Al-Mahani

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Abu Abdallah Mohammed ibn Isa al-Mahani, was a Persian ^[1] mathematician and astronomer from Mahan, Kerman, Persia.

The book Al-fihrist ("Index") by the bookseller Ibn al-Nadim in 988 mentions Mahani, not for his work in astronomy, but rather for his work in geometry and arithmetic. However the work which Mahani did in mathematics may well have been motivated by various problems of an astronomical nature.

A series of observations of lunar and solar eclipses and planetary conjunctions, made by him from 853 to 866, was in fact used by Ibn Yunus.

He wrote commentaries on Euclid and Archimedes, and improved Ishaq ibn Hunain's translation of Menelaus's spherics. He tried vainly to solve an Archimedean problem: to divide a sphere by means of a plane into two segments being in a given ratio. That problem led to a cubic equation, x³ c²b = cx², which Muslim writers called al-Mahani's equation.

Omar Khayyám is quite correct to rate Mahani's work highly, despite his failure in the mentioned problem. The fact that Mahani conceived the idea of reducing problems such as duplicating the cube to problems in algebra was an important step forward by itself.

[edit] References

^ Islamic desk reference: compiled from the Encyclopaedia of Islam - by E. van Donzel - - Page 287

H. Suter: Die Mathematiker und Astronomen der Araber (26, 1900. His failure to solve the Archimedean problem is quoted by 'Omar al-Khayyami'). See Fr. Woepcke: L'algebra d'Omar Alkhayyami (2, 96 sq., Paris, 1851).