Latitudes and Visibility Periods
In all the planetary models of the Almagest the whole machinery of equant, deferent, epicycle, etc., has hitherto been regarded as situated in the plane of the ecliptic. This proved justifiable in so far as the longitudes derived from these models were considered to be in sufficient agreement with experience. Even the complicated longitude variations around the retrograde periods could be accounted for by such flat models as we saw in the preceding chapter. However, until now the various planetary theories have given us an insufficient description of the motions of the planets in so far as even crude observations show that almost all the time they are found outside the ecliptic. In the case of the Moon this is obvious since otherwise we would have a total solar and a total lunar eclipse every month. In order to avoid such a flagrant contradiction with experience it was necessary to develop a theory of the Moon's latitude (see page 200). For the sake of completeness Ptolemy now develops in the final Book of his great composition a similar theory of planetary latitudes. Half of Book XIII (Chapters 1-6) is devoted to this purpose while the remaining chapters (7-10), apart from the final one, give a theory of visibility periods and heliacal risings and settings of the planets.