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Al-Battani
Al-Batt?n?
A modern artist's impression of al-Batt?n? holding an astrolabe
Ab? ?Abd All?h Mu?ammad ibn J?bir ibn Sin?n al-Raqq? al-?arr?n? a?-bi? al-Batt?n?^{[n 1]}(Arabic: ? ? ? ?) (Latinized as Albategnius, Albategni or Albatenius) (c. 858 - 929) was a Syrian^{[2]}Arab^{[3]}^{[4]}^{[5]}astronomer, and mathematician. He introduced a number of trigonometric relations, and his Kit?b az-Z?j was frequently quoted by many medieval astronomers, including Copernicus.^{[6]}
Often called the "Ptolemy of the Arabs",^{[7]} al-Battani is perhaps the greatest and best known astronomer of the medieval Islamic world.^{[8]}^{[9]}^{[10]}^{[11]}
Life
Little of al-Batt?n?'s life is known other than his birthplace in Harran near Urfa, in Upper Mesopotamia, (today in Turkey) and his father's fame as a maker of scientific instruments.^{[6]} Jabir ibn Sinan al-Harrani was likely this famous instrument maker, although this is not something that has been proven.^{[12]}Ibn Khallikan expresses ignorance on the question of his Muslim faith, and points out that his epithet a?-?abi' suggests possible Sabian-sect ancestry.^{[13]}^{[14]} Although his ancestors were likely of the Sabian-sect, he is a Muslim, as his name is Muhammad, with his kunya being Abu Abd Allah.^{[12]} The Encyclopædia Britannica Eleventh Edition stated that he had noble origins as an Arab prince,^{[15]} but traditional Arabic biographers make no mention of this.^{[6]} Between 877 and 918/19, over a forty-year period, he lived in the ancient city of Raqqa, in north central Syria, recording his astronomical observations. He died at Qasr al-Jiss, which is located near Samarra, Iraq.^{[12]} He was returning from Baghdad to al-Raqqa after resolving a dispute on behalf of the people of al-Raqqa.^{[12]}
Astronomy
De scientia stellarum, 1645
One of al-Batt?n?'s best-known achievements in astronomy was the determination of the solar year as being 365 days, 5 hours, 46 minutes and 24 seconds, which is only 2 minutes and 22 seconds off.^{[14]}
Another of al-Batt?n?'s accomplishments is that he concluded how an annular solar eclipse occurs.^{[12]} He did this by observing that the radius between the Earth and the Sun changes throughout the year.^{[12]} This led him to arrive to the conclusion that when the Sun is farthest from the Earth, an annular solar eclipse occurs.^{[12]} He was the first to make this observation and inference.
The twelfth-century Egyptian encyclopedist al-Qif, in his biographical history Ta'r?kh al-?ukam?', mentions al-Batt?n?'s contribution to advances in astronomical observation and calculations based on Ptolemy's Almagest.^{[1]}
Al-Batt?n? amended some of Ptolemy's results and compiled new tables of the Sun and Moon, long accepted as authoritative.^{[15]} Some of his measurements were more accurate than ones taken by Copernicus many centuries later and some ascribe this phenomenon to al-Batt?n?'s location lying closer to the equator such that the ecliptic and the Sun, being higher in the sky, are less susceptible to atmospheric refraction.^{[14]} Al-Batt?n? observed that the direction of the Sun's apogee, as recorded by Ptolemy, was changing.^{[16]}^{[n 2]}
He also solved the equation sin x = a cos x discovering the formula:
$\sin x={\frac {a}{\sqrt {1+a^{2}}}}$
He gives other trigonometric formulae for right-angled triangles such as:^{[14]}
$b\sin(A)=a\sin(90^{\circ }-A)$
Al-Batt?n? used al-Marwazi's idea of tangents ("shadows") to develop equations for calculating tangents and cotangents, compiling tables of them. He also discovered the reciprocal functions of secant and cosecant, and produced the first table of cosecants, which he referred to as a "table of shadows" (in reference to the shadow of a gnomon), for each degree from 1° to 90°.^{[21]}
Using these trigonometrical relationships, Al-Batt?n? created an equation for finding the qibla, which Muslims must face in each of the five prayers they practice everyday.^{[22]} The equation he created did not give accurate directions, as it did not take into account the fact that Earth is a sphere.^{[22]} The relationship Al-Batt?n? used was fairly precise when a person is in Mecca, or close to Mecca, but resulted in more and more inaccurate results as one gets more distant from Mecca.^{[22]} However, it was still a widely used method at the time. The equation is as follows:^{[22]}
Kit?b az-Z?j (? or ?, "Book of Astronomical Tables"); Al-Batt?n?'s magnum opus reflects Ptolemaic and Greco-Syriac astronomical theory, with Indo-Persian influences to a lesser degree.^{[6]}^{[23]} The word zij is a Persian word that was used to describe a rug warp.^{[12]} Al-Batt?n?'s zij contains a description of a quadrant instrument.^{[24]} Of the many early translations into Latin and Spanish, a Latin version De Motu Stellarum by Plato of Tivoli (1116), was reprinted with annotations by Regiomontanus,^{[15]} and again at Bologna in 1645. The original manuscript is preserved at the Vatican library in Rome.^{[15]}
Kit?b az-Z?j a?-bi' (? ) published by Carlo Alfonso Nallino (1899-1907) under the Latin title Al-Batt?n? sive Albatenii opus astronomicum: ad fidem codicis Escurialensis Arabice editum;^{[25]} a multi-volume scientific treatise on geography and astronomical chronology from an Arabic manuscript with Latin annotations. The manuscript is held at the Escorial library.
