Astronomy in the medieval Islamic world

Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age (9th–13th centuries),[1] and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and later in the Far East and India. It closely parallels the genesis of other Islamic sciences in its assimilation of foreign material and the amalgamation of the disparate elements of that material to create a science with Islamic characteristics. These included Greek, Sassanid, and Indian works in particular, which were translated and built upon.[2]

An 18th-century Persian astrolabe, kept at the Whipple Museum of the History of Science in Cambridge, England.

Islamic astronomy played a significant role in the revival of Byzantine[3] and European[4] astronomy following the loss of knowledge during the early medieval period, notably with the production of Latin translations of Arabic works during the 12th century. Islamic astronomy also had an influence on Chinese astronomy[5] and Malian astronomy.[6][7]

A significant number of stars in the sky, such as Aldebaran, Altair and Deneb, and astronomical terms such as alidade, azimuth, and nadir, are still referred to by their Arabic names.[8][9] A large corpus of literature from Islamic astronomy remains today, numbering approximately 10,000 manuscripts scattered throughout the world, many of which have not been read or catalogued. Even so, a reasonably accurate picture of Islamic activity in the field of astronomy can be reconstructed.[10]

Pre-Islamic ArabsEdit

Ahmad Dallal notes that, unlike the Babylonians, Greeks, and Indians, who had developed elaborate systems of mathematical astronomical study, the pre-Islamic Arabs relied entirely on empirical observations. These observations were based on the rising and setting of particular stars, and this area of astronomical study was known as anwa. Anwa continued to be developed after Islamization by the Arabs, where Islamic astronomers added mathematical methods to their empirical observations.[11]

Early IslamEdit

Following the Islamic conquests, under the early caliphate, Muslim scholars began to absorb Hellenistic and Indian astronomical knowledge via translations into Arabic (in some cases via Persian).

The first astronomical texts that were translated into Arabic were of Indian[12] and Persian origin.[13] The most notable of the texts was Zij al-Sindhind,[a] an 8th-century Indian astronomical work that was translated by Muhammad ibn Ibrahim al-Fazari and Yaqub ibn Tariq after 770 CE with the assistance of Indian astronomers who visited the court of caliph Al-Mansur in 770.[12] Another text translated was the Zij al-Shah, a collection of astronomical tables (based on Indian parameters) compiled in Sasanid Persia over two centuries. Fragments of texts during this period indicate that Arabs adopted the sine function (inherited from India) in place of the chords of arc used in Greek trigonometry.[11]

According to David King, after the rise of Islam, the religious obligation to determine the qibla and prayer times inspired more progress in astronomy for centuries.[14]

Golden AgeEdit

 
The Tusi-couple is a mathematical device invented by Nasir al-Din al-Tusi in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger circle.

The House of Wisdom was an academy established in Baghdad under Abbasid caliph Al-Ma'mun in the early 9th century. Astronomical research was greatly supported by the Abbasid caliph al-Mamun through the House of Wisdom. Baghdad and Damascus became the centers of such activity.

The first major Muslim work of astronomy was Zij al-Sindhind by Persian mathematician al-Khwarizmi in 830. The work contains tables for the movements of the Sun, the Moon and the five planets known at the time. The work is significant as it introduced Ptolemaic concepts into Islamic sciences. This work also marks the turning point in Islamic astronomy. Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. Al-Khwarizmi's work marked the beginning of nontraditional methods of study and calculations.[15]

Doubts on PtolemyEdit

In 850, al-Farghani wrote Kitab fi Jawami (meaning "A compendium of the science of stars"). The book primarily gave a summary of Ptolemic cosmography. However, it also corrected Ptolemy based on findings of earlier Arab astronomers. Al-Farghani gave revised values for the obliquity of the ecliptic, the precessional movement of the apogees of the Sun and the Moon, and the circumference of the Earth. The book was widely circulated through the Muslim world, and translated into Latin.[16]

By the 10th century texts appeared regularly whose subject matter was doubts concerning Ptolemy (shukūk).[17] Several Muslim scholars questioned the Earth's apparent immobility[18][19] and centrality within the universe.[20] From this time, independent investigation into the Ptolemaic system became possible. According to Dallal (2010), the use of parameters, sources and calculation methods from different scientific traditions made the Ptolemaic tradition "receptive right from the beginning to the possibility of observational refinement and mathematical restructuring".[21]

Egyptian astronomer Ibn Yunus found fault in Ptolemy's calculations about the planet's movements and their peculiarity in the late 10th century. Ptolemy calculated that Earth's wobble, otherwise known as precession, varied 1 degree every 100 years. Ibn Yunus contradicted this finding by calculating that it was instead 1 degree every 70​14 years.

