Levi Ben Gerson and the Brightness of Mars

See, for example, Almagest x.7; Toomer G. J. , Ptolemy's Almagest (New York and Berlin, 1984), 484.

This variation is clearly stated in Rheticus's Narratio prima , ed. and transl. by Hugonnard-Roche H. (Warsaw, 1982), 55 (Latin), 107 (French), 162 n. 86; and in Copernicus's De revolutionibus (Nuremberg, 1543), i.10, 10r.

Goldstein B. R. , The Arabic version of Ptolemy's Planetary Hypotheses (Philadelphia, 1967), 8.

The best known passage is in Simplicius's Commentary on Aristotle's De caelo: For the text with translation, see de Pitane Autolycos , La sphère en mouvement, Levers et couchers héliaques, Testimonia, ed. and transl. by Aujac G. (Paris, 1979), 179; for passages in Proclus , see Procli diadochi Hypotyposis astronomicarum positionum , ed. and transl. by Manitius C. (Leipzig, 1909), i.18, 10–11; and Proclus , Commentaire sur la République, transl. by Festugière A. J. (3 vols, Paris, 1970), iii, 171.

Notable among Ptolemy's early critics who discussed the problems of Mars were al-'Urḍī, Levi ben Gerson, Henry of Hesse, and Regiomontanus. According to al-'Urḍī, the difficulty with Ptolemy's data was that Mars at opposition should appear to be larger than Venus but this has not been observed; according to ben Gerson Levi , the observed ratio of sizes at maximum and minimum distances is 2 to 1 whereas Ptolemy's model implies a ratio of 6 to 1; according to Henry of Hesse, Mars can be smaller than a first magnitude star whereas the size of Mars in the Ptolemaic tradition is equal to that of a first magnitude star; and according to Regiomontanus, the ratio of apparent areas of Mars at maximimum and minimum distances with Ptolemy's data should be 52 to 1, but Mars never appears so large. On al-'Urḍī, see Goldstein B. R. and Swerdlow N. , “Planetary distances and sizes in an anonymous Arabic treatise preserved in Bodleian Ms. Marsh 621”, Centaurus, xv (1970–71), 135–70, espec. pp. 148, 163 (reprinted, with additional notes, in Goldstein B. R. , Theory and observation in ancient and medieval astronomy (London, 1985), chap. VI). On ben Gerson Levi , see Goldstein B. R. , The astronomy of Levi ben Gerson (1288–1344) (New York and Berlin, 1985), chap. 17, 105–6. On Henry of Hesse, see Mancha J. L. , “Henry of Hesse's criticism of Ptolemaic cosmology” (in preparation). On Regiomontanus, see Swerdlow N. M. , “Regiomontanus on the critical problems in astronomy”, in Nature, experiment and the sciences , ed. by Levere T. H. and Shea W. R. (Dordrecht and Boston, 1990), 165–95, espec. p. 173. For similar discussions of Venus, see Goldstein B. R. , “The pre-telescopic treatment of the phases and apparent size of Venus”, Journal for the history of astronomy, xxvii (1996), 1–12.

See Goldstein B. R. , “Medieval observations of solar and lunar eclipses”, Archives internationales d'histoire des sciences, xxix (1979), 101–56, and idem, “A new set of fourteenth century planetary observations”, Proceedings of the American Philosophical Society, cxxxii (1988), 371–99.

Goldstein , The astronomy of Levi ben Gerson (ref. 5), 106–7. For the Latin version of this discussion of the comet of 1337, see Mancha J. L. , “The Latin translation of Levi ben Gerson's Astronomy”, in Studies on Gersonides: A fourteenth-century Jewish philosopher-scientist, ed. by Freudenthal G. (Leiden, 1992), 21–46, espec. pp. 32 and 44.

Goldstein , The astronomy of Levi ben Gerson (ref. 5), 188; and Goldstein B. R. , “Theory and observation in medieval astronomy”, Isis, lx (1972), 39–47, espec. p. 45.

These computed values were kindly provided to me by Marsden B. and his assistant, Williams G. , based on the following formula for the magnitude of Mars at opposition: M = −1.52 + 5 log (r·d), where r is the heliocentric distance of Mars, and d is the geocentric distance of Mars, in astronomical units.

Newcomb S. , Popular astronomy, 5th edn (New York, 1884), 326–7; and Flammarion G. C. and Danjon A. , The Flammarion book of astronomy, transl. by Pagel A. and Pagel B. (New York, 1964), 283–4.

Tuckerman B. , Planetary, lunar, and solar positions, a.d. 2 to a.d. 1649 (Philadelphia, 1964), 684, 686, 687.

Westman R. S. , “The Melanchthon circle, Rheticus, and the Wittenberg interpretation of the Copernican theory”, Isis, lxvi (1975), 165–93; Kusukawa S. , The transformation of natural philosophy: The case of Philip Melanchthon (Cambridge, 1995).

Bretschneider C. G. (ed.), Philippi Melanchthonis Opera quae supersunt omnia (28 vols, Halle, 1834–60), xiii, cols. 268 (Jupiter) and 274 (Mars).

Cf. Van Helden A. , Measuring the universe (Chicago, 1985), 70–76.