Al-Mahani's known mathematical works included his commentaries on Euclid's Elements, Archimedes' On the Sphere and Cylinder and Menelaus' Sphaerica, as well as two independent treatises.
16 Facts About Al-Mahani
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Al-Mahani unsuccessfully tried to solve a problem posed by Archimedes of cutting a sphere into two volumes of a given ratio, which was later solved by 10th century mathematician Abu Ja'far al-Khazin.
3.
Al-Mahani's only known surviving work on astronomy was on the calculation of azimuths.
4.
Al-Mahani was 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.
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Al-Mahani was active in the 9th century CE or 3rd century AH, lived in Baghdad c 860 and died c 880.
6.
Al-Mahani wrote commentaries on Greek mathematical works: Euclid's Elements, Archimedes' On the Sphere and Cylinder and Menelaus of Alexandria's Sphaerica.
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Al-Mahani wrote a standalone treatise Fi al-Nisba and another on the squaring of parabola.
8.
Al-Mahani called square roots "plane irrationalities" and cubic roots "solid irrationalities", and classified the sums or differences of these roots, as well as the results of the roots' additions or subtractions from rational magnitudes, as irrational magnitudes.
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Al-Mahani then explained Book X using those rational and irrational magnitudes instead of geometric magnitudes like in the original.
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Al-Mahani's edition was later updated by Ahmad ibn Abi Said al-Harawi.
11.
Al-Mahani attempted to solve a problem posed by Archimedes in On the Sphere and Cylinder, book II, chapter 4: how to divide a sphere by a plane into two volumes of a given ratio.
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Al-Mahani's work led him to an equation, known as "Al-Mahani's equation" in the Muslim world:.
13.
Ibn Yunus quoted Al-Mahani as saying that he calculated their timings with an astrolabe.
14.
Al-Mahani claimed his estimates of the start times of three consecutive lunar eclipses were accurate to within half an hour.
15.
Al-Mahani wrote a treatise, Maqala fi ma'rifat as-samt li-aiy sa'a aradta wa fi aiy maudi aradta, his only known surviving work on astronomy.
16.
Al-Mahani wrote another treatise, whose title, On the Latitude of the Stars, is known but its content is entirely lost.