# Muhammad ibn Jābir al-Harrānī al-Battānī

Abu Abdallah Muhammad ibn Jabir ibn Sinan ar-Raqqi al-Harrani as-Sabi al-Batani (Arabic محمد بن جابر بن سنان البتاني Abū Abd Allāh Muḥammad ibn Jābir ibn Sinān ar-Raqqī al-Ḥarrānī aṣ-Ṣābi` al-Battānī c. 858, Harran – 929, Qasr al-Jiss, near Samarra) Latinized as Albategnius, Albategni or Albatenius was an Arab [1] astronomer, astrologer, and mathematician, born in Harran near Urfa, which is now in Turkey. 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 was Muslim.[2]

## 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.

His work, the Zij influenced great European astronomers like Tycho Brahe, Johannes Kepler, etc. Nicholas Copernicus repeated what Al-Battani worte nearly 700 years before him as the Zij was translated into Latin thrice.

The modern world has paid him homeage and named a region of the moon Albategnius after him.

Al Battani worked in Syria, at ar-Raqqah and at Damascus, where he died. He was able to correct some of Ptolemy's results and compiled new tables of the Sun and Moon, long accepted as authoritative, discovered the movement of the Sun's apogee, treats the division of the celestial sphere, and introduces, probably independently of the 5th century Indian astronomer Aryabhata, the use of sines in calculation, and partially that of tangents, forming the basis of modern trigonometry. He also calculated the values for the precession 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 of trepidation attributed to his colleague Thabit ibn Qurra.

His most important work is his zij, or set of astronomical tables, known as al-Zīj al-Sābī with 57 chapters, which by way of Latin translation as De Motu Stellarum by Plato Tiburtinus (Plato of Tivoli) in 1116 (printed 1537 by Melanchthon, annotated by Regiomontanus), had great influence on European astronomy. The zij is based on Ptolemy's theory, showing little Indian influence.[3] A reprint appeared at Bologna in 1645. Plato's original manuscript is preserved at the Vatican; and the Escorial 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.[4] His times for the new moon, lengths for the solar year and sidereal year, prediction of eclipses, and work on the phenomenon of parallax, carried astronomers "to the verge of relativity and the space age."[5]

Copernicus mentioned his indebtedness to Al-Battani and quoted him, in the book that initiated the Copernican Revolution, the De Revolutionibus Orbium Coelestium.

## Mathematics

In mathematics, Battānī produced a number of trigonometrical relationships:

$\tan a = \frac{\sin a}{\cos a}$
$\sec a = \sqrt{1 + \tan^2 a }$

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 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°.[6]

## Honors

• The crater Albategnius on the Moon is named after him.
• In the fictional Star Trek universe, the Excelsior-class starship USS Al-Batani [sic] NCC-42995, mentioned on Star Trek: Voyager as Kathryn Janeway's first deep space assignment, was named for him.

## Related

• List of Arab scientists and scholars
• zij

## Notes

1. ^ Albategnius (Al-Battani, Muhammad ibn Jabir) (c. 850-929)
2. ^ O'Connor, John J.; Robertson, Edmund F., "Muhammad ibn Jābir al-Harrānī al-Battānī", MacTutor History of Mathematics archive .
3. ^ 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.
4. ^ C. Singer (1959), A Short History of Scientific Ideas, p. 151, Oxford University Press (cf. Salah Zaimeche (2002), Muslim Observatories, FSTC)
5. ^ 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), Muslim Observatories, FSTC)
6. ^ "trigonometry". Encyclopædia Britannica. Retrieved 2008-07-21.