selective norepinephrine reuptake inhibitors

 Town & City Cities

Harran

 Site of Ancient Harran

By then, Harran had produced two of the greatest minds of Islam: Thabit Ibn Qurra and al-Battani.

Al Battani

Al-Battani (850-929 CE) comes from the province of Harran. It was he who developed the science of trigonometry muthallathat and extended it to spherical trigonometry.[10] He computed to a very high degree of accuracy the first complete tables of sines, tangents and co-tangents, and established the fundamental trigonometrical relations by introducing the notion of trigonometrical ratios as we use them today.[11] And, aware of the superiority of his own sines over the Greek chords, he made use of them. Al-Battani also applied algebraic operations to trigonometric identities. His works are some of the most translated by European scholars of the twelfth and thirteenth centuries, including the very influential Plato of Tivoli and Robert of Chester.[12] The modern word 'sine' appears for the first time in a translation of Al-Battani by Plato of Tivoli.[13]

Al-Battani's Sabian tables (al-Zij al-Sabi) is what Morellon calls `a monumental book', which had a great influence on the astronomy of the Latin West and was studied until recently.[14] His Zij al-Sabi included a trigonometrical summary wherein not only sines, but also tangents and cotangents, are regularly used.[15] It contains a table of cotangents by degrees and a theorem equivalent to our formula giving the cosine of a side of a spherical triangle in function of the cosine of the opposite angle and of the sines and cosines of the other sides. [16]

Al-Battani, from his observatory in Raqqa, began making observations in 877 which lasted forty years. He observed the stars and planets, which ended in the compilation of a first catalogue of stars for the year 880, and the accurate determination of astronomical coefficients.[17] Al-Battani's observations of eclipses (made in the 9th-10th century) were still used as late as 1749 for comparative purposes.[18] Al-Battani also worked on the timing of the new moons, the length of the solar and sideral year, the prediction of eclipses, and the phenomenon of parallax, which is `fundamental to astronomers,' and which `brings us to the verge of relativity and the space age.'[19] According to the early twentieth Italian historian of science, Nallino, Al-Battani determined the obliquity of the ecliptic, and the length of the tropical year and the seasons.[20] He confuted the Ptolemaic doctrine of solar immobility, demonstrating that the sun was subject to the precession of the equinoxes, and the equation of time subject in consequence to a slow variation in the apparent angular diameter of the sun, and the possibility of annular eclipses.[21] He made his personal calculations for the geocentric distances of the planets; and rectified several estimates of the motions of the moon and the planets, and finally refuted the trepidation hypothesis.[22] Al-Battani, along with other Muslim scientists, was an original researcher who, as already noted, made many emendations to (the Greek) Ptolemy's science, and corrected calculations for the orbits of the moon and certain planets.[23] His works are some of the most translated by European scholars of the twelfth and thirteenth centuries, including the very influential Plato of Tivoli and Robert of Chester. He was not just translated, his methods were also copied in Western Europe by the fifteenth century astronomer Regiomontanus.[24]

Finally, Al-Battani had a clear vision of the progress of science. 'It is not impossible,' he said 'that in the course of time something may be added to his observations, as something has been added by him to those of his predecessors.'[25]

