Abū Sahl al-Qūhī

Who was Abū Sahl al-Qūhī?

Abū Sahl Wayjan ibn Rustam al-Qūhī was a Persian mathematician, physicist and astronomer. He was from Kuh, an area in Tabaristan, Amol, and flourished in Baghdad in the 10th century. He is considered one of the greatest Muslim geometers, with many mathematical and astronomical writings ascribed to him.

He was the leader of the astronomers working in 988 AD at the observatory built by the Buwayhid Sharaf al-Dawla in Badhdad. He wrote a treatise on the astrolabe in which he solves a number of difficult geometric problems.

In mathematics he devoted his attention to those Archimedean and Apollonian problems leading to equations higher than the second degree. He solved some of them and discussed the conditions of solvability. For example, he was able to solve the problem of inscribing a regular pentagon into a square, resulting in an equation of fourth degree. He alse wrote a treatise on the "perfect compass", a compass with one leg of variable length that allows to draw any conic section: straight lines, circles, ellipses, parabolas and hyperbolas. It is likely that al-Quhi invented the device.

Like Aristotle, al-Quhi proposed that the heaviness of bodies vary with their distance from the center of the Earth.