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Mo'ayyeduddin Urdi : ウィキペディア英語版
Mu'ayyad al-Din al-'Urdi
Mu’ayyad al-Din al-’Urdi (sometimes given the epithet al-ʿĀmirī al-Dimashqī; born c. 1200 probably in Urd, Syria – 1266 Maragha, Iran)〔 was a major figure in 13th-century Islamic astronomy. He worked as an engineer and teacher of geometry in Damascus, and built instruments for al-Malik al-Mansur of Hims. In the 1250s, he moved to Maragha after being asked by Nasir al-Din al-Tusi to help establish the Maragha observatory under the patronage of Hulagu.〔 ((PDF version ))〕
He is known for being the first of the Maragha astronomers to develop a non-Ptolemaic model of planetary motion.〔Saliba (1979).〕 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.
Urdi's most notable works are ''Risālat al-Raṣd'', a treatise on observational instruments, and ''Kitāb al-Hayʾa'', a work on theoretical astronomy. His influence can be seen on Bar Hebraeus and Qutb al-Din al-Shirazi, in addition to being quoted by Ibn al-Shatir.〔
As an architect and engineer, he was responsible for constructing the water supply installations of Damascus, Syria, in his time.〔(Al-Urdi's Article on 'The Quality of Observation' ), FSTC Limited〕
==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 Ibn 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.

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