In Books X and XI, we’ve begun developing a theory for the motion of the planets and have that pretty much complete for all of the planets in longitude; we haven’t begun addressing their latitude. But, before getting to that, Ptolemy wants to explore retrograde motion.
While the models already account for this, Ptolemy is wanting to be able to predict when it will happen1. That will be our focus for Book XII and we’ll get to latitudes in Book XIII.
Ptolemy tells us that he wants to “examine the greatest and least retrogradations associated with each of the five planets, and to show that the sizes of these, [as computed] from the above hypotheses, are in as close agreement as possible with those found from observations.” Continue reading “Almagest Book XII: Preliminary Lemma from Apollonius”