I imagine that Ptolemy’s epicycles were performed as real circles - around equants - in two dimensions, e.g that he was able not only to give the angles to planets and the Sun as seen from the Earth, but actually able to point out the location in space in a projection in two dimensions or otherwise, of all then known planets in the system. He would then have had the same type of knowledge as Kepler had, at least in principle, albeit with lower accuracy.

Is that actually the case?

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    $\begingroup$ I think it would be helpful if you could add some links or references where a detailed explanation of the topic could be found $\endgroup$ Jan 13 at 14:55
  • $\begingroup$ In discussing the orbits Kepler must have known all internal distances between the Sun and the planets, and I wondered whether this also was ancient knowledge. I take Paquette's answer to imply that this was the case. $\endgroup$ Jan 14 at 18:10

I suppose you mean in three dimensions, but anyhow…

Yes, Ptolemy did know that planets move also in latitude, not only in longitude, and thus the Almagest includes sections for how to predict the latitude of a planet for a given moment. In fact, Book XIII of the Almagest is entirely written about this specific subject of the latitude of the planets.

  • $\begingroup$ @Paquette I am mainly thinking of the difference between knowing the angles e.g. from city A to city B and C vs. knowing the layout of the whole map as seen from above, although I do realize it is a 3-dimentionel map. I take it Ptolemy might indeed have had the whole picture. $\endgroup$ Jan 14 at 18:06

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