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Problems Raised by Ptolemy's Lunar Tables

S. J. Goldstein, JrView all authors and affiliations

Volume 13, Issue 3

https://doi.org/10.1177/002182868201300303

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1. LeMonnier P. C., quoted by Lalande in Mémoires de l'Académie Royale des Sciences, 1757, p. 420: “One knows beyond doubt that Ptolemy was never able to measure the position of any star.” LeMonnier is author of the work: Observations de la lune, du soleil et des étoiles fixes, pour servir à la physique céleste et aux usages de la navigation (Paris, 1751–73).

2. Lalande J. J. F., Astronomie (3rd edn, Paris, 1792), i, 119: “One is convinced that Ptolemy was not an observer, that he had taken from Hipparchus and from others that preceded him all that there is of value in his work…. But that does not prevent his work from being precious, since it is the only major remnant we have of ancient observations and history.”

3. Delambre J. B. J., in his Histoire de l'astronomie ancienne (Paris, 1817), i, p. XXV, remarks, “Has Ptolemy observed? The observations that he tells us that he has made, are they not calculations from the tables and examples that serve to explain his theories?” Delambre specifically questioned the reality (not the accuracy) of the equinox and solstice observations, the observation of the obliquity of the ecliptic, the observations of lunar eclipses, and observations of the star catalogue.

4. Peters C. H. F. and Knobel E. B., in Ptolemy's catalogue of stars, a revision of the Almagest (Washington, D.C., 1915), 15, comment: “Notwithstanding Ptolemy's statement that he observed as many stars as it was possible to perceive, even to the sixth magnitude, it will be seen that the above evidence confirms the theory that the catalogue is in all probability that of Hipparchus reduced by the addition of a constant to the longitudes, and retaining his original latitudes.”

5. Tannery P., in Recherches sur l'histoire de l'astronomie ancienne (Paris, 1893), 154, wrote: “These comparisons amply justify the doubts which have been raised on the truthfulness of Ptolemy on the subject of observations of equinoxes and solstices that he reports to have made himself.”

6. Newton R. R., in The crime of Claudius Ptolemy (Baltimore, 1977), 378, concluded: “All of his own observations that Ptolemy uses in the Syntaxis are fraudulent, so far as we can test them. Many of the observations that he attributes to other astronomers are also frauds that he has committed.” Newton specifically concluded (pp. 115–30) that at least ten of the lunar eclipse observations on which the lunar tables are based are fabricated.

7. Britton's J. P. Yale University Ph.D. thesis, “On the quality of solar and lunar observations and parameters in Ptolemy's Almagest” (1967), is based on obsolete accelerations for the Sun and Moon.

8. Tannery, op. cit., 164.

9. At least one must be based on observation to explain the agreement between the tables and the modern theory.

10. Halley E., “A discourse concerning a method of discovering the true moment of the Sun's ingress into the tropical signs”, Philosophical transactions, xix (1695), 12–20.

11. Halley E., “Considerations on the change of the latitudes of some of the principal fixt stars”, ibid., xxx (1717), 736–8.

12. Tannery, op. cit., 160.

13. Nautical Almanac Office, Explanatory Supplement (1961), p. 107.

14. Brown E. W., “The elements of the Moon's orbit”, Monthly notices of the Royal Astronomical Society, lxxv (1915), 508–16.

15. Jones Spencer H., “The rotation of the Earth, and the secular accelerations of the Sun, Moon and planets”, ibid., xcix (1939), 541–58.

16. Newcomb S., “Tables of the Sun: Introduction”, Astronomical Papers, American Ephemeris and Nautical Almanac, vi (1898), 7–32.

17. Stumpff P., “The motion of the Earth-Moon system between 1700 and 2100 in Newcomb's theory and in JPL-Ephemerides”, Astronomy and astrophysics, ci (1981), 52–71.

18. Van Flandern T. C., preprint, “Improved mean elements for the Earth and Moon” (1981).

19. Morrison L. V. and Ward C. G., “An analysis of the transits of Mercury, 1677–1973”, Monthly notices of the Royal Astronomical Society, clxxiii (1975), 183–206.

20. Newton R. R., The Moon's acceleration and its physical origins (Baltimore, 1980), 457.

21. Newton R. R., Ancient astronomical observations (Baltimore, 1970), 272.

22. Muller P. M., “An analysis of the ancient astronomical observations”, thesis (1975), School of Physics, University of Newcastle, Newcastle upon Tyne.

23. Muller P. M. and Stephenson F. R., “The accelerations of the Earth and Moon from early astronomical observations”, in Growth rhythms and the history of the Earth's rotation, ed. by Rosenberg G. D. and Runcorn S. K. (New York, 1975), 459–534.

24. Schnabel P., Berossos und die Babylonisch-Hellenistische Literatur (Leipzig, 1923).

25. Fotheringham J. K., “The indebtedness of Greek to Chaldaean astronomy”, Observatory, li (1928), 301–15.

26. Neugebauer O., “The alleged Babylonian discovery of the precession of the equinoxes”, Journal of the American Oriental Society, lxx (1950), 1–8.

27. See The Alexandrian Library by Parsons E. A. (New York, 1952), ch. 14 and its appendix.

28. See the article on Berosus in the latest edition of the Encyclopedia Britannica (Micropaedia, i, 1015).

29. From Neugebauer O., History of mathematical astronomy (Berlin, 1975), i, 309, the synodic month used in Seleucid-era tablets is 29; 31, 50, 8, 20 days. Fotheringham J. K., op. cit., attributes the same value to the Babylonian astronomer, Kidinnu, who lived c. −380. Dividing this synodic month into 360° gives 12·1907469367, which differs by 1 in the 12th digit from the mean motion in elongation in Table 3. Such agreement does not arise by chance.

30. Rome A., Commentaires de Pappus et de Théon d'Alexandrie (Cittá del Vaticano, Biblioteca Apostolica Vaticana, 1943), iii, 818.

31. Dreyer J. L. E., “On the origin of Ptolemy's catalogue of stars”, Monthly notices of the Royal Astronomical Society, lxxvii (1917), 528–39. See also Vogt H., “Versuch einer Wiederherstellung von Hipparchs Fixsternverzeichnis”, Astronomische Nachtrichten, ccxxiv (1925), 18–54. Vogt shows that the star positions from Commentary on Aratus were not those of Ptolemy's catalogue.

32. Pannekoek A., “Ptolemy's precession”, Vistas in astronomy, i (1955), 60–66, p. 65.

33. Britton, op. cit., p. ix.

34. Gingerich O., Quarterly journal of the Royal Astronomical Society, xxi (1980), 253–66, p. 259.

35. Neugebauer, A history of mathematical astronomy, i, 1–2.

36. Pedersen, op. cit., 408.

37. Pedersen, op. cit., 371, concludes that the observations Ptolemy uses to obtain the inclination of the orbits of Venus and Mercury are impossible. Neugebauer, A history of mathematical astronomy, i, 101, concludes that Ptolemy's observation to find the inclination of the Moon's orbit “does not look very real”. Neugebauer also dismisses Ptolemy's claim to have measured equinoxes with an indirect statement: “In the same passage from Hipparchus it is also stated that he found the length of the (tropical) year to be 365 ¼ days minus 1/300 day (i.e. 365; 14,48 days), a value which Ptolemy confirmed and constantly used in his computations” (p. 293).

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