al-Mahani

Abu Abdullah Muhammad ibn Isa al-Mahani ( Persian أبو عبد الله محمد بن عيسى المهاني Abu-Abdollah Mohammad ebn-e Isa Mahani , * in Mahan ; † around 880 in Baghdad ) was a Persian astronomer and mathematician of the 9th century.

From astronomical tables (Hakimit tables) from Ibn Yunus he made astronomical observations of conjunctions and eclipses between 853 and 866. According to Ibn Yunus, he determined the beginning of three successive lunar eclipses to within half an hour. He has received a treatise on the calculation of the azimuth .

In Fihrist he is not mentioned as an astronomer, but only as a mathematician. He wrote commentaries on the elements of Euclid (Book 1, 5, 10, 13), which have survived except for the comments on Book 1, On the Sphere and Cylinder of Archimedes and the Sphaerica of Menelaus (not preserved). The commentary on Menelaus Sphaerica was revised by Ahmad ibn Abi Said al-Harawi in the 10th century, but Nasir al-Din al-Tusi rejected both comments and created his own, which became best known in the Islamic world.

In particular, he tried to solve Archimedes' problem (On Sphere and Cylinder, Book 2, Chapter 4) of dividing a sphere by a plane into volumes of a given ratio. This leads to a cubic equation ( ), which he could not solve according to Omar Chayyam . But he was the first to reduce the problem to an algebraic equation. The problem was only solved geometrically with conic sections by Abu Dscha'far al-Khazin in the 10th century. ${\displaystyle x^{3}+a=cx^{2}}$

literature

• Yvonne Dold-Samplonius : Al-Māhānī , in: Helaine Selin (Ed.): Encyclopaedia of the history of science, technology and medicine in non-western countries, Kluwer 2008
• Yvonne Dold-Samplonius: Al-Māhānī, Abū 'Abd Allāh Muḥammad Ibn' Īsā , in: Dictionary of Scientific Biography , Volume 9, pp. 21-22

Web links

• John J. O'Connor, Edmund F. Robertson :  Al-Mahani. In: MacTutor History of Mathematics archive .