Between 1025 and 1028, Ibn al-Haytham wrote his Al-Shukuk ala Batlamyus (meaning "Doubts on Ptolemy"). While maintaining the physical reality of the geocentric model, he criticized elements of the Ptolemic models. Many astronomers took up the challenge posed in this work, namely to develop alternate models that resolved these difficulties. In 1070, Abu Ubayd al-Juzjani published the Tarik al-Aflak where he discussed the "equant" problem of the Ptolemic model and proposed a solution.[citation needed] In Al-Andalus, the anonymous work al-Istidrak ala Batlamyus (meaning "Recapitulation regarding Ptolemy"), included a list of objections to the Ptolemic astronomy.

Earth rotationEdit

 
An illustration from al-Biruni's astronomical works, explains the different phases of the moon, with respect to the position of the sun.

Abu Rayhan Biruni (b. 973) discussed the possibility of whether the Earth rotated about its own axis and around the Sun, but in his Masudic Canon, he set forth the principles that the Earth is at the center of the universe and that it has no motion of its own.[22] He was aware that if the Earth rotated on its axis, this would be consistent with his astronomical parameters,[23] but he considered this a problem of natural philosophy rather than mathematics.[24][4]

His contemporary, Abu Sa'id al-Sijzi, accepted that the Earth rotates around its axis.[25] Al-Biruni described an astrolabe invented by Sijzi based on the idea that the earth rotates:

I have seen the astrolabe called Zuraqi invented by Abu Sa'id Sijzi. I liked it very much and praised him a great deal, as it is based on the idea entertained by some to the effect that the motion we see is due to the Earth's movement and not to that of the sky. By my life, it is a problem difficult of solution and refutation. [...] For it is the same whether you take it that the Earth is in motion or the sky. For, in both cases, it does not affect the Astronomical Science. It is just for the physicist to see if it is possible to refute it.[26]

The fact that some people did believe that the earth is moving on its own axis is further confirmed by an Arabic reference work from the 13th century which states:

According to the geometers [or engineers] (muhandisīn), the earth is in constant circular motion, and what appears to be the motion of the heavens is actually due to the motion of the earth and not the stars.[24]

At the Maragha and Samarkand observatories, the Earth's rotation was discussed by al-Kātibī (d. 1277),[27] Tusi (b. 1201) and Qushji (b. 1403). The arguments and evidence used by Tusi and Qushji resemble those used by Copernicus to support the Earth's motion.[18][19] However, it remains a fact that the Maragha school never made the big leap to heliocentrism.[28]

Alternative geocentric systemsEdit

In the 12th century, non-heliocentric alternatives to the Ptolemaic system were developed by some Islamic astronomers in al-Andalus, following a tradition established by Ibn Bajjah, Ibn Tufail, and Ibn Rushd.

A notable example is Nur ad-Din al-Bitruji, who considered the Ptolemaic model mathematical, and not physical.[29][30] Al-Bitruji proposed a theory on planetary motion in which he wished to avoid both epicycles and eccentrics.[31] He was unsuccessful in replacing Ptolemy's planetary model, as the numerical predictions of the planetary positions in his configuration were less accurate than those of the Ptolemaic model.[32] One original aspects of al-Bitruji's system is his proposal of a physical cause of celestial motions. He contradicts the Aristotelian idea that there is a specific kind of dynamics for each world, applying instead the same dynamics to the sublunar and the celestial worlds.[33]

Later periodEdit

In the late thirteenth century, Nasir al-Din al-Tusi created the Tusi couple, as pictured above. Other notable astronomers from the later medieval period include Mu'ayyad al-Din al-'Urdi (c. 1266), Qutb al-Din al Shirazi (c. 1311), Sadr al-Sharia al-Bukhari (c. 1347), Ibn al-Shatir (c. 1375), and Ali al-Qushji (c. 1474).[34]

In the fifteenth century, the Timurid ruler Ulugh Beg of Samarkand established his court as a center of patronage for astronomy. He studied it in his youth, and in 1420 ordered the construction of Ulugh Beg Observatory, which produced a new set of astronomical tables, as well as contributing to other scientific and mathematical advances.[35]

Several major astronomical works were produced in the early 16th century, including ones by 'Abd al-Ali al-Birjandi (d. 1525 or 1526) and Shams al-Din al-Khafri (fl. 1525). However, the vast majority of works written in this and later periods in the history of Islamic sciences are yet to be studied.[19]

InfluencesEdit

EuropeEdit

 
Ibn al-Shatir's model for the appearances of Mercury, showing the multiplication of epicycles using the Tusi-couple, thus eliminating the Ptolemaic eccentrics and equant.

