The Accomplishments of Muslim Astronomy at a Glance

 

 Astronomy was one of the earliest sciences to thrive in Islam. In the 8th century, Al-Fazari (d.777) became the first to construct astrolabes. The astrolabe was a multi functional instrument that served for nearly ten centuries to make all sorts of calculations. Al-Fazari also wrote on the armillary sphere, and the calendar.[1] Soon after, Mash’allah (d.815) took part with the Persian al-Naubakht in the preliminary surveying of the foundation of Baghdad  in 762-763. His De Mercibus, is the oldest scientific work in Arabic,[2] and was translated by Gerard of Cremona in the 12th century.[3]

Under Al-Mamun (r. 813-833), an observatory was completed in 829, a major landmark in the history of astronomy, from which, in the year 830, the position of the solar apogee was determined at 82039'.[4] Astronomers at Al-Mamun’s court also found the inclination of the ecliptic to be 23033’.[5] Al-Mamun also supervised two geodetic surveys in Iraq  for the purpose of determining the length of a degree of the meridian, reaching a result of a degree being equal to 562/3 miles.[6] The earth’s circumference was found to be 40,253.4 kms (the accurate figure being 40,068.0 km through the equator, and 40,000.6 km through the poles.)[7]

One of the astronomers at the court was Habash al-Hasib (d.864). A number of works are ascribed to him, and they include the Mumtahan Zij (The Tested Astronomical Table), The Ma’muni Zij; on the Rukhamat (Measurements); on the celestial sphere; on astrolabes; on the Oblique and perpendicular Planes; and on the Distance of the stars.[8] He made observations of solar and lunar eclipses and of planetary positions at Baghdad , Samarra and Damascus .[9] He compiled astronomical tables and gave the first instance of determination of time by altitude, besides introducing the notion of shadow (umbra versa) corresponding to our tangent, and compiling a table of tangents, probably the earliest of its kind.[10]

Also at the court was al-Khwarizmi (d.863) better known as a mathematician, on which much will be said further on. He wrote on the astrolabe, compiled a set of astronomical tables of future planetary and stellar positions, and also became one of the first to compute astronomical and trigonometrical tables.[11]

Al-Farghani (fl. 861) also worked at the same court. His best known work Kitab fi Harakat Al-Samawiyah wa Jaamai Ilm al-Nujum (The Book on the Movement of the Planets , and Compendium of the Science of the Stars) is a manual of cosmography of thirty chapters. It includes a description of the inhabited part of the earth, its size, the distances of the heavenly bodies from the earth and their sizes, and other matters. Relying on measurements made at the court, Al-Farghani made many corrections to Ptolemy.[12] He published astronomical tables, and wrote about sundials.[13] He gave the radius of the earth at 3250 miles, and the greatest distance to the moon as 64 1/6, Mercury 167, Venus 1120, the sun 1220, Mars 8876, Jupiter 14405, and Saturn 20110 earth radii respectively; gave the apparent diameter of the sun and moon as 31 2/5, and the apparent diameters of the planets at mean distance as Mercury  1/15, Venus 1/10, Mars 1/20, Jupiter 1/12, and Saturn 1/18 solar diameters.[14] Amongst Al-Farghani’s other contributions are his establishment of the Nilometer of Fustat (old Cairo ), and two unpublished treatises one on the astrolabe, and the other on the construction of sundials.[15] Gerard of Cremona translated his Liber 30 differentiarum also known as Compilatio astronomica;[16] and through much of the centuries to follow this work remained much prized through the Latin  and Hebrew translations.[17]

 

Much of modern astronomy derives from the pioneering studies of Al-Battani  (d.929). For the major part of his life, Al-Battani worked at al-Raqqa on the Euphrates. He made observations from 877 onwards, which ended in the compilation of a catalogue of stars for the year 880, and the accurate determination of astronomical coefficients. His Sabian Tables (al-Zij al-Sabi) had great impact on his successors, Muslim and Christian, in equal measure.[18] This Zij or collection of astronomical tables with rules for their use, is one of the very few works of its kind published in a modern, critical edition.[19] The arrangement of the 57 chapters in it, unlike Ptolemy’s Almagest, is dictated by practical rather than theoretical considerations.[20] Al Battani starts his Zij with purely practical definitions and problems: the division of the celestial sphere into signs and degrees, and prescriptions for multiplication and division of sexagesimal fractions.[21] It includes a trigonometrical summary wherein not only sines, but tangents and cotangents, are regularly used.[22] It contains a table of cotangents by degrees and a theorem equivalent to the modern formula giving the cosine of a side of a spherical triangle as function of the cosine of the opposite angle and of the sines and cosines of the other sides.[23] Known in the Latin  Middle Ages as the De scientia stellarum, it was influential in select circles in medieval Europe after it had been translated into Latin by Robert of Chester (lived in Spain 1141-1147). Another version was by made by Plato of Tivoli (lived in Barcelona about 1134-1145) at about the same time.[24] It impacted most particularly on Abraham Ibn Ezra, Richard of Wallingford; Levi Ben Gerson; Regiomontanus; Peurbach; and Copernicus.[25]

