Albategnius (c. 858-929), Latin name of Abu Abdallah Muhammad Ibn Jabir Ibn Sinan al-Battani al-Harrani was born around 858 C.E. in Harran, and according to one account, in Battan, a State of Harran, near Urfa, which is now in Turkey. Battani was first educated by his father Jabir Ibn San'an al-Battani, who was also a well-known scientist. Battani was a famous astronomer, mathematician and astrologer. He has been held as one of the greatest astronomists of Islam. He is responsible for a number of important discoveries in astronomy, which was the result of a long career of 42 years of research beginning at Ar Raqqa, Syria, when he was young. His well-known discovery is the remarkably accurate determination of the solar year as being 365 days, 5 hours, 46 minutes and 24 seconds, which is very close to the latest estimates. He found that the longitude of the sun's apogee had increased by 16°, 47' since Ptolemy. This implied the important discovery of the motion of the solar apsides and of a slow variation in the equation of time. He did not believe in the trepidation of the equinoxes, although Copernicus held it.

**Mathematics**

He also made important contributions to pure mathematics; he was the first to replace the use of Greek chords by singes, with a clear understanding of their superiority in mathematical calculations, computed a table of cotangents and formulated certain propositions in spherical trigonometry. Battānī produced a number of trigonometrical relationships:

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

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°.

**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 Damascus, Syria, at ar-Raqqah, 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 sub-continent’s astronomer Aryabhata, the use of signs 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; 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 equivalent to the Earth is moving in an elliptical orbit around the Sun. 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.

Abu Abdullah Muhammad Ibn Jabar Ibn Sinan Al-Battani wrote many books on Astronomy. His astronomical works, published as De Motu Stellarum (Concerning the Motion of the Stars, 1537), and corrected errors of the Alexandrian astronomer Ptolemy in regard to the inclination of the ecliptic and the length of the year. His most famous book was translated into Latin in the 12th Century and is known by the title 'De Scienta Stellarum – De Numeris Stellarum et Motibus'. It is an Astronomical article with tables. An old translation of De Scienta Stellarum – De Numeris Stellarum et Motibus can be found at the Vatican. Copernicus in his ever-famous book 'De Revelutionibus Orbium Celestium' expresses his gratitude to Al-Battani.

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