Al-Battani

Al-Battani (approx. 855 - 923) was a Astronome and Arab Mathématicien (one writes also Al Batani , and in Latin: Albategnius , Albategni , Albatenius ; complete name: Abū ʿAbdullāh Muḥammad ibn Jābir ibn rear-Raqqī Sinān Al-Ḥarrani aṣ-Ṣabiʾ Al-Battānī ), born with Harran close to Urfa. Its epithet have-Sabi suggests that its ancestors were members of the sect of the Sabéens which adored stars, but its complete name affirms that it was Moslem. Sometimes one indicates it like the “Ptolémée of the Arabs”.

Al-Battani worked in Syria, with Ar-Raqqa and Damas where he died.

Its major work, the Kitāb az-Zīj (the “Book of the tables”) composed of 57 chapters, translated into Latin under the title of De Motu Stellarum by Plato de Tivoli (Plato Tiburtinus) in 1116 (printed paper form in 1537 by Melanchthon, annotated by Regiomontanus), influenced the European Astronomie considerably. A republication appeared with Bologna in 1645. The original manuscript of Plato is preserved at the Bibliothèque of the Vatican. The library of Escorial has an astronomical manuscript of Al-Battani chronology.

Astronomy

It corrected certain calculations of Ptolémée and it produced new tables for the Sun and the the Moon, which made authority a long time. It also treated the division of the celestial Sphère. He discovered the movement of the Apogée Sun, calculated the values of the Précession of the equinoxes (54.5" per annum) and the slope of the terrestrial axis (23° 35 ').

Mathematics

Probably without knowing work of the Indian astronomer of the 5th century Âryabhata, it introduced the use of the sine into calculations, and partly that of the tangent , thus forming the bases of the modern Trigonométrie.

It used the ideas of Al-Marwazi on the tangents (or “shades”) to develop methods of calculating of the tangents and cotangents, and it drew up tables of them.

It created several trigonometrical formulas:

$\backslash \; tan\; has\; =\; \backslash \; frac\; \{\backslash \; sin\; has\}\; \{\backslash \; cos\; has\}$

$\backslash \; dry\; has\; =\; \backslash \; sqrt\; \{1+\; \backslash \; tan^2a\}$

It also solved the equation

$\backslash \; sin\; X\; =\; has\; \backslash \; cos\; X\; \backslash ,$

by translating it by the following equation:

$\backslash \; sin\; X\; =\; \backslash \; frac\; \{has\}\; \{\backslash \; sqrt\; \{1+a^2\}\}$

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