Several works of Islamic astronomy were translated to Latin starting from the 12th century.

The work of al-Battani (d. 929), Kitāb az-Zīj ("Book of Astronomical Tables"), was frequently cited by European astronomers and received several reprints, including one with annotations by Regiomontanus.[36] Copernicus, in his book that initiated the Copernican Revolution, the De Revolutionibus Orbium Coelestium, mentioned al-Battani no fewer than 23 times,[37] and also mentions him in the Commentariolus.[38] Tycho Brahe, Riccioli, Kepler, Galileo and others frequently cited him or his observations.[39] His data is still used in geophysics.[40]

Around 1190, Al-Bitruji published an alternative geocentric system to Ptolemy's model. His system spread through most of Europe during the 13th century, with debates and refutations of his ideas continued to the 16th century.[41] In 1217, Michael Scot finished a Latin translation of al-Bitruji's Book of Cosmology (Kitāb al-Hayʾah), which became a valid alternative to Ptolemy's Almagest in scholastic circles.[33] Several European writers, including Albertus Magnus and Roger Bacon, explained it in detail and compared it with Ptolemy's.[41] Copernicus cited his system in the De revolutionibus while discussing theories of the order of the inferior planets.[41][33]

Some historians maintain that the thought of the Maragheh observatory, in particular the mathematical devices known as the Urdi lemma and the Tusi couple, influenced Renaissance-era European astronomy and thus Copernicus.[4][42][43][44][45] Copernicus used such devices in the same planetary models as found in Arabic sources.[46] Furthermore, the exact replacement of the equant by two epicycles used by Copernicus in the Commentariolus was found in an earlier work by Ibn al-Shatir (d. c. 1375) of Damascus.[47] Copernicus' lunar and Mercury models are also identical to Ibn al-Shatir's.[48]

While the influence of the criticism of Ptolemy by Averroes on Renaissance thought is clear and explicit, the claim of direct influence of the Maragha school, postulated by Otto E. Neugebauer in 1957, remains an open question.[28][49][50] Since the Tusi couple was used by Copernicus in his reformulation of mathematical astronomy, there is a growing consensus that he became aware of this idea in some way. It has been suggested[51][52] that the idea of the Tusi couple may have arrived in Europe leaving few manuscript traces, since it could have occurred without the translation of any Arabic text into Latin. One possible route of transmission may have been through Byzantine science, which translated some of al-Tusi's works from Arabic into Byzantine Greek. Several Byzantine Greek manuscripts containing the Tusi-couple are still extant in Italy.[53] Other scholars have argued that Copernicus could well have developed these ideas independently of the late Islamic tradition.[54] Copernicus explicitly references several astronomers of the "Islamic Golden Age" (10th to 12th centuries) in De Revolutionibus: Albategnius (Al-Battani), Averroes (Ibn Rushd), Thebit (Thabit Ibn Qurra), Arzachel (Al-Zarqali), and Alpetragius (Al-Bitruji), but he does not show awareness of the existence of any of the later astronomers of the Maragha school.[38]

It has been argued that Copernicus could have independently discovered the Tusi couple or took the idea from Proclus's Commentary on the First Book of Euclid,[55] which Copernicus cited.[56] Another possible source for Copernicus's knowledge of this mathematical device is the Questiones de Spera of Nicole Oresme, who described how a reciprocating linear motion of a celestial body could be produced by a combination of circular motions similar to those proposed by al-Tusi.[57]

ChinaEdit

Islamic influence on Chinese astronomy was first recorded during the Song dynasty when a Hui Muslim astronomer named Ma Yize introduced the concept of seven days in a week and made other contributions.[58]

Islamic astronomers were brought to China in order to work on calendar making and astronomy during the Mongol Empire and the succeeding Yuan Dynasty.[59][60] The Chinese scholar Yeh-lu Chu'tsai accompanied Genghis Khan to Persia in 1210 and studied their calendar for use in the Mongol Empire.[60] Kublai Khan brought Iranians to Beijing to construct an observatory and an institution for astronomical studies.[59]

