Ptolemy's ‘planets’ of course included the Sun and Moon as well as Mercury, Venus, Mars, Jupiter and Saturn. For the general historical context of the Almagest, see NeugebauerO., A history of ancient mathematical astronomy (Berlin, 1975). For the Almagest itself, see ToomerG. J., Ptolemy's Almagest (London and New York, 1984).
2.
The standard notation for a sexagesimal number is, for example, 3;36,57 = 3 + 36/60 + 57/602 Errors in tabulated values are given in units of the last place. Thus, if the correct value of the entry (to two fractional places) is 3;36,57 and the tabulated value is 3;37,4, the error is given as +7. A complete recomputation of every numerical table in the Almagest may be found in Van BrummelenG., “Mathematical tables in Ptolemy's Almagest”, Ph.D. dissertation, Simon Fraser University, 1993.
3.
See PetersenV. M., “The three lunar models of Ptolemy”, Centaurus, xiv (1969), 142–71, for a full description of the lunar longitude theory.
4.
See PedersenO., “Logistics and the theory of functions: An essay in the history of Greek mathematics”, Archives internationales d'histoire des sciences, xxiv (1974), 29–50.
5.
Ibid., 42.
6.
See Petersen, op. cit. (ref. 3).
7.
For a full description, see PedersenO., A survey of the Almagest (Odense, 1974).
8.
To see this, drop a perpendicular from P onto EGAV and consider the resulting right-angled triangle.
9.
This corrects a small error in Pedersen, Survey (ref. 7), 294.
10.
Clustering cannot be detected in the fourth sexagesimal place, because other errors are an order of magnitude greater and obscure the clustering effect.
11.
Ptolemy does not calculate a value for com in the text.
12.
For a description of the Mercury model, see HartnerW., “The Mercury horoscope of Marcantonio Michiel of Venice”, Vistas in astronomy, i (1955), 84–138.
