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“Function and probable origin of Ptolemy’s Equant” citation :

• Hipparchus’ reasons for the eccentric and epicycles
  • Before the round 430 B.C., Meton and Euktemon of Athens observed differences in the lengths of seasons. This can be observed in the lengths of seasons, given by equinoxes and solstices that indicate when the sun traveled 90 degrees along its path. Though others tried, Hipparchos calculated and presented the most exact lengths of seasons around 130 B.C.. According to these calculations, Spring lasted about 94.5 days, Summer about 92.5, Fall about 88.125, and Winter about 90.125, showing that seasons did indeed exist differences in lengths of seasons. This was later used as evidence for the zodiacal inequality, or the appearance of the sun to move at a rate that is not constant, with some parts of its orbit including it moving faster or slower. The sun’s annual motion as understood by Greek astronomy up to this point did not account for this, as it assumed the sun had a perfectly circular orbit that was centered around the Earth that it traveled around at a constant speed. According to the astronomer Hipparchos, moving the center of the sun’s path slightly away from earth would satisfy the observed motion of the sun rather painlessly, thus making the sun’s orbit eccentric.
  • Function and probable origin of ptolemy’s equant (pg.3)

• Previous models forgotten and lost
  • James Evans reports 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.
  • Function and probable origin of ptolemy’s equant (pg.8)

• Evolution of the Theory
  • 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 may 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.
  • Ptolemy himself then introduced the equant in his writing Almagest IX, 5, 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. 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.
  • Function and probable origin of ptolemy’s equant (pg.8-9)