Several Chinese astronomers worked at the Maragheh observatory, founded by Nasir al-Din al-Tusi in 1259 under the patronage of Hulagu Khan in Persia.[61] One of these Chinese astronomers was Fu Mengchi, or Fu Mezhai.[62] In 1267, the Persian astronomer Jamal ad-Din, who previously worked at Maragha observatory, presented Kublai Khan with seven Persian astronomical instruments, including a terrestrial globe and an armillary sphere,[63] as well as an astronomical almanac, which was later known in China as the Wannian Li ("Ten Thousand Year Calendar" or "Eternal Calendar"). He was known as "Zhamaluding" in China, where, in 1271,[62] he was appointed by Khan as the first director of the Islamic observatory in Beijing,[61] known as the Islamic Astronomical Bureau, which operated alongside the Chinese Astronomical Bureau for four centuries. Islamic astronomy gained a good reputation in China for its theory of planetary latitudes, which did not exist in Chinese astronomy at the time, and for its accurate prediction of eclipses.[5]

Some of the astronomical instruments constructed by the famous Chinese astronomer Guo Shoujing shortly afterwards resemble the style of instrumentation built at Maragheh.[61] In particular, the "simplified instrument" (jianyi) and the large gnomon at the Gaocheng Astronomical Observatory show traces of Islamic influence.[5] While formulating the Shoushili calendar in 1281, Shoujing's work in spherical trigonometry may have also been partially influenced by Islamic mathematics, which was largely accepted at Kublai's court.[64] These possible influences include a pseudo-geometrical method for converting between equatorial and ecliptic coordinates, the systematic use of decimals in the underlying parameters, and the application of cubic interpolation in the calculation of the irregularity in the planetary motions.[5]

Hongwu Emperor (r. 1368-1398) of the Ming Dynasty (1328–1398), in the first year of his reign (1368), conscripted Han and non-Han astrology specialists from the astronomical institutions in Beijing of the former Mongolian Yuan to Nanjing to become officials of the newly established national observatory.

That year, the Ming government summoned for the first time the astronomical officials to come south from the upper capital of Yuan. There were fourteen of them. In order to enhance accuracy in methods of observation and computation, Hongwu Emperor reinforced the adoption of parallel calendar systems, the Han and the Hui. In the following years, the Ming Court appointed several Hui astrologers to hold high positions in the Imperial Observatory. They wrote many books on Islamic astronomy and also manufactured astronomical equipment based on the Islamic system.

The translation of two important works into Chinese was completed in 1383: Zij (1366) and al-Madkhal fi Sina'at Ahkam al-Nujum, Introduction to Astrology (1004).

In 1384, a Chinese astrolabe was made for observing stars based on the instructions for making multi-purposed Islamic equipment. In 1385, the apparatus was installed on a hill in northern Nanjing.

Around 1384, during the Ming Dynasty, Hongwu Emperor ordered the Chinese translation and compilation of Islamic astronomical tables, a task that was carried out by the scholars Mashayihei, a Muslim astronomer, and Wu Bozong, a Chinese scholar-official. These tables came to be known as the Huihui Lifa (Muslim System of Calendrical Astronomy), which was published in China a number of times until the early 18th century,[65] though the Qing Dynasty had officially abandoned the tradition of Chinese-Islamic astronomy in 1659.[66] The Muslim astronomer Yang Guangxian was known for his attacks on the Jesuit's astronomical sciences.

KoreaEdit

 
Korean celestial globe based on the Huihui Lifa.

In the early Joseon period, the Islamic calendar served as a basis for calendar reform being more accurate than the existing Chinese-based calendars.[67] A Korean translation of the Huihui Lifa, a text combining Chinese astronomy with Islamic astronomy works of Jamal ad-Din, was studied in Korea under the Joseon Dynasty during the time of Sejong in the fifteenth century.[68] The tradition of Chinese-Islamic astronomy survived in Korea up until the early nineteenth century.[66]

ObservatoriesEdit

 
Work in the observatorium of Taqi al-Din.

The first systematic observations in Islam are reported to have taken place under the patronage of al-Mamun. Here, and in many other private observatories from Damascus to Baghdad, meridian degrees were measured, solar parameters were established, and detailed observations of the Sun, Moon, and planets were undertaken.

