If I were to summarize the books of the Almagest so far, I’d say that Book I is a mathematical introduction to a key theorem and an introduction to the celestial sphere for the simplest case of phenomenon at sphaera recta. In Book II, much of that work is extended to sphaera obliqua, but in both cases, we’ve only dealt with more or less fixed points on the celestial sphere: The celestial equator, ecliptic, and points within the zodiacal constellations based on the immovable stars.
But the ultimate goal of the Almagest and my project isn’t to study the unchanging sky; it’s to understand the changing sky: The sun, moon, and planets. Ptolemy decides to start with the position of the sun is a prerequisite to understanding the phases of the moon, and planets are more complicated with their retrograde motions. And to kick off the investigation of the motion of the sun, Ptolemy first begins by carefully defining a “year” noting
when one examines the apparent returns [of the sun] to [the same] equinox of solstice, one finds that the length of the year exceeds 365 days by less than $\frac{1}{4}$-day, but when one examines its return to the fixed stars, it is greater [than 365 $\frac{1}{4}$-days].
Continue reading “Almagest Book III: On the Length of the Year”
