Abu-Abdullah Muhammad ibn Īsa Māhānī (Persian: ابوعبدالله محمد بن عیسی ماهانی, flourished c. 860 and died c. 880) was a Persian[1][2] mathematician and astronomer born in Mahan, (in today Kermān, Iran) and active in Baghdad, Abbasid Caliphate.
His known mathematical works included his commentaries on Euclid's Elements, Archimedes' On the Sphere and Cylinder and Menelaus' Sphaerica,[3] as well as two independent treatises.
He was also known to make astronomical observations, and claimed his estimates of the start times of three consecutive lunar eclipses were accurate to within half an hour.
[4][5] From a reference in Ibn Yunus' Hakimite Tables, he was known to make astronomical observations between 853 and 866, allowing historians to estimate the time of his life and activities.
[4] He wrote commentaries on Greek mathematical works: Euclid's Elements, Archimedes' On the Sphere and Cylinder and Menelaus of Alexandria's Sphaerica.
[4] In his commentaries he added explanations, updated the language to use "modern" terms of his time, and reworked some of the proofs.
Later, Nasir al-Din al-Tusi (1201–1274) dismissed Al-Mahani and Al-Harawi's edition and wrote his own treatment of the Sphaerica, based on the works on Abu Nasr Mansur.
However, as documented later by Omar Khayyam, "after giving it lengthy meditation", he eventually failed to solve the problem.
The problem was then considered unsolvable until 10th century Persian mathematician Abu Ja'far al-Khazin solved it using conic sections.
According to later astronomer Ibrahim ibn Sinan (908–946), Al-Mahani also wrote a treatise on calculating the ascendant using a solar clock.