In the tenth century, the Buwayhid dynasty encouraged the undertaking of extensive works in astronomy, such as the construction of a large-scale instrument with which observations were made in the year 950. We know of this by recordings made in the zij of astronomers such as Ibn al-Alam. The great astronomer Abd Al-Rahman Al Sufi was patronised by prince Adud o-dowleh, who systematically revised Ptolemy's catalogue of stars. Sharaf al-Daula also established a similar observatory in Baghdad. Reports by Ibn Yunus and al-Zarqall in Toledo and Cordoba indicate the use of sophisticated instruments for their time.

It was Malik Shah I who established the first large observatory, probably in Isfahan. It was here where Omar Khayyám with many other collaborators constructed a zij and formulated the Persian Solar Calendar a.k.a. the jalali calendar. A modern version of this calendar is still in official use in Iran today.

The most influential observatory was however founded by Hulegu Khan during the thirteenth century. Here, Nasir al-Din al-Tusi supervised its technical construction at Maragha. The facility contained resting quarters for Hulagu Khan, as well as a library and mosque. Some of the top astronomers of the day gathered there, and from their collaboration resulted important modifications to the Ptolemaic system over a period of 50 years.

In 1420, prince Ulugh Beg, himself an astronomer and mathematician, founded another large observatory in Samarkand, the remains of which were excavated in 1908 by Russian teams.

And finally, Taqi al-Din Muhammad ibn Ma'ruf founded a large observatory in Ottoman Constantinople in 1577, which was on the same scale as those in Maragha and Samarkand. The observatory was short-lived however, as opponents of the observatory and prognostication from the heavens prevailed and the observatory was destroyed in 1580.[69] While the Ottoman clergy did not object to the science of astronomy, the observatory was primarily being used for astrology, which they did oppose, and successfully sought its destruction.[70]

InstrumentsEdit

Our knowledge of the instruments used by Muslim astronomers primarily comes from two sources: first the remaining instruments in private and museum collections today, and second the treatises and manuscripts preserved from the Middle Ages. Muslim astronomers of the "Golden Period" made many improvements to instruments already in use before their time, such as adding new scales or details.

Celestial globes and armillary spheresEdit

 
A Large Persian Brass Celestial Globe with an ascription to Hadi Isfahani and a date of 1197 AH/ 1782-3 AD of typical spherical form, the globe engraved with markings, figures and astrological symbols, inscriptive details throughout

Celestial globes were used primarily for solving problems in celestial astronomy. Today, 126 such instruments remain worldwide, the oldest from the 11th century. The altitude of the Sun, or the Right Ascension and Declination of stars could be calculated with these by inputting the location of the observer on the meridian ring of the globe.

An armillary sphere had similar applications. No early Islamic armillary spheres survive, but several treatises on "the instrument with the rings" were written. In this context there is also an Islamic development, the spherical astrolabe, of which only one complete instrument, from the 14th century, has survived.

AstrolabesEdit

Brass astrolabes were a Hellenistic invention. The first Islamic astronomer reported as having built an astrolabe is Muhammad al-Fazari (late 8th century).[71] Astrolabes were popular in the Islamic world during the "Golden Age", chiefly as an aid to finding the qibla. The earliest known example is dated to 927/8 (AH 315).

The instruments were used to read the time of rise of the Sun and fixed stars. al-Zarqali of Andalusia constructed one such instrument in which, unlike its predecessors, did not depend on the latitude of the observer, and could be used anywhere. This instrument became known in Europe as the Saphea.

Mechanical calendarEdit

Abu Rayhan Biruni made an instrument he called "Box of the Moon", which was a mechanical lunisolar calendar, employing a gear train and eight gear-wheels.[72] This was an early example of a fixed-wired knowledge processing machine.[73]

SundialsEdit

Muslims made several important improvements[which?] to the theory and construction of sundials, which they inherited from their Indian and Greek predecessors. Khwarizmi made tables for these instruments which considerably shortened the time needed to make specific calculations.

Sundials were frequently placed on mosques to determine the time of prayer. One of the most striking examples was built in the fourteenth century by the muwaqqit (timekeeper) of the Umayyad Mosque in Damascus, ibn al-Shatir.[75]

QuadrantsEdit

Several forms of quadrants were invented by Muslims. Among them was the sine quadrant used for astronomical calculations, and various forms of the horary quadrant, used to determine time (especially the times of prayer) by observations of the Sun or stars. A center of the development of quadrants was ninth-century Baghdad.[76]

EquatoriumsEdit

The Equatorium is an invention from Al-Andalus, by Al-Zarqali. The earliest known was made in the eleventh century.[77] It is a mechanical device for finding the positions of the moon, sun, stars and planets, without calculation using a geometrical model to represent the celestial body's mean and anomalistic position.


