I've researched multiple histories of Greek astronomy, and have not found a satisfactory answer to this. When describing multiple deferents, each with a first order epicycle, many illustrations show the epicycles at different phases of their rotations: Mars will be at 37 degrees, Jupiter at 123, Venus straight up at 0, Saturn at 280. Other illustrations have them all in lock-step, all at, say, 190 degrees and all rotating (if it is an animation) in sync. In fact, the deferents of the sun, Mercury and Venus around the Earth are also synced to them, to keep them near the sun. This is, of course, the correct way of showing them, the only way that works, because these first level epicycles and the three interior deferents (not the moon's!) all must be in sync with the sun and therefore have periods of exactly a year, because they all represent the correction brought to Ptolemy's model by placing the Earth at the (near) center of the solar system. The question is, who determine that the first order epicycles had all to be equivalent in phase and period? Eratosthenes? Ptolomy? The results that Ptolemy produced are proof that his were that way, but the Almagest treats each planet/Earth pair as being entirely independent in all ways from all the others (in fact, he uses a normalized deferent and appropriate ratios rather than hard numbers) EXCEPT that all the epicycles were in phase. Does anyone know who invented that fact, and what the justification for demanding it was? A citation in the literature would be welcome.