Thabit ibn Qurra

Abu-l-Hasan Thabit ibn Qurra ibn Marwan al-Harrani, (that is, from Harran) more commonly known as Thabit Ibn Qurra, (born 826-27 died in 901), was a physician, mathematician and astronomer. Thabit Ibn Qurra was born as a Christian, but his sympathies were with the Arab Muslims and he was expelled from his own church.[26] He translated into Arabic a large number of works, and made major contributions to pure mathematics. His abilities so impressed a passing Muslim scientist called Ibn Shakir that the latter persuaded him to leave for Baghdad [27] Although Thabit contributed to a number of areas the focus of his work was in mathematics where he played an important role in preparing the way for such significant mathematical discoveries as the extension of the concept of number to (positive) real numbers, integral calculus, theorems in spherical trigonometry, analytic geometry, and non-Euclidean geometry.[28] Thabit translated the Introduction to Arithmetic of Nichomachus of Gerasa, a part of which is devoted to music, besides writing a highly valuable introduction to the Elements of Euclid, and advancing the theory of perfect and amicable numbers.[29] Many mathematical, astronomical, also anatomical and medical, writings are ascribed to him (most of them in Arabic, some in Syriac).[30] Thabit's work on paraboloids have also been much written about in German.[31] These texts are very important and they give a very high opinion of Thabit's mathematical talent.[32] His treatise on the conclusiveness of proof by algebraic calculation ranks him as one of the greatest of Muslim geometers.[33]

Thabit also wrote on music, anatomy of birds, works on the circulation of the blood, logic, psychology, ethics, the classification of sciences, the grammar of the Syriac language, the customs of the Sabians, and so on. [34] He also was a distinguished physician, said to have cured a butcher who was taken for dead.[35]

In astronomy Thabit was one of the first reformers of the Ptolemaic system, and in mechanics he was a founder of statics.[36] He was one of the early Muslim astronomers,[37] and his corpus in the field is examined in good detail by Morelon.[38] It demonstrates, amongst others, the great achievements by Thabit, and also how, subsequently Islamic astronomy came to build upon his initial studies.[39] Thabit was also responsible for a work on the system of the universe.[40] He published solar observations, explaining his methods. Thabit also wrote about the sundial and studied the sun's apparent motion across the sky, making notes of its acceleration and deceleration at different times of the year.[41] It is Thabit who mathematised astronomical reasoning, and a very good outline of the procedure is given by Morelon.[42] A study of the precession of the equinoxes led him to postulate the 'trepidation of the fixed stars', by which he hoped to reconcile Greek and Muslim observations as regards the variations of the obliquity of the ecliptic and of the precession.[43] This hypothesis, which allowed for a kind of periodic oscillation in the equinoctial precession, was of considerable influence in the formation of several pre-Copernican cosmogonies. [44]

Thabit was also responsible further for a treatise on the Roman balance, on which is determined the special weight that should be placed on the shorter arm.[45] He is renowned for his work on the Qariston, early attention to which was paid in a German translation of the text, Latin versions of which were among the most popular medieval writings on mechanics.[46] Two of Thabit's treatises on weight: kitab fi sifat al-wazn wa ikhtilafihi (book on the properties of weight and non equilibrium) and kitab fi'l qarastun (Book on Beam Balance) deal with mechanics.[47] The first of these formulates Aristotle's dynamic principle, as well as the conditions of equilibrium of a beam, hung or supported in the middle and weighted on the ends.

Kitab al-Qarastun (Liber karastonis in Latin) includes a doctrine of virtual displacements, elaborated in formal geometric proofs, which offered the theoretical basis for the equilibration of an ideal balance.[48] There is a fairly recent (1976) re-edition by Jaouiche of this work by Thabit in French, and it does indeed include some fascinating points.[49] After a lengthy introduction, Jaouiche presents an historical commentary in two parts: the first places Thabit's work within the context of other works on mechanics known from antiquity and concludes with a genealogical chart relating these with one another; the second is devoted to a genealogical study of the propositions found in Kitab al-Qarastun; the text itself is brought into focus with an analytical commentary of some thirty pages.[50] One feature of Thabit's work, according to J.E. Brown, was that his approach was clearer and more sure than that of his Aristotelian predecessor. His treatise contained none of the `inept geometry or the confusion' about how to specify the component of natural motion that had affected the Greek Mechanical Problems.[51] In the Qarastun, Thabit proves the principle of equilibrium of levers and demonstrates that `two equal loads, balancing a third, can be replaced by their sum at a midpoint without destroying equilibrium.'[52] Greek science, on the whole, was indeed plagued by its major defect, that is it was based on speculation, and hardly involved any experiments or calculation. And Thabit, indeed, was one of the first who most correctly recognised that the pure reasoning (of the Greeks) cannot always match observation in accuracy and he declared that `What is perceived by sense does not lend itself to such precision.'[53]

