Al‐Māhānī, Abū ˓Abd Allāh Muḥammad ibn ˓Īsā, was born in Māhān, Kerman, Iran. He lived in Baghdad, ca. 860 and died ca. 880.
Little is known about al‐Māhānī's life, and few of his works are extant. In the ḥākimite Tables Ibn Yūnus cites observations of conjunctions and lunar and solar eclipses made by al‐Māhānī between 853 and 866. In the only extant astronomical work, Maqāla fī Ma'rifat as‐samt li‐aiy sā'a aradta wa‐fī aiy mauḍi' aradta (On the Determination of the Azimuth for an Arbitrary Time and an Arbitrary Place), al‐Māhānī added arithmetical solutions to two of the graphic ones. His method corresponds to the cosine formula in spherical trigonometry, and is later applied by al‐Battānī.
Al‐Māhānī worked on the fundamental problems of mathematics of his time and is especially known for his commentaries to Euclid's Elements, to Archimedes' De Sphaera et Cylindro (On Spheres and Cylinders), and to the Sphaericaby Menelaus. In the last treatise, now lost, he inserted explanatory...
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