Abstract
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.
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- 1.
Manitius (German transl. vol. 2, p. 334) talks about Himmelsgloben, but what Ptolemy had in mind was probably some kind of orrery or planetarium. Already Plato refers to such an instrument {Timaios 40 d 2). Later, Archimedes constructed a mechanical model of the universe, driven by water and showing the motion of the Sun, Moon, and planets; Cicero mentions having seen it with his own eyes. Also Posidonius is credited with the construction of a similar apparatus. Hero's model of the universe has been studied by A. G. Drachmann (1971). Finally, in the Planetary Hypotheses Ptolemy himself dealt with the construction of a model illustrating the celestial spheres (page 397).
- 2.
In return Herz (1887, p. 87) speaks of die von Delambre vollig unverstandene Theorie der Breiten-bewegung des Almagests.
- 3.
The only possible exception is the exposition given by Herz (1887, pp. 143-159). A brief exposition of the essential features of the theory, valid only for the inferior planets, was given by E. S. Kennedy (1951).
- 4.
See e.g. al-Birimi, The Book of Instruction in the Elements of Astrology, transl. R. R. Wright, London, 1934, p. 102.
- 5.
Thus Dreyer (1906, 198) was wrong when he asserted that the epicycles in their turn were inclined at the same angles to the plane of the deferents, so that their planes were always parallel to that of the ecliptic. Later (p. 199) he seems to consider the values of jm quoted above as foreign to the Almagest and resulting from Ptolemy's changing his mind before he composed the Canopus Inscription.
- 6.
In the literature on the Ptolemaic theory of latitude it is a common mistake to assume that the latitude function of the superior planets is a sum of 2 components, stemming from the inclination and the deviation respectively. This error may be due to the fact that Ptolemy based his Handy Tables on a theory of this kind in order to establish a uniform procedure for calculating latitudes of all the five planets (cf. below page 400).
- 7.
I think this is what is behind the curious statement by Manitius, that die Bahn der Venus keinen niedersteigenden, die Bahn des Merkurs keinen aufsteigenden Knoten hat (see his German Almagest-translation, vol. 2, p. 328). What is true is, of course, that the first latitude component (due to the inclination) is always northern in the case of Venus, and southern in the case of Mercury.
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Pedersen, O. (2011). Latitudes and Visibility Periods. 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_12
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DOI: https://doi.org/10.1007/978-0-387-84826-6_12
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