Thabit ibn Qurra also had a grandson called Ibrahim ibn Sinan, a mathematician who, in confronting the problem of squaring the parabola, perfected the procedure of Archimedes and devised a method which was not improved on until the advent of the integral calculus.[54]

Bibiography:

-Ibn al-Athir:Kitab al-kamil fi'l tarikh (the perfect in history).Edit , J. Tornberg, Leiden, 1851-1876.

-J.E. Brown: The Science of Weights, in Science in the Middle Ages, edited by D. C. Lindberg; The University of Chicago Press. Chicago and London. 1978; pp 179-205.

-C.R. Conder: The Latin Kingdom of Jerusalem; The Committee of the Palestine Exploration Fund; London; 1897.

-L. E. Dickson: History of the Theory of Numbers; vol. 1, p. 5, 36, Washington, 1919.

-P.K. Hitti: History of the Arabs, tenth edition, Mac Millan St Martin's Press, 1970.

- K. Jaouiche: Le livre du Qarastun de Thabit Ibn Qurra; Collections de Travaux de l'Academie Internationale d'Histoire des Sciences; avec le CNRS (France) 25; E. J. Brill; Leiden; 1976.

-R Morelon: Eastern Arabic Astronomy, in Encyclopaedia of the History of Arabic Science, edited by R. Rashed; Routledge, London and New York: 1996. pp20-57.

-C.A.Nallino, C.A: Raccolta di scritti Editi e Inediti, Roma, 1944.

-Thabit Ibn Qurra: Oeuvres d'astronomie: texte etabli et traduit par R. Morelon; Paris; Belles Lettres; 1987.

- The First and second Crusades from an Anonymous Syriac Chronicle: Translated by A.S. Tritton; with notes by H.A.R. Gibb: Journal of The Royal Asiatic Society (JRAS) 1933. pp 69-101.

-C. A. Ronan: The Arabian Science; in The Cambridge Illustrated History of the World's Science, Cambridge University press. Newness Books, 1983. pp 201-244.

-B. Rosenfeld and A.T. Grigorian: Thabit Ibn Qurra: in Dictionary of Scientific Biography: Editor Charles C. Gillispie; Charles Scribner's Sons, New York, 1973, vol XIII, pp 288-95.

- S. Runciman: A history of the Crusades, Cambridge University Press; 1951;Vol 2.

-G.Sarton: Introduction to the History of Science; 3 vols; The Carnegie Institute of Washington; 1927-48, vol I

-H. Suter: Die Mathematiker und Astronomen der Araber (34-38, 1900; Nachtrage, 162-163, 1902).

-W.M. Watt: The Influence of Islam on Medieval Europe, Edinburgh University Press, 1972.

-T.H. Weir: Harran; Encyclopaedia of Islam; 1st series; vol 2.

-G.M Wickens: The Middle East as a world centre of science and medicine; in Introduction to Islamic Civilisation, edited by R.M. Savory; Cambridge University Press, Cambridge, 1976; pp 111-8.

-E Wiedemann: Die Schriftuber den Qarastun; Bibliotheca Mathematica, vol. 12, 21-39, 1912.

-E. Wiedemann und J. Frank: Uber die Konstruktion der Schattenlinien auf horizontalen Sonnenuhren von Thabit ben Qurra (Det Kgl. Danske videnskabernes selskab, math. medd., IV, 9, 24 p., 1922; ISIS, V, 209).

-G.Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; Vol 3: The Great medieval Civilisations; Translated from the French; George Allen &Unwin Ltd; UNESCO; 1975.

[1] T.H. Weir: Harran; Encyclopaedia of Islam; 1st series; vol 2; p. 270.

[2] T.H. Weir: Harran; p. 270.

