Editing Equant (section)

===Ptolemy===
Between Hipparchus's model and Ptolemy's there was an intermediate model that was proposed to account for the motion of planets in general based on the observed motion of Mars. In this model, the deferent had a center that was also the equant, that could be moved along the deferent's line of symmetry in order to match to a planet's retrograde motion. This model, however, still did not align with the actual motion of planets, as noted by Hipparchos. This was true specifically regarding the actual spacing and widths of retrograde arcs, which could be seen later according to Ptolemy's model and compared.<ref name=Evans/>

Ptolemy himself rectified this contradiction by introducing the equant in his writing<ref name=Ptolemy-Almagest>{{cite book |author-link=Ptolemy |first=Claudius |last=Ptolemy |title={{math|Μαθηματικὴ Σύνταξις}} (Mathēmatikē Syntaxis) |title-link=Almagest |trans-title=Mathematical Treatise ("Almagest") |at=IX, 5}}</ref> when he separated it from the center of the deferent, making both it and the deferent's center their own distinct parts of the model and making the deferent's center stationary throughout the motion of a planet.<ref name=Evans/> The location was determined by the deferent and epicycle, while the duration was determined by uniform motion around the equant. He did this without much explanation or justification for how he arrived at the point of its creation, deciding only to present it formally and concisely with proofs as with any scientific publication. Even in his later works where he recognized the lack of explanation, he made no effort to explain further.<ref name=Evans/>

Ptolemy's model of astronomy was used as a technical method that could answer questions regarding astrology and predicting planets positions for almost 1,500&nbsp;years, even though the equant and eccentric were regarded by many later astronomers as violations of pure [[Aristotelian physics]] which presumed all motion to be centered on the Earth. It has been reported that Ptolemy's model of the cosmos was so popular and revolutionary, in fact, that it is usually very difficult to find any details of previously used models, except from writings by Ptolemy himself.<ref name=Evans/>