Al-Battani ’s other accomplishments were many. Amongst others, he determined the longitude of the sun’s apogee at 830 15’; he also gave the greatest distance of the moon as 641/6, Mercury 166, Venus 1070, the sun 1146, Mars 8022, Jupiter 12924, and Saturn 18094 earth radii respectively.[26] Al-Battani also discovered the motion of the solar apsides,[27] besides working on the timing of the new moons, the length of the solar and sideral year, the prediction of eclipses, and the phenomenon of parallax, carrying us according to Wickens ‘to the verge of relativity and the space age.'[28] Al-Battani  fixed precisely the ‘Obliquity of the Ecliptic’ i.e the inclination of the celestial equator with reference to the Zodiacs at 230 35’.[29] Al-Battani's observations of eclipses made in the 10th century were still used as late as 1749 for comparative purposes.[30] His improved tables of the sun and the moon helped him discover that the direction of the sun's eccentric as recorded by Ptolemy was changing, which means that the earth is moving in a varying ellipse.[31] Al-Battani was sceptical of Ptolemy's practical results, and relying on his own observations, he corrected Ptolemy's errors.[32] The corrections cover the main parameters of planetary motion no less than erroneous conclusions drawn from insufficient or faulty observations, such as the invariability of the obliquity of the ecliptic or of the solar apogee.[33] According to Al Battani:

‘After having lengthily applied myself in the study of this science (astronomy), I have noticed that the works on the movements of the planets differed consistently with each other, and that many authors made errors in the manner of undertaking their observation, and establishing their rules. I also noticed that with time, the position of the planets changed according to recent and older observations; changes caused by the obliquity of the ecliptic, affecting the calculation of the years and that of eclipses. Continuous focus on these things drove me to perfect and confirm such a science.’[34]

After he had completed pinpointing and demonstrating diverse astronomical operations, which he supported by  mathematical calculations, Al-Battani  summoned others after himself: ‘to continue observation, and to search,’ saying that it was no impossibility that with the passing of time, more could be found, just as he himself had added to his predecessors. ‘Such is the majesty of celestial science, so vast, that none could ever encompass its study by himself.’[35]

One of the major contributions of al-Battani to the science was his use of the widest variety of instruments. He used an astrolabe in connection with a problem which did not require a very exact measurement.[36] There occurs a gnomon for careful observations which was divided into twelve parts but was capable of divisions into smaller fractions.[37] He had sun clocks both horizontal and vertical.[38] He had an armillary sphere, whose dimensions are not mentioned.[39] He used parallactic rulers whose dimensions are not known with certainty, but he recommends the use of one whose measurements are equivalent to those performed on a circle of about five meters diameter.[40] He had a mural quadrant; for this instrument he recommends a radius of not less than one meter, and adds that the larger the dimension the more exact it becomes.[41] His opting for the largest instruments is evident, and the measures taken by the parallax rules relate to a circle of no less than five meters in diameter; and the quadrant was no less than one meter.[42] Speaking of measurements of the obliquity of the ecliptic, he says:

‘We have observed it in this time of ours with the parallactic ruler and the mural quadrant…. After having made their divisions very precise and securing them in their place as carefully as possible.’[43]

The impact of Al-Battani  on Western Christian science is considerable. Copernicus’ indebtedness to him is widely known, as he quotes him fairly often, just as does Peurbach in the chapters dealing with the subjects of solar motion and of precession; and so did Tycho Brahe, Kepler and Galileo, who all showed interest in his observations.[44] And whilst Regiomontanus valued very highly Al-Battani’s spheric trigonometry, Denton profited much from his observation of the eclipses as late as 1749.[45]  Such was the impact of Al-Battani on the science, Lalande considered him one of the twenty most important scholars that ever lived.[46]

 