[3]C.R. Conder: The Latin Kingdom of Jerusalem; The Committee of the Palestine Exploration Fund; London; 1897; p. 85;

[4] The First and second Crusades from an Anonymous Syriac Chronicle: Translated by A.S. Tritton; with notes by H.A.R. Gibb: Journal of The Royal Asiatic Society (JRAS) 1933. pp 69-101. p.79.

[5] See S. Runciman: A history of the Crusades, Cambridge University Press; 1951;Vol 2; pp. 235-ff.

[6] See -Ibn al-Athir:Kitab al-kamil fi'l tarikh (the perfect in history).Edit , J. Tornberg, Leiden, 1851-1876.

[7] T.H. Weir: Harran; p. 270.

[8] T.H. Weir: Harran; p. 270.

[9] T.H. Weir: Harran; p. 270.

[10]For details on al-Battani's works see: C.A.Nallino, C.A: Raccolta di scritti Editi e Inediti, Roma, 1944.

[11] P.K. Hitti: History of the Arabs, tenth edition, Mac Millan St Martin's Press, 1970, at p. 572.

[12]See G.M Wickens: The Middle East as a world centre of science and medicine; in Introduction to Islamic Civilisation, edited by R.M. Savory; Cambridge University Press, Cambridge, 1976; pp 111-8.

[13] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; Vol 3: The Great medieval Civilisations; Translated from the French; George Allen &Unwin Ltd; UNESCO; 1975; p. 647.

[14] Regis Morelon: Eastern Arabic Astronomy, in Encyclopaedia of the History of Arabic Science, edited by R. Rashed; Routledge, London and New York: 1996. pp20-57.; pp. 46-7.

[15] G.Sarton: Introduction to the History of Science; 3 vols; The Carnegie Institute of Washington; 1927-48, vol I, op cit; p.585.

[16] C.A.Nallino, C.A: Raccolta di scritti;op cit; 1944.

[17] Regis Morelon: Eastern Arabic Astronomy, op cit; pp. 46-7.

[18] W.M. Watt: The Influence of Islam on Medieval Europe, Edinburgh University Press, 1972; p. 35.

[19]G.M Wickens: The Middle East; op cit; pp. 117-8.

[20] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; op cit; p. 647.

[21] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; p. 647.

[22] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; p. 647.

[23] P.K. Hitti: History of The Arabs, op cit, p. 376.

[24]C. A. Ronan: The Arabian Science; in The Cambridge Illustrated History of the World's Science, Cambridge University press. Newness Books, 1983. pp 201-244; at p. 224.

[25] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; Vol 3: The Great medieval Civilisations; Translated from the French; George Allen &Unwin Ltd; UNESCO; 1975; p. 647.

[26] G. Sarton: Introduction; I; p. 599.

[27] For the life and works of Thabit, see: B. Rosenfeld and A.T. Grigorian: Thabit Ibn Qurra: in Dictionary of Scientific Biography: Editor Charles C. Gillispie; Charles Scribner's Sons, New York, 1973, vol XIII, pp 288-95.

[28] B. Rosenfeld and A.T. Grigorian: Thabit Ibn Qurra. p. 288.

[29] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; Vol 3: The Great medieval Civilisations; Translated from the French; George Allen &Unwin Ltd; UNESCO; 1975; p. 646.

[30] G. Sarton: Introduction; op cit; I; p. 599.

[31] H. Suter: Uber die Ausmessung der Parabel von Thabit (Sitzungsber. d. physik. mediz. Sozietat, vol. 48, 65-86, Erlangen, 1918; Isis, IV, 400); Die Abhandlungen Thabits und Abu Sahl al-Kubls ilber die Ausmessung der Parabolide; ibidem, 186-227; Isis,IV,400

[32] G. Sarton: Introduction; op cit; I; p. 599.

[33] G.Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind;op cit; p. 646.

[34] B. Rosenfeld and A.T. Grigorian: Thabit Ibn Qurra; op cit; p. 288.

