Adjusting Venus: The Use of Maximum Elongations in the Almagest and Ptolemy’s Theory of Knowledge

ABSTRACT

There has been much debate surrounding the way in which Ptolemy handled the observations that are behind his planetary models. This article aims at presenting an interesting case of manipulation of observational data within the epistemological frame of what we may call Ptolemy’s philosophy of knowledge. It deals with an interesting case from the Almagest, that of the determination of the longitudes of the apogee and perigee of Venus’s deferent, and shows that the selections and adjustments Ptolemy carried out in order to obtain the needed results are nothing but an analogous application of the epistemological doctrines expressed in his On the Kriterion and in his Harmonics.

Acknowledgements

The author would like to thank Dr Christián Carman for his many, many suggestions during the preparation of this paper, and Prof. Magdalena Battaglia for her help with the English. The author would also like to thank Dr James McAllister and the two anonymous referees of this journal for their comments and criticisms to previous versions of this paper.

Notes

1 Jones presented some of the main contents of that chapter at the IV International Workshop on Epistemology and History of Astronomy, Rio de Janeiro, July 2017.

2 The Zodiac can be precisely determined by reference to the ecliptic line. This line is the one on which the Sun is always located, and through which it performs its apparent yearly motion around the Earth. The band of the Zodiac is the area which is located 10° to the north and south of the ecliptic. All the planets visible to the naked eye, the Moon, and obviously the Sun, move within these limits.

3 From the ancient Greek πλανήτης, planétes, wanderer. Although they usually marked a distinction between them, Greek astronomers frequently listed the Sun and Moon among the planets, because they shared this characteristic of not having a sidereal fixed movement.

4 In fact, the fixed stars also show a departure from a simple circular and uniform motion. As it was already known to Hipparchus (2nd century BCE), the celestial sphere performs a second motion, different from its daily rotation and much slower than it, in the direction of the signs. This second movement is a result of what we now call the precession of the equinoxes. Cf. Ptolemy (1984), 327ff.

5 The belt of the Zodiac was defined as the one whose limits were parallel to the ecliptic and located 10° to its north and south. It was divided into 12 parts called signs, of 30° each, which were associated with particular constellations. The longitudinal origin point of the ecliptic and the Zodiac was the vernal equinoctial point, which marked 0° and the beginning of Aries. The direction was determined by the tropical movement of the sun.

6 An example of a previous solution to the same problem is the system of homocentric spheres, famously explained in Aristotle’s Metaphysics (cf. 1073a15–1074b15). Cf. Mendell (1998), Schiaparelli (1998).

7 In order to produce a retrogradation, a certain relation between the sizes of the circles and their angular velocities has to be met, that is, , where r is the epicycle’s radius, R the deferent’s radius, vE the angular velocity of the epicycle on the deferent and vP the angular velocity of the planet on the epicycle. In his Almagest, Ptolemy made a detailed study of this relation (Ptolemy 1984, 555ff.).

8 To know which point is which, Ptolemy goes through a separate discussion, looking at where the epicycle looked bigger and where it looked smaller (Ptolemy 1984, 470–471).

9 Calculated with Alcyone Ephemeris v4.3 (Meeus and Meshier algorithms).