Muḥammad ibn Jābir al-Ḥarrānī al-Battānī

Muhammad ibn Jabir al - Battani or Abū ʿ Abdullāh Muhammad ibn Jabir ibn al - Sinaan Harrani as- Sabi al - Battani, أبو عبد الله محمد بن جابر بن سنان الحراني الصابي البتاني, Abū ʿ DMG Abdullāh Muḥammad ibn Ǧābir ibn al - Sinaan Harrani aṣ - Sabi al - Battani latinized, Albategnius or Albatanius (* about 850-869 in Harran near Şanlıurfa - Turkey today; † 929 on the trip from Baghdad to Raqqa in Qasr al - Dschiss ( Samarra ) ) was an Arab scholar and is considered one of the greatest astronomers in the Middle East.

Al- Battani mediated the Arab world, the basics of Indian Mathematics ( textbook " Retha Ganita ": Indian numerals, the concept of zero, the foundations of geometry and algebra ). Further developed by the Arabs these foundations came later to Europe.

The astronomical tables of Al - Battânîs were first printed under the title Scientia Stellarum in 1537 in Nuremberg.

Al- Battani was governor of the Caliphs in Syria. He has partly, partly employed in Damascus in Aracta in Mesopotamia His astronomical observations, which is why it is also called Mohammedes Aractensis. He calculated the length of the solar year of 365 days 5 hours 46 minutes 24 seconds, ie up to around two minutes exactly. Al- Battani subjugated the (apparent) eccentricity of the solar orbit a new scrutiny, noting first the motion of the apogee and calculated the motion of the planets very accurately. He also added new tables and many modifications of the conventional theory of the Ptolemaic system, added. But significance is mainly Al- Battânîs service to the trigonometry, in which he used the first place geometric tendons the sinus. He found and proved to be the first to the law of sines.

He also proved that the ratio of sine by cosine equals the tangent:

He solved the equation sin x = a cos x:

The lunar crater Albategnius is named after him.