Most of Ptolemy’s calculations are set in the plane of the ecliptic. But clearly, only motion in longitude can be determined in this manner. A looping reversal, such as those in Figs. 8 , 9 , 10 and 11 , requires some account of motion in latitude, as had been obvious to Eudoxus and Kalippus. Accordingly, Ptolemy tilted the orbit of Mars 1° from the ecliptic; Jupiter’s was tipped 1°30′, and Saturn’s 2°30′. The apogees of these orbits were north of the ecliptic, but the epicycles themselves were tilted so that their planes were parallel to the ecliptic (see Fig. 46).