Almagest Book XI: Second Iteration for Saturn

With our corrections for the intervals from Saturn’s oppositions in hand, we’re ready to repeat the calculation. As with before, I’m doing this in a Google Sheet to speed things along. This means that I’ll be using modern trig and that the figures I give her may be subject to some rounding as we go since the Sheet is saving higher precision behind the curtain.

We’ll begin with the same diagram as before:

Continue reading “Almagest Book XI: Second Iteration for Saturn”

Almagest Book IX: On the Order of the Spheres

Having laid out “the sum total of the chief topics one may mention as having to do with the fixed stars, in so far as the phenomena [observed] up to now provide the means of progress in our understanding” Ptolemy now moves on to “the treatment of the five planets” each one getting a book to itself.

But before diving in, Ptolemy first proposes that we “avoid repetition” by “explain[ing] the theory of the [planets] by means of an exposition common [to all five], treating each of the methods [for all planets] together.”

Beginning this discussion, Ptolemy introduces us to the order of the spheres for these planets, the sun, and moon. Continue reading “Almagest Book IX: On the Order of the Spheres”