An Analysis of Errors in the Star Catalogues of Ptolemy and Ulugh Beg

Dreyer J. L. E. (ed.), Tychonis Brahe Dani opera … (Copenhagen, 1913–29), ii, 151.

Newton R. R. , The crime of Claudius Ptolemy (Baltimore, 1977), 245–54.

Laplace P. S. , Exposition du système du monde (Paris, 1835), 391–2.

Włodarczyk J. , “Observing with the armillary astrolabe”, Journal for the history of astronomy xviii (1987), 173–95, p. 182.

Evans J. , “On the origin of the Ptolemaic star catalogue”, ibid., 155–72, 233–78.

Ibid., 162–5.

Włodarczyk , op. cit.

Delambre J. B. , Histoire de l'astronomie ancienne, ii (Paris, 1817), 265–97.

Peters C. and Knobel E. , Ptolemy's catalogue of stars: A revision of the Almagest (Washington, 1915), 16.

Toomer G. L. (transl.), Ptolemy's Almagest (London, 1984), V.1, 217–19; VII.2, 327–8; VII.4, 339–40.

In this case the astronomical refraction acts only in one direction, as the observations with an armillary sphere can begin only in the evening. On the possibility of morning observations cf. Dreyer J. L. E. , “On the origin of Ptolemy's catalogue of stars: Second paper”, Monthly notices of the Royal Astronomical Society, cxxviii (1918), 343–9, p. 344; Rawlins D. , “An investigation of the ancient star catalog”, Publications of the Astronomical Society of the Pacific, xciv (1982), 359–73, p. 372.

For points (2) and (3), cf. Włodarczyk , op. cit., 186–7, 193; the error due to the setting (point (4)) can be estimated from the computation of mean square errors ( Newton , op. cit., 216).

Grasshoff's charts ( Grasshoff G. , Die Geschichte des Ptolemaeischen Sternenkatalogs (doctoral diss., Hamburg, 1986), 270–323) indicate with high probability that the stars were observed by constellations; this was noted by Evans (op. cit., 276).

All calculations are based on data from Grasshoff , op. cit., 228–68. The longitudes are reduced to the epoch +137.5. In my preprint ( Shevchenko M. Yu. , “Almagest: Analysis of method and results of star positional observations”, Preprint no. 12 (1988), Institute for the History of Natural Science and Technology, USSR Academy of Science), the calculations were based on data from Peters and Knobel , op. cit.

Ptolemy in Almagest VII.2 (ed. Toomer , 328) remarks that the method used for measuring the coordinates of α Leonis was applied to α Virginis: “… and the brightest among those stars near the ecliptic….” Then, in VII.4 (ed. Toomer, 339) he wrote that these brightest stars were used to determine the positions of other stars. On reference stars see also Pedersen O. , A survey of the Almagest (Odense, 1974), 236–7.

This confirms Evans's conclusion about the use of α Virginis as a reference star ( Evans , op. cit., 245).

Neugebauer O. , A history of ancient mathematical astronomy (Berlin and New York, 1975), Pt 1, 286.

Boll F. , “Die Sternkatalogue des Hipparch und des Ptolemaios”, Bibliotheca mathematica, Folge 3, ii (1901), 185–95, p. 187.

Ptolemy , Almagest VII.1 (ed. Toomer , 322–4).

Evans , op. cit., 239–49.

Knobel E. B. , Ulugh Beg's catalogue of stars (Washington, 1917), 11.

Evans , op. cit., 162–3.

All calculations used data from Knobel , op. cit.