Islamic astronomers take the equant apart
Al-Battani re-measured every planetary motion, Ibn al-Haytham argued the equant was physically impossible, and Ibn al-Shatir built the models Copernicus would mirror.
For forty years, from 877 to 918, al-Battani observed the sky from ar-Raqqa on the Euphrates with a gnomon, sundials, a triquetrum, parallactic rulers, a new kind of armillary sphere and a mural quadrant. The result was the Zij al-Sabi: fifty-seven chapters, a star catalogue of 489 entries, and — this is the part that matters for Mars — every planetary mean motion determined again from scratch rather than copied out of the Almagest. He confirmed what al-Ma'mun's astronomers had found before him, that the Sun's apogee moves, by roughly a degree in 66 Julian years, where Ptolemy had held it fixed. His value for the Sun's eccentricity is reckoned better than the ones Copernicus and Tycho Brahe would arrive at six and seven centuries later.
Then came the attack on the mechanism itself. Between 1025 and 1028, working in Cairo, Ibn al-Haytham wrote al-Shukuk 'ala Batlamyus — Doubts Concerning Ptolemy. His objection to the equant was not that it predicted badly; it predicted well. It was that the equant requires a solid sphere to turn uniformly about a point that is not its centre, and no real sphere can do that. If the Almagest's Mars could not correspond to any physical object, then it was a calculating device pretending to be an account of the heavens. The Doubts offered no replacement. He left the problem standing in the open.
The tools arrived at Maragha. In 1259, under the Ilkhanid ruler Hulagu, Nasir al-Din al-Tusi founded an observatory in Azerbaijan with a library, instrument workshops and a staff that included Mu'ayyad al-Din al-Urdi. Out of it came the Tusi couple — a small circle rolling inside one twice its diameter, converting two uniform circular motions into a straight-line oscillation — and the Urdi lemma. With these an astronomer could reproduce the equant's effect using only uniform rotations about genuine centres. The doctrine was saved and the predictions kept.
Ibn al-Shatir finished the job. Born in Damascus about 1305 and dead there about 1375, he held a working job: head muwaqqit, timekeeper at the Umayyad Mosque, and he designed the marble sundial on its northern minaret. In Nihayat al-sul fi tashih al-usul — "The Final Quest Concerning the Rectification of Principles" — he eliminated both the equant and the eccentric from the planetary models, substituting additional epicycles. His lunar and Mercury models are mathematically identical to the ones Copernicus published in 1543. For the other planets, including Mars, Copernicus deploys the same devices at the same points, with the Sun and Earth exchanged.
Nobody has found the document that carried any of this to Poland. Copernicus never names Ibn al-Shatir. George Saliba argued for transmission through Byzantine Greek manuscripts and Jewish intermediaries; Viktor Blåsjö and others make the case for independent rediscovery. The mathematics is demonstrably the same. The route is not settled, and calling this era "the Islamic preservation of Greek learning" gets it backwards: the equant was dismantled here, three hundred years before Europe touched it.