Around the same time as Al-Battani , there flourished three astronomers of great accomplishment: Al-Sufi, Ibn Yunus, and Al-Biruni . Al-Sufi’s (903-986) contribution is wide ranging, including critical revisions of Ptolemy; writing on the astrolabe (more on which further on), as well as observations on the obliquity of the ecliptic and the motion of the sun (or the length of the solar year.)[47] He was better known for his observations and descriptions of the stars, though. He set out his results constellation by constellation, discussing the stars, their positions, their magnitudes (brightness) and their colour, and for each constellation, providing two drawings, one from the outside of a celestial globe, and the other from the inside (as seen from the sky).[48] Al-Sufi was the first to critically revise the star catalogue of Ptolemy, adding the differing or additional results of his own observations which are embodied in his compendium: Kitab suwar al-Kawakib al-Thabita (On the Constellations of the Fixed Stars).[49] The work has the exact identifications of several hundred of the old Arabic star names, and it is fairly appropriate to mention here that the Muslims named many of the stars and constellations (several of which are still with us: Aldeberan, Altair and Betelgeuse, for instance), and devised such good star maps that they were used in both Europe and the Far East for centuries to come.[50] (To glean more on this subject of stars, there is no better authority than Kunitzsch.)[51] Al-Sufi also wrote a book on the use of the celestial globe, and he constructed astronomical instruments as well. A silver celestial globe manufactured by him is said to have been extant in Egypt  around 1043.[52]

Ibn Yunus (d. 1009), from Egypt , is better known for his Hakemite tables, which he devised after nearly thirty years (977-1003) of observation. He, too, maintained the tradition of using a wide variety of instruments, including a large astrolabe of nearly 1.4 m in diameter. His tables contain more than 10,000 entries of the sun's position throughout the years.[53]

Al Biruni’s (973-1050) contribution to science is vast, and his name will keep on re-appearing. He wrote a total of 150 works on all the sciences of his time, including 35 treatises on pure astronomy, of which only six have survived.[54] One of his early claims was that the earth rotated around its own axis.[55] He also calculated the earth’s circumference, and there is an exceptionally good account by Baloch on his experiment at Nandana (India ) to measure the earth’s circumference.[56] Al-Biruni  also fixed scientifically the direction of Makkah  from any point of the globe.[57]

 

Unlike what is generally asserted by mainstream historians, the overwhelming majority of Muslim scholars, whether east or west, condemned astrology.[58] Al-Biruni , just named, spent a great deal of time in serious study of the subject,[59] his astrological sections of Al-Qanun al-Masudi (The Masudi Canon) warning against belief in astrology.[60] He goes so far as to say that he discussed astrology in detail in order to warn the intelligent man away from it.[61] Krause has collected passages in which al-Biruni not only heaps ridicule upon ignorant or unscrupulous astrological practitioners, but indicates disbelief in the basic tenets of this pseudo science.[62] Al-Biruni's book that would have elaborated his attack against astrology is only known by name, its title, Warning Against the Craft of Deceit, meaning astrology, leaving very little doubt as to Al-Biruni’s position on the matter.[63]

A great number of other Muslim astronomers and scholars warned against astrology. Al-Farabi (d. 948) is one of them.[64] Ibn Sina  dwells upon the falseness of the doctrines and assumptions upon which astrology is based, and he speaks of the credulity of people with regard to their belief in astrology and similar pseudo sciences.[65] In their defence, for making errors in their predictions, astrologers held that physicians, too, made errors,[66] to which Ibn Sina responded that this analogy was without basis, and that in contrast to medicine, astrology lacks any scientific foundation.[67] According to Fakhr Eddin al-Razi (d. 1209) Abu Sahl al-Masihi, teacher of Ibn Sina, was against astrology and had written a special treatise refuting it.[68] Fakhr Eddin himself was antagonistic to it.[69] Ibn Khaldun  also attacked astrology on the ground that it had no utility and that it causes spiritual and material injury to humans.[70] The stance against astrology in Islam follows a long tradition from the time of the Prophet who said:

‘Those who say the rain that we receive comes from the kindness of God and from His mercy believe in me and do not believe in the stars but those who say the rain that we receive comes from the star do not believe me but believe in the stars.’[71]

 

 

In Muslim Spain, astronomers pursued the tradition of the Muslim East, and wrote on a diversity of matters, giving a prominent place to instruments, and once more, mounting an  onslaught on Ptolemy’s astronomy. Maslama (al-Majriti) (d.1007) wrote ‘some chapters indispensable for everyone who wishes to construct an astrolabe,'.[72] He also edited and adapted Al-Khwarizmi ’s tables to places in Spain.