Arba?u Maq?l?t (? , "Four discourses");^{[26]} a commentary on Ptolemy's Quadripartitum de apotelesmatibus e judiciis astrorum, known as the Tetrabiblos. The tenth-century encyclopedist Isq al-Nad?m in his Kit?b al-Fihrist lists al-Batt?n? among a number of authors of commentaries on this work.^{[27]}^{[n 4]}
Ma?rifat Mali?i l-Bur?j (, "Knowledge of the rising-places of the zodiacal signs")^{[n 5]}^{[13]}
Kit?b f? Miqd?r al-Ittil?t (? ); treatise on the four quarters of the sphere.
^Al-Qif gives his name: Ibn Sin?n Ab? 'Abd All?h Al-Harran?, known as al-Batt?n? and mentions that Said al-Andalusi in his book Kit?b al-Q?s? (? ) gives: Ab? J?far Mu?ammad ibn Sin?n ibn J?bir al-Harran?, known as al-Batt?n?, ^{[1]}
^In modern heliocentric terms this is due to the changing direction of the eccentricity vector of the Earth's orbit.
^Probably independently of the 5th-century Indian astronomer Aryabhata
^Ptolemy's treatise was translated into Arabic by Ibrahim ibn al-Salt and this translation was amended by Isq.
^This may have been about zodiac amplitude calculations. See McGuckin. ^{[28]}
^Barlow, Peter; Kater, Henry; Herschel, Sir John Frederick William (1856). The Encyclopaedia of Astronomy: Comprising Plane Astronomy. R. Griffin. p. 494.
^Schlager, Neil; Lauer, Josh (2001). Science and Its Times: 700-1449. Gale Group. p. 291.
^Griffin, Rosarii (2006). Education in the Muslim World: different perspectives. Symposium Books Ltd. p. 31.
^Angelo, Joseph A. (2014). Encyclopedia of Space and Astronomy. Infobase Publishing. p. 78.
^Ben-Mena?em, Ari (2009). Historical Encyclopedia of Natural and Mathematical Sciences. Springer Science & Business Media. p. 541.
^Freely, John (2015-03-30). Light from the East: How the Science of Medieval Islam Helped to Shape the Western World. I.B.Tauris. p. 179. ISBN9781784531386.
^E. S. Kennedy, A Survey of Islamic Astronomical Tables, (Transactions of the American Philosophical Society, New Series, 46, 2), Philadelphia, 1956, pp. 10-11, 32-34.
^Moussa, Ali (2011). "Mathematical Methods in Ab? al-Waf's Almagest and the Qibla Determinations". Arabic Sciences and Philosophy. 21 (1): 1-56. doi:10.1017/S095742391000007X.
Al-Batt?n? sive Albatenii, Opus Astronomicum. Ad fidem codicis escurialensis arabice editum, ed. by Carlo Alfonso Nallino. Milan, Ulrico Hoepli, 1899-1907 [= Pubblicazioni del Reale Osservatorio di Brera in Milano, nr. XL], 412 + 450 + 288 pp. (anast.: I-III, [La Finestra editrice], Lavis 2002 ISBN978-8888097-26-8
Nad?m (al-), Ab? al-Faraj Mu?ammad ibn Isq Ab? Ya'q?b al-Warr?q (1970). Dodge, Bayard (ed.). The Fihrist of al-Nadim; a tenth-century survey of Muslim culture. New York & London: Columbia University Press.