circle’s center. The model for Mars illustrates these concepts (figure). Planet B is assumed to
revolve uniformly around an epicycle RQ. The center of this epicycle S revolves around an
eccenter AP, the center of which C is displaced from the Earth T. The motion of S around
the eccenter is uniform as seen, not from C, but from an “equant” point E which in this
model is twice as far from the Earth as the eccenter’s center.
The central argument of the Almagest begins, after various mathematical and geographical
preliminaries, in Book 3 with the theory of the Sun, chosen because it can be established
without recourse to assumptions about the motions of other heavenly bodies. In this and
subsequent sections, Ptolemy follows a recurring pattern. First, the basic structure of the
model is supported by very general observed facts. Then Ptolemy applies a geometrical and
trigonometrical analysis to a small number of dated observations of the positions of the
body to acquire numerical details. In his solar theory the deduction is straightforward and
final, but for the other bodies Ptolemy must correct the initial data in the light of his first
approximate results, so that the arguments are recursive and depend on convergence.
In discussing solar and lunar theory (Books 4–5), Ptolemy acknowledges Hipparkhos, who
had developed some of the same deductive methods and arrived at some of the same
results. However, Ptolemy explicitly takes credit for the discovery that the Moon has two
periodicities. Book 6 applies the solar and lunar models to the study and prediction of
eclipses. In Books 7–8, where Ptolemy again draws on Hipparkhos, Ptolemy shows that the
stars, while maintaining configurations relative to each other, make a gradual revolution
(“precession”) around the poles of the ecliptic, and he presents a catalogue of 1022 stars.
Books 9–13 are devoted to the five planets known to antiquity (Mercury, Venus, Mars,
Jupiter, and Saturn). Ptolemy asserts that Hipparkhos contributed little to planetary theory;
and it is striking that he acknowledges no debt in the Almagest to any astronomers during the
intervening centuries except as observers.
The Almagest does not profess to be a historical account of discovery, and internal analysis
of its details reveals that many of its results cannot have been obtained originally in the way
that Ptolemy deduces them. Moreover, some of Ptolemy’s reports of his own observations –
perhaps all – have been adjusted or fabricated to agree closely with the theories. How much
Ptolemy’s model for the motion of Mars © Jones
PTOLEMY