- Muhammad ibn Jābir al-Harrānī al-Battānī
**transl|ar|ALA|Abū Abd Allāh Muḥammad ibn Jābir ibn Sinān al-Raqqī al-Ḥarrānī al–Ṣābiʾ al-Battānī**(c. 858,Harran – 929, Qasr al-Jiss, nearSamarra )Latinized as**Albategnius**,**Albategni**or**Albatenius**was anArab [*[*] astronomer, astrologer, and mathematician, born in*http://www.daviddarling.info/encyclopedia/A/Albategnius.html Albategnius (Al-Battani, Muhammad ibn Jabir) (c. 850-929)*]Harran nearUrfa , which is now inTurkey . His epithet "as-Sabi" suggests that among his ancestry were members of the Sabian sect who worshipped the stars; however, his full name affirms that he wasMuslim . [*MacTutor Biography|id=Al-Battani*]**Astronomy**One of his best-known achievements in astronomy was the determination of the solar year as being 365 days, 5 hours, 46 minutes and 24 seconds.

Al Battani worked in

Syria , atar-Raqqah and atDamascus , where he died. He was able to correct some ofPtolemy 's results and compiled new tables of theSun andMoon , long accepted as authoritative, discovered the movement of the Sun'sapogee , treats the division of the celestial sphere, and introduces, probably independently of the 5th centuryIndia n astronomerAryabhata , the use ofsine s in calculation, and partially that of tangents, forming the basis of moderntrigonometry . He also calculated the values for theprecession of the equinoxes (54.5" per year, or 1° in 66 years) and the inclination of Earth's axis (23° 35'). He used a uniform rate for precession in his tables, choosing not to adopt the theory oftrepidation attributed to his colleagueThabit ibn Qurra .His most important work is his

zij , or set of astronomical tables, known as "transl|ar|ALA|al-Zīj al-Sābī" with 57 chapters, which by way of Latin translation as "De Motu Stellarum" byPlato Tiburtinus (Plato of Tivoli) in 1116 (printed 1537 byMelanchthon , annotated byRegiomontanus ), had great influence onEurope an astronomy. The zij is based on Ptolemy's theory, showing little Indian influence. [*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.*] A reprint appeared atBologna in 1645. Plato's original manuscript is preserved at the Vatican; and theEscorial Library possesses in manuscript a treatise by Al Battani on astronomical chronology.During his observations for his improved tables of the Sun and the Moon, he discovered that the direction of the Sun's eccentric was changing, which in modern astronomy is equivalent to the Earth moving in an

elliptical orbit around the Sun. [*C. Singer (1959), "A Short History of Scientific Ideas", p. 151,*] His times for theOxford University Press (cf. Salah Zaimeche (2002), [*http://www.muslimheritage.com/topics/default.cfm?ArticleID=235 Muslim Observatories*] , FSTC)new moon , lengths for thesolar year andsidereal year , prediction ofeclipse s, and work on the phenomenon ofparallax , carried astronomers "to the verge ofrelativity and thespace age ." [*G. M. Wickens, "The Middle East as a world Centre of science and medicine", in R. M. Savory, "Introduction to Islamic Civilization", pp. 111-118,*]Cambridge University Press (cf. Salah Zaimeche (2002), [*http://www.muslimheritage.com/topics/default.cfm?ArticleID=235 Muslim Observatories*] , FSTC)Copernicus mentioned his indebtedness to Al-Battani and quoted him, in the book that initiated theCopernican Revolution , the "De Revolutionibus Orbium Coelestium ".**Mathematics**In mathematics, Battānī produced a number of trigonometrical relationships:

::$an\; a\; =\; frac\{sin\; a\}\{cos\; a\}$

::$sec\; a\; =\; sqrt\{1\; +\; an^2\; a\; \}$

He also solved the equation sin "x" = "a" cos "x" discovering the formula:

::$sin\; x\; =\; frac\{a\}\{sqrt\{1\; +\; a^2$

He also used

al-Marwazi 's idea of tangents ("shadows") to develop equations for calculating tangents and cotangents, compiling tables of them. He also discovered theinverse trigonometric function s 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 agnomon ), for each degree from 1° to 90°.cite web|title=trigonometry|url=http://www.britannica.com/EBchecked/topic/605281/trigonometry|publisher="Encyclopædia Britannica "|accessdate=2008-07-21]**Honors*** The Albategnius crater on the

Moon was named after him.

* In the fictional Star Trek universe, theExcelsior-class starship "USS Al-Batani " [sic] " NCC-42995", mentioned on "" asKathryn Janeway 's first deep space assignment, was named for him.**ee also***

List of Arab scientists and scholars

*zij **Notes****External links***

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