We’re almost to the end of book II. There’s really 2 chapters left, but the next one is almost entirely a table laying out the values we’ve been looking at here recently, so this is the last chapter in which we’ll be working out anything new.
In this chapter, we’ll tackle the angle between the ecliptic and a “circle through the poles of the horizon”. If you imagine standing outside, the zenith is directly overhead which is the pole for your local horizon. Directly opposite that, beneath you, is the nadir. If these two points are connected with a great circle, that’s the great circle we want to find the angle of with respect to the ecliptic. Because we measure upwards, from the horizon, along an arc of these great circles, to measure the altitude of a star, these are often called altitude circles.
But while we’re at it, Ptolemy promises that we’ll also determine “the size of the arc…cut off between the zenith and…the ecliptic.” In other words, because the ecliptic is tilted with respect to the horizon, the arcs between the two will be different.
To get us started, Ptolemy begins with the following diagram.
Continue reading “Almagest Book II: Angle Between Ecliptic And Altitude Circle – Relationships”