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. [1] 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.[2] 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.[3] The modern word 'sine' appears for the first time in a translation of Al-Battani by Plato of Tivoli.[4]

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.[5] His Zij al-Sabi included a trigonometrical summary wherein not only sines, but also tangents and cotangents, are regularly used.[6] 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. [7]

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.[8] Al-Battani's observations of eclipses (made in the 9th-10th century) were still used as late as 1749 for comparative purposes.[9] 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.'[10]

According to the early twentieth century Italian historian of science, Nallino, Al-Battani determined the obliquity of the ecliptic, and the length of the tropical year and the seasons.[11] 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.[12] 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.[13] 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.[14] 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.[15]

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.'[16]



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

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

[3]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.

[4] 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.

[5] 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.

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

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

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

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

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

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

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

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

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

[15] 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.

[16] 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.

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