Al-Zarqali (1029-1087) wrote two treatises on instruments, devised the Toledan Tables for the year 1080; and amended Ptolemy's exaggerated estimate of the length of the Mediterranean  sea from 620 to nearer to its correct value of 420.[73] Al-Zarqali is said to have found the movement of the solar apogee, which he held to be 1degree in 299 years, on the basis of twenty five years of observation.[74] The motion of the solar apogee with reference to the stars, he said, amounted to 12.04'' a year. He also gave a value of 770 50' for the longitude of the sun's apogee, and concluded that the inclination of the ecliptic oscillated between 23033' and 23053'.[75] Al-Zarqali’s Tratado de la lamina de los siete planetas is a predecessor to the Aequatorium planetarium of the Renaissance, and its Arabic text contains the clarification of one of the most debated passages of medieval astronomy.[76] In the graphic representation included in the Castilian translation ordered by Alfonso the Wise, the orbit of mercury is not circular.[77] On this basis, Al-Zarqali might have anticipated Kepler in stating that orbits (the orbit of Mercury in this case) are elliptical. Al-Zarqali treated Mercury in the same deductive way that Kepler dealt with Mars in his Astronomia Nova.[78] The conclusion by Hartner is that ‘it is not known whether Kepler knew of al-Zarqali’s text,’[79] which is somehow unfair on the Muslim scholar, for whilst Muslim scholars and scholarship are condemned for their borrowing from the Greeks, however faint the resemblance between the two, when it comes to later Western scientific findings, the same principle of resemblance is never applied, even when such resemblance between the Islamic and the Western is very obvious.

Jabir Ibn Aflah (d. 1150) is specially noted for his work on spherical trigonometry,[80] a real step forward, including, for instance, a new method of solving a right angled spherical triangle.[81] Jabir has also been credited with the invention of the turquet,[82] and other instruments. He devoted great effort to amend Ptolemy’s theory of the planets. Lorch has examined this issue in detail.[83] In the section on the sphericity of the heavens, Jabir describes Ptolemy’s reasoning as, ‘extremely compact and abbreviated-hence the worthlessness of the reasoning.’[84]

The most famous of Jabir’s criticisms concerns the position of Venus and Mercury. Ptolemy placed them between the Moon and the Sun, which thus divided the planets of limited elongation from those which could have any elongation. They have never eclipsed the Sun because they have never been in line with it-just as most conjunctions of Sun and Moon produce no eclipse. The question cannot be settled, Ptolemy says, because Venus and Mercury show no parallax, from which their distance from Earth could be measured, and placing them nearer the Sun would not entail any parallax even at their perigees.[85] Jabir begins:

‘I am very puzzled by what kind of man this is. I am quite at a loss to account for this inconsistency and confusion of his, which he did not notice. Such a thing must be very alien to anyone who makes any considerable study of these things, as he did. He did not see his inconsistency.’ [86]

Jabir then points out that Ptolemy himself had reckoned a maximum solar parallax at 2’51’’, and that if Venus and Mercury were within the Sun’s sphere, Venus would have a parallax of about a third of degree (the figure is almost exactly 19’, actually) at its perigee and Mercury 7’. Jabir reasons that Venus’ apogee must at best be the same distance from the Earth as the Sun’s perigee, and scales up the parallax accordingly, a procedure that is accurate enough for such small angles. He is evidently considering Mercury as fitting beneath the Sun separately, for if he had calculated for both planets’ being beneath the Sun (when Mercury’s apogee is the same distance from the Earth as Venus’ perigee), then Mercury’s maximum parallax becomes just over 47’. Jabir considers it possible that the parallaxes he has calculated have not been observed, since to show them the planets would have to be in conjunction with the Sun. So he calculates the parallaxes for maximum elongation, 6’ for Venus and 4’ for Mercury (actually, 7’ and 4’ are better figures).[87] The argument is brought to a triumphant climax:

‘Since, therefore, no parallax worth bothering about (according to Ptolemy) is to be found in either of them, and the Sun does have a sensible parallax worth bothering about, how can they be below the Sun.?’[88] 

Al-Bitruji (d. c 1204), too, modified Ptolemy’s system of planetary motions; but unlike Jabir, in his planetary theory, he positioned the Sun between Venus and Mercury.[89] Al-Bitruji’s Kitab al-Haya, is, according to Hetherington (who relies on MacKenzie and Sarton in his summing up):

‘An attempt to revive in a modified form the theory of homocentric spheres: each heavenly body is attached to a sphere and the motive power is the ninth sphere outside the fixed stars. The prime mover produces in every sphere a motion from east to west; this motion is faster in the eighth sphere, and it decreases as the distance from the prime mover increases, e.g., the fixed stars complete a revolution in 24 hours, while the moon, which is carried by the innermost sphere, requires almost 25 hours for the same revolution. The pole of the ecliptic being different from that of the equator, the planetary orbits are not closed; moreover, the planets do not remain at an invariable distance from the pole of the ecliptic; each has its own motion in latitude, and a variable velocity in longitude. The eighth sphere has two motions, the one in longitude (precession), and another caused by the rotation of the pole of the ecliptic around a mean position (this is the imaginary trepidation of the equinoxes). The pole of each planet revolves around the pole of the ecliptic, each in its own way. His theory was called the theory of spiral motion.’[90]  

