Mu'ayyad al-Din al-'Urdi

Mu’ayyad al-Din al-’Urdi (died 1266) was an Muslim astronomer, mathematician, architect and engineer working at the Maragheh observatory. He was born in Aleppo,todays Syria, and later moved to Maragheh, Azarbaijan, to work at the Maragha observatory under the guidance of Nasir al-Din Tusi.^[1]He is known for being the first of the Maragha astronomers to develop a non-Ptolemaic model of planetary motion.^[2] In particular, the Urdi lemma he developed was later used in the geocentric model of Ibn al-Shatir in the 14th century and in the heliocentric Copernican model of Nicolaus Copernicus in the 16th century. As an architect and engineer, he was responsible for constructing the water supply installations of Damascus, Syria, in his time

The Urdi Lemma

"Urdi's lemma" was an extension of Apollonius' theorem that allowed an equant in an astronomic model to be replaced with an equivalent epicycle that moved around a deferent centered at half the distance to the equant point. Anythony Grafton's demonstration of Maestlin's proof to Kepler may help to visualize. You can also drag the al-Shatir and al-Tusi sliders to zero in Dennis Duke's animation to see al-'Urdi's equant-less model for Mars in operation.