Abstract
In the previous Chapters 5, 6, 9, and 10 we have seen how Ptolemy solved the problem of determining the ecliptic longitude λ(t) of the Sun, Moon, and planets at any given instant of time t. The solution was given in the form of a number of fairly similar standard procedures which we have summarized in the final formulae (5.32–33) of the solar theory, (6.8) of the lunar theory, and (9.43–44) together with (10,12) in the case of the five planets. This was an intellectual feat of the highest importance for the development of astronomy. For not only did Ptolemy complete what his predecessors had begun, but his achievement meant that the purpose of planetary theory became definitively fixed in a new direction.
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- 1.
There is no great amount of secondary literature to this chapter. The reader is referred to Delambre (1817, II, 381-392), Herz (1887, 47–50 and 159–161), and O. Neugebauer (1959 a). 2) The following proof is taken from B. L. van der Waerden, Science Awakening, p. 238.
- 2.
G. J. Toomer says (1970, p. 190) that The procedure is worthy of Apollonius, and is indeed a particular case of the pole-polar relationship treated in Conies III, 37. But Ptolemy (who of all ancient authors is most inclined to give credit where it is due) seems to introduce this device as his own, and return to Apollonius only later.
- 3.
Delambre (1817, II, 382 f.) noticed that the same figure may be applied to both the eccentric and the epicyclic model, but nobody seems to have realized that the transformation involved is a geometrical inversion until O. Neugebauer published his paper on Apollonius (1959 a) from which we quote: The most conspicuous feature of this discussion is the method of transforming eccentric and epicyclic models into each other by means of an inversion on a fixed circle which serves as eccenter or as epicycle. It seems to have escaped attention, however, that Ptolemy refers to exactly the same method also in Book IV, Chapter 6, on the occasion of his discussion of the determination of the epicycle radius (or of the eccentricity) of the simple lunar theory. I have no doubt that also this section belongs to Apollonius.
- 4.
Considering this I am unable to understand why Delambre (1817, II, 384) wrote that Les Grecs ne trouvaient ces points […] que par tatonnement.
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Pedersen, O. (2011). Retrograde Motions and Maximum Elongations. In: Jones, A. (eds) A Survey of the Almagest. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York, NY. https://doi.org/10.1007/978-0-387-84826-6_11
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