[57] The changing latitudes of the planets, for instance, which gave Ptolemy much trouble, are much more easily explained when it is granted that they partly depend upon Earth’s motion in an orbit whose plane is slightly inclined to the planes of their orbits.
[58] It therefore really approached more nearly the sidereal year, although the cycle was based on the tropical year.
[59] De Mon. II. vii., “Temple Classics” edition.
[60] De Senectute.
[61] The average year was the same, 365¼ days, in the old 8-year cycle of the Greeks, and also in the Calippic cycle, which did not come into practical use. The average year of the Metonic cycle was longer, and therefore departed further from the true tropical year.
[63] Ezekiel, v. 5.
[64] Arabic gib = Latin sinus, a fold; i.e. the chord folded in two.
[65] The Arabian mile was equal to 4000 “black cubits,” and if this is the Egyptian and Babylonian cubit, the values are rather too large, being in round numbers 26,500 and 8,500 English miles, instead of 25,000 and 8000.
[66] The Catalogue of Hipparchus is said to have contained 1080 stars, but Ptolemy’s has only 1022.