Essay Review: The Sources of Ptolemy's Parameters: The Origins of Ptolemy's Astronomical Parameters

Mémoires de l'Académie des Sciences , année 1757, 420–1, my translation.

Willy Hartner , “The Mercury horoscope of Marcantonio Michiel of Venice”, Vistas in astronomy , i, 84–138, pp. 109 Kepler ff. , early on, seems to have suspected the same thing; see Gesammelte Werke , xv, 267–8. In the Epitome ( Gesammelte Werke , vii, 435–6), he tries to explain how Ptolemy might have been led to the double perigee, but then goes on to suggest that the Ptolemaic observations were ‘improved’ by the ancient copiers, and are very inexact.

Goldstein Bernard R. , “The Arabic version of Ptolemy's Planetary hypotheses”, Transactions of the American Philosophical Society , lvii, Part 4 (1967), 7.

On this point see my essay, “The inner planets and the Keplerian Revolution”, Centaurus , xvii (1973), 205–48, p. 234.

See Aaboe A. , “Scientific astronomy in Antiquity”, Philosophical transactions of the Royal Society of London , A cclxxvi, 21–42, p. 35, and “Observation and theory in Babylonian astronomy”, Centaurus , xxiv (1980), 14–35.

The calculated results on which these numbers are based for the inner planets are given in my “Inner planets and the Keplerian Revolution”, passim. Those for the outer planets are as follows: Planet Date Ptolemy's ‘observations’ +66′ Tuckerman Difference. Mars 26–27 Tybi, Hadrian 15 82°; 6 81°;25 +41′. (Syntaxis X.7,8) 6–7 Pharmouthi, Hadrian 19 149°;56 150°;15 −19′. 12–13 Epiphi, Antonine 2 243°;40 242°;49 +51′. 15–16 Epiphi, Antonine 2 242°;42 241°;55 +47′. Jupiter 1–2 Epiphi, Hadrian 17 234°;17 234°;11 + 6′.(Syntaxis XI.1,2) 13–14 Phaophi, Hadrian 21 339°; 0 339°; 3 – 3′. 20–21 Athyr, Antonine 1 15°;29 15°;29 + 0′. >26–27 Mesore, Antonine 2 76°;51 76°;34 + 17′. >Saturn 7–8 Pachon, Hadrian 11 182°;19 182°;30 −11′. >(Syntaxis XI.5,6) 18 Epiphi, Hadrian 17 250°;46 250°;54 – 8′. >24 Mesore, Hadrian 20 285°;20 285°;20 + 0′. >6–7 Mechir, Antonine 2 310°;10 310°; 6 + 4′.

Wilson , “The inner planets and the Keplerian Revolution”, 228–9.

Ibid. , 212–13.

Syntaxis I.1; Great books of the Western World (hereafter: GBWW), xvi, 5 (translation modified).

Syntaxis I.1; GBWW , xvi, 6 (translation modified).

Syntaxis XIII.2; GBWW , xvi, 429 (translation modified).

Syntaxis I.1; GBWW , xvi, 6 (translation modified).

Willy Hartner , “The role of observations in ancient and medieval astronomy”, Journal for the history of astronomy , viii (1977), 1–11.