I think using ellipses only really gets you good mileage once you have the planets moving around the sun. If, like Aristotle, you have the planets moving around the earth, then epicycles are just being a very general way of representing periodic motion phenomenologically.
Apollonius introduced epicycles and proved a theorem of the commutativity of addition: a small epicycle about a large orbit appears the same as a large epicycle about a small orbit. This makes it seems like he was using them to represent heliocentrism, not just fitting data.
The Ptolemaic model has an epicycle and an equant for each planet. One of them corresponds to heliocentrism and the other to the non-circularity of an orbit. (That’s very vague because the correspondence is different for the inner planets vs the outer planets. The role of epicycle vs deferant gets switched and (thus) which orbit, the planet or the earth’s has its non-circularity approximated differs.)
I think using ellipses only really gets you good mileage once you have the planets moving around the sun. If, like Aristotle, you have the planets moving around the earth, then epicycles are just being a very general way of representing periodic motion phenomenologically.
Apollonius introduced epicycles and proved a theorem of the commutativity of addition: a small epicycle about a large orbit appears the same as a large epicycle about a small orbit. This makes it seems like he was using them to represent heliocentrism, not just fitting data.
The Ptolemaic model has an epicycle and an equant for each planet. One of them corresponds to heliocentrism and the other to the non-circularity of an orbit. (That’s very vague because the correspondence is different for the inner planets vs the outer planets. The role of epicycle vs deferant gets switched and (thus) which orbit, the planet or the earth’s has its non-circularity approximated differs.)
Heliocentrism was around then as well, e.g. Aristarchus of Samos.