[35] B. Rosenfeld and A.T. Grigorian: Thabit Ibn Qurra:. p. 292.

[36] B. Rosenfeld and A.T. Grigorian: Thabit Ibn Qurra:. p. 288.

[37] H. Suter: Die Mathematiker und Astronomen der Araber (34-38, 1900; Nachtrage, 162-163, 1902).

[38] Thabit Ibn Qurra: Oeuvres d'astronomie: texte etabli et traduit par R. Morelon; Paris; Belles Lettres; 1987:

[39] Thabit Ibn Qurra: Oeuvres d'astronomie.

[40] G.Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind;op cit; ; p. 646.

[41] C.A. Ronan: The Arabian Science, op cit, p. 208.

[42] R. Morelon: Eastern Arabic Astronomy, op cit, at pp 35-46.

[43] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; op cit; p. 646.

[44] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; p. 646.

[45] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind;; p. 646.

[46] Texts and Translation: Eilhard Wiedemann: Die Schriftuber den Qarastun; Bibliotheca Mathematica, vol. 12, 21-39, 1912.

[47] E. Wiedemann und J. Frank: Uber die Konstruktion der Schattenlinien auf horizontalen Sonnenuhren von Thabit ben Qurra (Det Kgl. Danske videnskabernes selskab, math. medd., IV, 9, 24 p., 1922; ISIS, V, 209). B. Rosenfeld and A.T. Grigorian: Thabit Ibn Qurra; op cit.

[48] J.E. Brown: The Science of Weights, in Science in the Middle Ages, edited by D. C. Lindberg; The University of Chicago Press. Chicago and London. 1978; pp 179-205 at p 187.

[49] K. Jaouiche: Le livre du Qarastun de Thabit Ibn Qurra; Collections de Travaux de l'Academie Internationale d'Histoire des Sciences; avec le CNRS (France) 25; E. J. Brill; Leiden; 1976.

[50] K.Jaouiche: Le Livre; reviewed by G. Saliba in ISIS; 1970; 1979; pp. 464-5.

[51] J.E. Brown: The Scienc eof weight; op cit; 187.

[52] B. Rosenfeld and A.T. Grigorian: Thabit Ibn Qurra, in The Dictionary, op cit.

[53] In R. Morelon: Eastern Arabic Astronomy, op cit, p. 46.

Al-Battani, Al-Bitruji were amongst many other Muslim scientists who criticised and corrected various aspects of Ptolemy's astronomy (see for example P. K. Hitti: History, op cit at pp. 571-2; and W.M Watt: Influence, op cit, at p. 35.

[54] G. Wiet; V. Elisseeff; P. Wolff; and J. Naudu: History of Mankind; op cit; p. 647.

by: FSTC Limited, Tue 22 February, 2005

Related Articles:
Transmission of Muslim Astronomy to Europe by: FSTC Limited
It was in Muslim Toledo, Spain, where flocked in the 12th century, in particular, scholars from all Christian lands to translate Muslim science, and start the scientific awakening of Europe.

An overview of Muslim Astronomers by: FSTC Limited
Al-Battani discovered the notions of trigonometrical ratios used today. Al-Biruni claimed the earth rotated around its own axis. Jabir Ibn Aflah made the first portable celestial sphere to measure and explain the movements of celestial objects. Read more...

Al-Khawarizmi (780 - 850 CE) by: FSTC Limited
Algebra, algorithm, quadratic equation, sine function... just some of the terms which would not be known to us but for Al-Khawarizmi. An astronomer, geographer and founder of several branches and basic concepts of mathematics.

Modelling the Stars by: FSTC Limited
The measurement of the positions of the stars was developed and refined by scientists of the Muslim world and many kinds of Models were developed. These are described here

Kufa by: FSTC Limited
Kufa had a key role in the history of science being the home of the encyclopaedic scholar Al-kindi and the great chemist Jabir Ibn Hayan.