Saving the Phenomena: The Background to Ptolemy's Planetary Theory

1. Cf. Jones A., “Hipparchus's computations of solar longitudes”, Journal for the history of astronomy, xxii (1991), 101–25 (espec. p. 122). The earliest dated observation in Greco-Latin scientific literature reported in the name of a specific individual is found in Pliny's Hist. nat. ii.180 (Pline l'Ancien, Histoire naturelle (37 vols [editors and translators vary], Paris, 1947–1985), ii [ed. and transl. by Beaujeu J.], 79), but this observation of a solar eclipse was not used to derive the parameters of a model. Earlier, in Aristotle's Meteorology, it is remarked that “we ourselves have observed Jupiter coinciding with one of the stars of the Twins and hiding it…” (343b30), but no date is given, and no attempt is made to use this observation to construct a model. For Ptolemy's use of observations in his lunar theory, including those of Hipparchus, see Goldstein B. R. and Bowen A. C., “The role of observations in Ptolemy's lunar theories”, in Ancient astronomy and celestial divination, ed. by Swerdlow N. M. (forthcoming).

2. A text Britton calls Text S is “the only [Babylonian] text known to combine observational material … with theoretical functions from mathematical lunar theory”: Britton J. P., “An early function for eclipse magnitudes in Babylonian astronomy”, Centaurus, xxxii (1989), 1–32 (espec. p. 1). But there are no direct comparisons between theory and observations even in that text, and certainly nothing on the derivation of the mathematical functions from the observations.

3. Almagest iii.1 (transl. by Toomer G. J., Ptolemy's Almagest (New York and Berlin, 1984), 133 and 133 n8). It is often assumed that the three equinoxes of 162 to 158 b.c. were observed by Hipparchus, but Toomer reports his view that they were not made by Hipparchus himself, “but were simply adduced by him for comparison”.

4. A passage in Almagest ix.2 (Toomer, op. cit. (ref. 3), 420) may be taken to be such an echo, but I think it more likely to be an allusion to Babylonian records than to Greek: “It is also [confusing] that most of the ancient [planetary] observations have been recorded in a way which is difficult to evaluate, and crude. For the more continuous series of observations concern stations and phases [i.e., first and last visibilities]”.

5. Cicero, De natura deorum, ii.51, ed. and transl. by Rackham H. (Cambridge, Mass. and London, 1933), 173; Cicero, De divinatione ii.89 in Cicero, De senectute, De amicitia, De divinatione, ed. and transl. by Falconer W. A. (New York and London, 1923), 471. I am grateful to Alan C. Bowen for searching the data bases, TLG (Thesaurus Linguae Graecae) and PHI (Packard Humanities Institute), for early occurrences of the relevant terms in Greek and Latin.

6. Oldfather C., Diodorus of Sicily (12 vols, Cambridge, Mass. and London, 1933), i, 278–9. Needless to say, Diodorus and other classical authors are no longer to be taken as reliable sources for the content of either Egyptian or Babylonian astronomy in the absence of support from the original documents of those ancient cultures that are now available.

7. Oldfather, op. cit. (ref. 6), i, 457; cf. Cicero, De divinatione i.2; Falconer, op. cit. (ref. 5), 223f; Pliny, Hist. nat. vii. 193; Pline l'Ancien, op. cit. (ref. 1), vii [ed. and transl. by Schilling R.], 113.

8. For Schiaparelli's account, see Heath T. L., Aristarchus of Samos (Oxford, 1913), 194ff.

9. Almagest i.3 (Toomer, op. cit. (ref. 3), 39); cf. Smith A. M., Ptolemy's theory of visual perception, Transactions of the American Philosophical Society, lxxxvi/2 (Philadelphia, 1996), 2, 151.

10. See Goldstein B. R., The Arabic version of Ptolemy's Planetary hypotheses, Transactions of the American Philosophical Society, lvii/4 (Philadelphia, 1967).

11. Toomer, op. cit. (ref. 3), 421.

12. Cf. Goldstein B. R., “Remarks on Gemma Frisius's De radio astronomico et geometrico”, in From ancient omens to statistical mechanics: Essays on the exact sciences presented to Asger Aaboe, ed. by Berggren J. L. and Goldstein B. R. (Copenhagen, 1987), 167–79.

13. See Smith, op. cit. (ref. 9), 27.

14. Pliny, Hist. nat. ii. 79; Beaujeu (ed.), op. cit. (ref. 1), 34.

15. Diodorus, Bib. hist. ii. 30; Oldfather, op. cit. (ref. 6), i, 451; cf. Hunger H. and Pingree D., MUL.AP1N: An astronomical compendium in cuneiform (Horn [Austria], 1989), 149f.

