of Beirut.
Berggren, J. L. (1980). “A Comparison of
Four Analemmas for Determining the Azimuth of the Qibla.” Journal for the History of Arabic Science 4: 69–80.
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