Kitab-al-Hay’ah’ was translated by the Sicilian based Michael Scot under the title ‘On the Sphere.' Its impact was strongly felt thereafter, the first author to be widely influenced being William of Auvergne, who endorses his system in his encyclopaedic work De Universo.[91]

 

 

Muslims compiled a great numbers of zijs, that is astronomical handbooks with text and tables; in 1956, E.S. Kennedy publishing a survey of 125 such Islamic Zij;[92] a number that has risen to close to 200, authored by names such as Al-Khwarizmi , al-Battani, al-Biruni, Ibn al-Banna (Marrakech  fl. 1300).[93]  Most Zij consist of several hundred pages of text and tables; the treatment of the material presented varying from one zij to another, but most contain chapters and tables relating to the following aspects of mathematical astronomy:

1: Chronology.

2: Trigonometry

3: Spherical astronomy

4: Planetary means motions

5: Planetary equations

6: Planetary latitudes

7: Planetary stations

8: Parallax

9: Solar and Lunar eclipses

10: Planetary and lunar visibility

11: Mathematical geography (lists of cities with geographical coordinates)

12: Uranometry (tables of fixed stars with coordinates)

13: Astrology.[94]

 

Mathematical astronomy is concerned with the determination of the position of the sun, the moon, planets and fixed stars; the prediction of planetary conjunctions, eclipses, visibility of lunar crescent, time keeping by the sun and the stars etc. King informs us that the science has a long Yemeni tradition, from the 10th century until the present; with about one hundred manuscripts dating from the medieval period that have survived.[95] Like the rest of Muslim works in other sciences, they can be found scattered in libraries across the world. The Yemeni works on astronomy are very precious not just in their own right, but also because they include material from sources since lost. Each year, almanacs and ephemerids were prepared for the Yemeni sultans by their astronomers that included tables of the position of the sun, moon, and planets for each day of the year. Two manuscripts on these subjects survive. The first Yemeni astronomer about whom there is reliable information is Al-Hamdani, who compiled a Zij. The second, Abu’l-Uqul worked for Sultan al-Mu’ayyad, and compiled a Zij based on the works of Ibn Yunus, which can no longer be found; this Yemeni work salvaging what would otherwise have been lost.[96] Abu’l-Uqul’s contribution was also to prepare tables for time-keeping by the Sun and the stars for the latitude of Ta’iz; a corpus that is the largest known for any medieval Islamic city, containing over one hundred thousand entries.[97] Yemeni rulers had their contributions, too, including Sultan al-Muzaffar, who sponsored two astronomers, al-Farisi and al-Kawashi. The first prepared a Zij containing tables for the Yemen , whilst the second prepared a Zij with tables specifically for Aden and Ta’izz. Sultan al-Ashraf, for his part, compiled a treatise on the construction of astrolabes and sundials, and also prepared new tables of coordinates for drawing the curves on astrolabe plates and the curves on horizontal sundials, computing these tables for the latitudes of the major centres of the Yemen and the Hijaz.[98] One of the astrolabes made by al-Ashraf is now at the Metropolitan Museum of Art in New York; but more crucially, as noted by King, al-Ashraf’s treatise contains in the appendix a discussion on the magnetic compass.[99] Like al-Ashraf, Sultan al-Afdal compiled an extensive compendium of astronomical treatises and tables, derived from various sources, now lost. And so were the works of the early Yemeni astronomers, with the exception of those few that survive scattered in the libraries of the world.

 

 

Whether east or west of the Islamic land, the mid-late 13th century brought a sharp decline in astronomical writing. In the West this followed the loss of Muslim Spain; in the East, this was due to the crusader-Mongol onslaught. The activity of worth east of Egypt  was represented by the Maragha observatory, whose erection was due not to Mongol scientific investigation, but rather to their leader Hulagu’s reliance on the stars for the conduct of his wars against the Muslims.[100] At his service was the astrologer Nasir Eddin Al-Tusi (b.1201), who advised him on the onslaught against Baghdad  in 1258.[101] There, subsequently, nearly a million lives were wiped out.[102] Al-Tusi was put in charge of the said observatory, which enabled him to prepare the Il-Khani Tables, a catalogue of fixed stars, and prepare a treatise on the Quadrilateral,[103] a work on spherical trigonometry.[104] In the same environment Ibn al-Shatir, al-Urdi, and Muhi Eddin al-Maghribi also worked. Al Urdi (d. 1266) of Aleppo  was the first to initiate the construction of planetary models, besides constructing other instruments, detailed in his The Instruments  of the Observatory  of Maragha.[105] Ibn al-Shatir is widely held to have been at the source of the planetary theory devised centuries later by Copernicus.[106]

