Editing Equant (section)

== Critics ==
The equant solved the last major problem of accounting for the anomalistic motion of the planets but was believed by some to compromise the principles of the ancient Greek philosophers, namely uniform circular motion about the Earth.<ref>{{cite web|last=Van Helden|title=Ptolemaic System| url=http://galileo.rice.edu/sci/theories/ptolemaic_system.html| access-date=20 March 2014}}</ref> The uniformity was generally assumed to be observed from the center of the deferent, and since that happens at only one point, only non-uniform motion is observed from any other point. Ptolemy displaced the observation point from the center of the deferent to the equant point. This can be seen as violating the axiom of uniform circular motion.

Noted critics of the equant include the Persian astronomer [[Nasir al-Din Tusi]] who developed the [[Tusi couple]] as an alternative explanation,<ref>{{cite book |author=Craig G. Fraser |year=2006 |title=The Cosmos: A Historical Perspective |publisher=Greenwood Publishing Group |isbn=978-0-313-33218-0 |page=39  |url=https://books.google.com/books?id=3tJr_vl6rYsC&pg=PA39}}</ref> and [[Nicolaus Copernicus]], whose alternative was a new pair of small epicycles for each deferent. Dislike of the equant was a major motivation for Copernicus to construct his heliocentric system.<ref>{{cite book |last = Kuhn |first = Thomas |author-link = Thomas Kuhn |year = 1957 |title = The Copernican Revolution |publisher = [[Harvard University Press]] |isbn = 978-0-674-17103-9 |pages=[https://archive.org/details/copernicanrevolu0008kuhn/page/70 70–71] | title-link = The Copernican Revolution (book)}} (copyright renewed 1985)</ref><ref>{{cite book |author-link=Arthur Koestler |author=Koestler, A. |year=1959 |title-link=The Sleepwalkers (Koestler book) |title=The Sleepwalkers: A history of man's changing vision of the universe |place=Harmondsworth, UK |publisher=Penguin Books |page=322; see also p.&nbsp;206 and refs there}} {{cite web |title=''The Sleepwalkers'' |type=archived copy |via=The Internet Archive (archive.org) |url=https://archive.org/details/ArthurKoestler-TheSleepwalkers-AHistoryOfMansChangingVisionOfThe}}</ref> 

The violation of uniform circular motion around the center of the deferent bothered many thinkers, especially Copernicus, who mentions the equant as a "monstrous construction" in ''[[De Revolutionibus]]''. Copernicus' displacement of the Earth from the center of the cosmos obviated the primary need for Ptolemy's epicycles: It explained [[Apparent retrograde motion|retrograde movement]] as an effect of perspective, due to the relative motion of the earth and the planets. However, it did not explain non-uniform motion of the Sun and Moon, whose relative motions Copernicus did not change (even though he did recast the Sun orbiting the Earth as the Earth orbiting the Sun, the two are geometrically equivalent). Moving the center of planetary motion from the Earth to the Sun did not remove the need for something to explain the non-uniform motion of the Sun, for which Copernicus substituted two (or several) smaller epicycles instead of an equant.