16. Cf. Ceragioli R. C., “Solving the puzzle of ‘red’ Sirius”, Journal for the history of astronomy, xxvii (1996), 93–128 (espec. pp. 95 and 122 n12).

17. Robbins F. E., Ptolemy: Tetrabiblos (Cambridge, Mass. and London, 1964), 217.

18. See Herschel J., Outlines of astronomy (London, 1849), 491ff.

19. Cf. Evans J., “On the origin of the Ptolemaic star catalogue”, Journal for the history of astronomy, xxviii (1987), 155–72, 233–78 (espec. pp. 260ff).

20. For a critical summary of this literature, see Swerdlow N. M., “The enigma of Ptolemy's catalogue of stars”, Journal for the history of astronomy, xxiii (1992), 173–83.

21. Aristotle, De caelo ii. 8; Aristotle, On the heavens, ed. and transl. by Guthrie W. (Cambridge, Mass. and London, 1960), 189.

22. Plutarch, Moralia: Concerning the face that appears in the orb of the Moon, ed. and transl. by Cherniss H. (Cambridge, Mass. and London, 1957), 41ff.

23. This view was taken by Bacon Roger, Buridan, and ben Gerson Levi, among others: See, e.g., Gabbey A., “The case of the rotating Moon”, in Revolution and continuity, ed. by Barker P. and Ariew R. (Washington, D.C., 1991), 95–129 (espec. pp. 115f).

24. Vitruvius, De arch. ix. 2; Vitruvius, On architecture, ed. and transl. by Granger F. (2 vols, Cambridge, Mass. and London, 1956), ii, 227ff.

25. Cherniss (ed.), op. cit. (ref. 22), 103.

26. Duhem P., To save the phenomena: An essay on the idea of physical theory from Plato to Galileo, transl. by Doland E. and Maschler C. (Chicago, 1969), 114.

27. Duhem, op. cit. (ref. 26), 6; emphasis in the original. Note that the “path” of a planet is a concept developed by Kepler rather than by Ptolemy (cf. Barker P. and Goldstein B. R., “Distance and velocity in Kepler's astronomy”, Annals of science, li (1994), 59–73). The English version of Duhem may be misleading here, for the original French (Paris, 1908, p. 3) has marche that can mean ‘progress’ as well as ‘path’.

28. Duhem, op. cit. (ref. 26), 16ff.

29. Duhem missed the passage in Plutarch, but he was aware of the use of this expression by Theon of Smyrna (date uncertain; most probably after Ptolemy, in the third or fourth century a.d.), and Proclus, as well as by Simplicius.

30. Cherniss (ed.), op. cit. (ref. 22), 55.

31. Geminus, Intro. ast. 1. 19–22; Géminos, Introduction aux phénomènes, e.d. and transl. by Aujac G. (Paris, 1975), 5; Bowen A. C. and Goldstein B. R., “Geminus and the concept of mean motion in Greco-Latin astronomy”, Archive for history of exact sciences, 1 (1996), 157–85 (espec. p. 180).

32. Smith (op. cit. (ref. 9), 19) understands the ancient view of “saving the phenomena” (particularly in optics) to mean that the appearances in the sensible world are illusions that have to be rationalized or “saved” by being reduced to perfect regularity.

33. The text of Simplicius appears in: Autolycos de Pitane, La sphère en mouvement, ed. and transl. by Aujac G. (Paris 1979), 159.

34. Toomer, op. cit. (ref. 3), 600–1.

35. On the distinction between arithmetic mean motion and periodic mean motion, see Bowen and Goldstein, op. cit. (ref. 31), 159.

36. Cf., e.g., Neugebauer O. and Parker R., “Two demotic papyri”, Journal of Egyptian archaeology, liv (1968), 231–5; Rochberg F., “Nabu-rimannu”, in Great lives from history: Ancient and medieval series, ed. by Magill F. N. (Pasadena, 1988), 1439–43; Jones A., “Evidence for Babylonian arithmetic schemes in Greek astronomy”, in Die Rolle der Astronomie, ed. by Gaiter H. D. (Graz, 1993), 77–94.

37. See Kuhrt A., “Berossus' Babyloniaka and Seleucid rule in Babylonia”, in Hellenism in the East, ed. by Kuhrt A. and Sherwin-White S. (Berkeley and Los Angeles, 1987), 32–56 (espec. pp. 36ff).

38. Vitruvius, De arch. ix. 6; Granger (ed.), op. cit. (ref. 24), ii, 245.

39. Cicero, De divinatione ii. 92; Falconer (ed.), op. cit. (ref. 5), 475.

40. Cf. Bowen and Goldstein, op. cit. (ref. 31).

41. Cf. Jones, op. cit. (ref. 1), and Jones, op. cit. (ref. 36), espec. p. 89.