In the final decades of the 13th century, Mamluk Egypt  had probably the best contribution to astronomy of this later period. Amongst its astronomers was Al-Marrakushi, who was of Moroccan origin but who worked in Cairo . He wrote Kitab al-mabadi wa’l ghayat fi ilm al-Miqat (A Compendium of Astronomical Time Keeping), a complete survey of spherical astronomy and astronomical instruments.[107] Shihab Eddin al-Maqsi, who flourished in Cairo, compiled a treatise on sundial theory, and a set of tables for time-keeping.[108] Najm Eddin al-Misri, also flourished in Cairo, and compiled a table for time keeping that could be used not only for all latitudes but also for time keeping by the Sun by day and by the stars by night.[109]

 

After the 13th century, just as with every other science, astronomical output dwindled considerably. Al-Kashi and his fellow members of the Samarqand observatory, to be considered further on, being the authors of a final flowering of Islamic astronomy (and mathematics). Other later figures include Ibn Qunfudh (d.1407), an Algerian historian, mathematician and astronomer, who wrote ‘Help to the Students for the Determination of the Positions of the Planets .’[110] In 1475, Al-Suyuti of Cairo  compiled a treatise on the references to astronomy in the Qur’an.[111] In 1480, Cyriacus wrote a zij entitled Durr al-Muntakhab (The Chosen Pearl), calculated for the city of Mardin in south-east modern Turkey; with one set of planetary tables, about 10,000 values for each planet, and instructions on how to determine the position of any planet at any time using only addition.[112] The Moroccan astronomer al-Rudani (1623-83) was probably the last Islamic astronomer of any worth. He invented a spherical engine, which functioned within shells, that was used to measure time, and that could be operated at any longitude or latitude.[113]



[1] H. Suter: Die Mathematiker; op cit; in G. Sarton: Introduction; vol I, op cit. p.530.

[2] Carra de Vaux: Astronomy and Mathematics, in The Legacy of Islam; ed by A. Guillaume and T.  Arnold; First Edition (Oxford University Press; 1931),  pp.376-97; at p. 380.

[3] G. Sarton: Introduction; vol I, op cit; p. 531.

[4] W. Hartner: The Role of Observations in ancient and medieval astronomy; in The Journal of History of Astronomy; Vol 8 (1977); pp 1-11; at p. 8.

[5] J.L.E. Dreyer: A History; op cit; p.246.

[6] Ibid.

[7] M. A. Kettani: Science and Technology  in Islam: The underlying value system, in The Touch of Midas; Science, Values, and Environment in Islam and the West; Z. Sardar ed (Manchester University Press, 1984), pp 66-90; at p. 75.

[8] S. Tekeli: Habash al-Hasib; Dictionary of Scientific Biography; vol 5; pp. 612-20; at p. 612.

[9] G. Sarton: Introduction; vol I, op cit; p.545.

[10] Ibid.

[11] Ibid.

[12] R. Morelon: Eastern Arabic Astronomy, in Encyclopaedia (Rashed ed) op cit; pp 20-57; at p. 24.

[13] W. Mackenzie: The Imperial Dictionary of Universal Biography; Six volumes (London; 1880?); vol 1; p. 100;  D. E. Smith: History of Mathematics  (Dover Publication; London;  New York; 1958); vol 1; p. 170.

[14] G. Sarton: Introduction; op cit; vol 1; p. 567; J.L. E. Dreyer: A History of Astronomy; pp. 257 and 288; in B. Hetherington: A Chronicle, op cit; p.94.

[15] H. Suter: Die Mathematiker; op cit; pp. 18-9.

[16] Also translated by J. Hispalensis (Ferrara 1493; later printed by Melanchton (Nuremberg 1537), New Latin  translated by Golius 1669; reprinted ( Frankfurt; 1986), also translated in 13th  century into Hebrew by J. Anatoli.

[17] G. Sarton: Introduction; op cit; vol 1; p.545.

[18] R.  Morelon: Eastern Arabic; op cit; pp. 46-7.

[19] A. Nallino: Albateni Opus Astronomicum (Arabic text with Latin  translation), 3 vols (Milan 1899-1907 reprinted Frankfurt 1969).

[20] W. Hartner: Al-Battani ; Dictionary of Scientific Biography; op cit; vol 1; pp. 507-16; at p. 508.

[21] Ibid.

[22] G. Sarton: Introduction, vol I, op cit; p.585.

