This chapter is easily the shortest one in Book III. It literally consists of a paragraph (which I’ll quote in its entirely but break into two for ease of reading) that gives a very quick description of how one calculates the position of the sun at any given time from the epoch derived in the last chapter.
So whenever we want to know the sun’s position for any required time, we take the time from epoch to the given moment (reckoned with respect to the local time at Alexandria), and enter with it into the table of mean motion. We add up the degrees [and their subdivisions] corresponding to the various arguments [18-year periods, years, months, etc.], add to this the elongation [from apogee at epoch], 265;15º, subtract the complete revolutions from the total, and count the result forward from Gemini 5;30º rearwards through [i.e. in the order of] the signs. The point we come to will be the mean position of the sun.
Next we enter the same number, that is the distance from apogee to the sun’s mean position, into the table of anomaly, and take the corresponding amount in the third column. If the argument falls in the first column, that is if it is less than 180º, we subtract the [equation] from the mean position; but if the argument falls in the second column, i.e. is greater than 180º, we add it to the mean position. Thus we obtain the true or apparent [position of] the sun. Continue reading “Almagest Book III: On the Calculation of the Solar Position”