Astronomy in Islamic ArtEdit

 
Qusayr' Amra Dome Fresco, 705–15, fresco on tepidarium, bathhouse dome ceiling, Jordan.

There are examples of cosmological imagery throughout many forms of Islamic art, whether that be manuscripts, ornately crafted astrological tools, or palace frescoes, just to name a few. Islamic art maintains the capability to reach every class and level of society.

Within Islamic cosmological doctrines and the Islamic study of astronomy, such as the Encyclopedia of the Brethren of Purity (alternatively called The Rasa'il of the Ikhwan al-Safa) there is a heavy emphasis by medieval scholars on the importance of the study of the heavens. This study of the heavens has translated into artistic representations of the universe and astrological concepts.[78] There are many themes under which Islamic astrological art falls under, such as religious, political, and cultural contexts.[79] It is posited by scholars that there are actually three waves or traditions of cosmological imagery, Western, Byzantine, and Islamic. The Islamic world gleaned inspiration from Greek, Iranian, and Indian methods in order to procure a unique representation of the stars and the universe. [80]

ExamplesEdit

 
Zodiac Ewer, first half 13th century, potentially Iran. Engraved Brass, inlaid with copper and silver, 8 3/4 in. x 6 7/8 in..

A place like Quasyr' Amra, which was used as a rural Umayyad palace and bath complex, coveys the way astrology and the cosmos have weaved their way into architectural design. During the time of its use, one could be resting in the bathhouse and gaze at the frescoed dome that would almost reveal a sacred and cosmic nature. Aside from the other frescoes of the complex which heavily focused on al-Walid, the bath dome was decorated in the Islamic zodiac and celestial designs.[81] It would have almost been as if the room was suspended in space. In their encyclopedia, the Ikhwan al' Safa describe the Sun to have been placed at the center of the universe by God and all other celestial bodies orbit around it in spheres.[82] As a result, it would be as if whoever was sitting underneath this fresco would have been at the center of the universe, reminded of their power and position. A place like Qusayr' Amra represents the way astrological art and images interacted with Islamic elites and those who maintained caliphal authority.

The Islamic zodiac and astrological visuals have also been present in metalwork. Ewers depicting the twelve zodiac symbols exist in order to emphasize elite craftsmanship and carry blessings such as one example now at the Metropolitan Museum of Art.[83] Coinage also carried zodiac imagery that bears the sole purpose of representing the month in which the coin was minted.[84] As a result, astrological symbols could have been used as both decoration, and a means to communicate symbolic meanings or specific information.

Notable astronomers[85]Edit

See alsoEdit

NotesEdit

  1. ^ This book is not related to al-Khwarizmi's Zij al-Sindh. On zijes see E. S. Kennedy, "A Survey of Islamic Astronomical Tables".

ReferencesEdit

CitationsEdit

  1. ^ (Saliba 1994b, pp. 245, 250, 256–257)
  2. ^ (Gingerich 1986)
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  4. ^ a b c Saliba (1999).
  5. ^ a b c d Benno, van Dalen (2002). Ansari, S.M. Razaullah (ed.). Islamic Astronomical Tables in China: The Sources for Huihui li. History of Oriental Astronomy. Astrophysics and Space Science Library. 274. pp. 19–32. doi:10.1007/978-94-015-9862-0. ISBN 978-94-015-9862-0.
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  8. ^ Arabic Star Names, Islamic Crescents' Observation Project, archived from the original on 2 February 2008, retrieved 11 November 2016
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  10. ^ (Ilyas 1997)
  11. ^ a b Dallal (1999), pg. 162
  12. ^ a b Sachau, Edward, ed. (1910), Alberuni's India: An Account of the Religion, Philosophy, Literature, Geography, Chronology, Astronomy, Customs, Laws and Astrology of India about A.D. 1030, 1, London: Kegan Paul, Trench, Trübner, p. xxxi, It was on this occasion [in the eighth century] that the Arabs first became acquainted with a scientific system of astronomy. They learned from Brahmagupta earlier than from Ptolemy.
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  15. ^ Dallal (1999), pg. 163
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