[23] Ibid.

[24] J. North: The Fontana History of Astronomy and Cosmology (Fontana Press; London; 1994), p. 187-8.

[25] Ibid.

[26] G. Sarton: Introduction; 1; 602; W. Mackenzie: The Imperial Dictionary; op cit; vol 1; p. 66; J.L. E. Dreyer: A History of Astronomy; op cit; pp. 257. All  in B. Hetherington: A Chronicle; op cit; p. 98.

[27] R. Morelon: Eastern Arabic; op cit; pp. 46-7.

[28] G.M Wickens: The Middle East as a world centre of science and medicine; in Introduction to Islamic Civilisation, op cit; pp 111-8; at pp. 117-8.

[29] Al-Battani : Kitab al-Zij al-Sabi; op cit; vol 3; p. 18.

[30] W. Montgomery Watt: The Influence; op cit; p. 35.

[31] C. Singer: A Short History of Scientific Ideas to 1900, (Oxford University Press, 1959); p. 151

[32] W. Hartner: Al-Battani ; op cit;  p. 510.

[33] Ibid.

[34] In Barron Carra de Vaux: Les Penseurs; op cit; pp. 208-13.

[35] Ibid.

[36] Al-Battani : Kitab al-Zij al-Sabi; op cit; vol 1 pp. XLV; p. 91.

[37] Ibid; pp. 22-3.

[38] Ibid; pp. 135-8.

[39] Ibid; pp. 138-42; and 319-21 .

[40] Ibid; pp. 143-4; 12; 85.

[41] Ibid; pp. 142-3; 12; 85.

[42] Barron Carra de Vaux: Les Penseurs; op cit; p. 211.

[43] Al-Battani : Kitab al-Zij al-Sabi; op cit; vol 1; p.12 .

[44] See W. Hartner: Al-Battani ;  op cit; pp. 512-3.

[45] S. Maqbul Ahmad: A History of Arab-Islamic Geography (Al-Bayt; Amman; 1995), p. 26.

[46] G. Le Bon: La Civilisation; op cit; p.361.

[47] R. Morelon: Eastern Arabic, op cit, p. 50.

[48] C. Ronan: The Arabian Science; in The Cambridge Illustrated History of the World’s Science (Cambridge University Press; 1983), pp. 201-44; at p. 213.

[49] P. Kunitzsch: Al-Sufi: Dictionary of Scientific Biography; op cit; vol 13; pp. 149-50; at p. 149.

[50] G.M Wickens: The Middle East; op cit; p. 117.

[51] P. Kunitzsch: The Arabs and the Stars: Texts and Traditions on the Fixed Stars, and Their Influence in Medieval Europe (Variorum; Aldershot; 1989).

[52] P. Kunitzsch: Al-Sufi; op cit; p. 149.

[53] C. Ronan: The Arabian Science, op cit p. 214.

[54] R. Morelon: Eastern Arabic, op cit, p. 52.

[55] M.A. Kettani: Science and Technology : op cit, p. 76.

[56] N.A. Baloch: Al-Biruni  and his experiment at Nandana; ERDEM, Vol 3; No 9 (1988); pp. 673-729.

[57] See, for instance, D.A. King: World Maps  for Finding the Direction and Distance to Mecca (Al-Furqan Islamic Heritage and Brill; Leiden; 1999).

[58] J.M. Millas Vallicrosa: Arab and Hebrew Contributions to Spanish Culture; in Cahiers d’Histoire Mondiale; vol 6 (1960), pp. 732-51, at p. 736.

[59] E.S. Kennedy: Al-Biruni ; in Dictionary of Scientific Biography; op cit; vol 2; pp. 147-58; at p. 156.

[60] G. Saliba: Al-Biruni ; Dictionary of Middle Ages; op cit; pp. 248-52; at p.250.

[61] Ibid.

[62] M. Krause: Al-Biruni . Ein iranischer Forscher des Mittelalters; in Der Islam; 26 (1940), pp. 1-5; at p. 10. in E.S. Kennedy: Al-Biruni; op cit; p. 156.

[63] G. Saliba: Al-Biruni ; op cit; p. 250.

[64] F. Dietrich: Al-Farabis Philosophische Abhandlungen; 1890; tr. 1892 (Leiden); pp. 104-14.

[65] M.A.F.  Mehren: Vues d’Avicenne sur l’Astrologies; Le Museon; Vol 3 (1884),  pp. 383-403.

[66] E.G. Browne: Arabian Medicine (Cambridge; 1921), p. 7.

[67] M.A.F. Mehren: Vues d’Avicenne; op cit;  pp. 397-8.

[68] P. Kraus: Les Controverses de Fakhr al-Din al-Razi; Bulletin de l’Institut d’Egypte; Vol 19 (1937);  pp. 203-4.

[69] Ibid.

[70] Ibn Khaldun : Muqaddima; Fr. Tr. Vol 3; pp. 240-7.

[71] Ibid; Fr. Tr. Vol 3; p. 245; Engl Tr. Vol 3; p. 262.

[72] D.E. Smith: History of Mathematics (Dover Publications; New York; 1958), p. 192.

[73] P.K. Hitti: History, op cit; p. 571.

[74] J. North: The Fontana History of Astronomy and Cosmology (Fontana Press; London; 1994), p. 208.

[75] B. Hetherington: A Chronicle; op cit; p. 120.

[76] J. Vernet: Al-Zarqali:  Dictionary of Scientific Biography; op cit; vol 14;  pp. 592-5; at p. 594.

[77] J. Millas Vallicrosa in J. Vernet: Al-Zarqali; p. 594.

[78] J. Vernet: Al-Zarqali; op cit;  p. 594.

[79] See W. Hartner: Oriens, Occidens (Hildesheim; 1968), pp. 474-8; at p. 486.

[80] W.M. Watt: The Influence, op cit, p. 35.

[81] G. Sarton: Introduction; op cit; Vol II, p.123.

[82] D.E. Smith: History; op cit; p. 206.

[83] R.P. Lorch: The Astronomy of Jabir Ibn Aflah; Centaurus; XIX (1975), pp. 85-107.

[84] Printed ed; pp. 48, 21, 1, 5960, etc; Ms Madrid 10006, ff 39 r, etc.. in R.P. Lorch: The Astronomy; p. 96.

[85] R.P. Lorch: The Astronomy; p 97.

[86] Printed ed; pp. 48, 21, 1, 5960, etc; Ms Madrid 10006, ff 39 r, etc.. in R.P. Lorch: The Astronomy; p. 97.

[87] R.P. Lorch: The Astronomy; pp. 97-8.

[88] Printed ed; pp. 48, 21, 1, 5960, etc; Ms Madrid 10006, ff 39 r, etc.. in R.P. Lorch: The Astronomy; pp. 97-8.

[89] A. Djebbar: Une Histoire; op cit; p.194.

[90] W. Mackenzie: The Imperial Dictionary; op cit; vol 1; p. 122; G. Sarton: Introduction; 2; 399; in B. Hetherington:  A Chronicle; op cit; p. 146.

[91] E.J. Dijksterhuis: The Mechanisation of the World Picture (Oxford at the Clarendon Press; 1961). p.212.

[92] E.S. Kennedy: A Survey of Islamic astronomical Tables; pp. 123-77 in D. A. King: Astronomy, in Religion, Learning  and Science (M.J.L. Young; et al ed), op cit; pp. 274-289; at p.276.

[93] D. A. King: Astronomy; p.276.

[94] Ibid; p.277.

[95] D.A. King: Mathematical Astronomy in medieval Yemen , in Arabian Studies; Vol 5; pp 61-65.

[96] Ibid; p. 63.

[97] Ibid.

[98] Ibid; pp. 62-3.

[99]  Ibid; p. 63.

[100] Baron G. D’Ohsson: Histoire des Mongols,  op cit, vol 3; pp. 224 ff.

[101] Ibid; pp. 225-6.

[102] 800, 000 people according to H.H. Howorth: History of the Mongols (London, 1927), in Y. Courbage and Fargues: Chretiens; op cit; p. 29.

[103] Edited with French translation by Caratheodory Pasha (Constantinople, 1891).

[104] Baron Carra de Vaux: Astronomy, op cit, p. 396.

[105] World Who’s Who in B. Hetherington: A Chronicle; op cit; p.40.

[106] On this, see:

-N. Swerdlow-O.Neugebauer: Mathematical Astronomy in Copernicus ‘‘De revolutionibus'' (New York, Springer Verlag, 1984).

G. Saliba at: http://www.columbia.edu/~gas1/project/visions/case1/sci.1.html

[107] D.A. King: The Astronomy of the Mamluks ; ISIS; 74 (1983), 531-55; p.539. 

[108] Ibid; p. 540. 

[109] Ibid. 

[110] World Who’s Who in Science; Chicago; 1968; in B. Hetherington: A Chronicle; op cit; p. 188.

[111] D. A. King: The Astronomy of the Mamluks ; op cit; at p. 549.

[112] G. Saliba: The Double Argument Lunar Tables of Cyriacus; Journal of History of Astronomy; 7; (1976), pp. 41-6; at p.41.

[113] M. A Kettani: Science and Technology , op cit, p. 77.