Historical Perspectives on Copernicus's Account of Precession

Rheticus G. J. , Narratio prima (1540), ed. and trans, by Hugonnard-Roche H. (Studia Copernicana, 20; Wroclaw , 1982), 43ff [Latin], 93ff [French], see also 151, note 26; cf. Copernicus , Letter Against Werner , transl. by Rosen E. , Three Copernican treatises (1939; reprint edn, New York, 1959); and Westman R. S. , “The Melanchthon circle, Rheticus, and the Wittenberg interpretation of the Copernican theory”, Air, lvi (1975), 165–93 (espec. p. 181).

See Regiomontanus's letter to Bianchini in Swerdlow N. , “Regiomontanus on the critical problems of astronomy”, in Nature, experiment, and the sciences, ed. by Levere T. H. and Shea W. R. (Dordrecht, 1990), 165–95 (espec. pp. 170ff, 175ff).

For an example of the subordination of past observations to “tradition”, see Copernicus , Letter against Werner. “However, by reason of the extreme slowness of this motion, the ancient mathematicians were unable to pass on to us a complete account of [the motion of the eighth sphere]. But if we desire to examine it, we must follow in their footsteps and hold fast to their observations, bequeathed to us like an inheritance. And if anyone on the contrary thinks that the ancients are untrustworthy in this regard, surely the gates of this art [astronomy] are closed to him” (transl. Rosen , op. cit. (ref. 1), 99). I intend to elaborate on this point in a future publication.

Let S be the length of the sidereal year, T be the length of the tropical year, μ be the daily solar motion, and p the annual increment in stellar longitudes due to precession. Then: P = μ · (S − T) For Ptolemy, μ · T = 360°. The parameter for precession of 1°/100 years is equivalent to 0;0,36°/y, and the daily solar motion is 0;59,8°. Hence p/μ = 0;0,36,32^d which, when added to 365;14,48^d, yields a sidereal year of 365; 15,24,32^d.

Cf. Pedersen O. , A survey of the Almagest (Odense, 1974), 423. Note that Rheticus (Narratio prima (ref. 1), 102) gives the length of the sidereal year as about 365;15,24^d.

Cf. Rheticus , Narratio prima (ref. 1), 95.

Goldstein B. R. , “Levi ben Gerson's analysis of precession”, Journal for the history of astronomy, vi (1975), 31–41 (espec. p. 36).

See Morelon R. , Thābit Ibn Qurra: Oeuvres d'astronomie (Paris, 1987), p. lii.

See Neugebauer O. , “Thäbit Ben Qurra ‘On the solar year’ and ‘On the motion of the eighth sphere’”, Proceedings of the American Philosophical Society, cvi (1962), 264–99 (espec. p. 264).

Morelon , op. cit. (ref. 8), 56; the Latin version has 43 instead of 33 in the last place: cf. Neugebauer , op. cit. (ref. 9), 280.

Morelon , op. cit. (ref. 8), 55, 205; Neugebauer , op. cit. (ref. 9), 279.

Morelon , op. cit. (ref. 8), 60; Neugebauer , op. cit. (ref. 9), 285.

Ragep F. J. , Naṣīr al-Dīn al-Ṭūsī's Memoir on astronomy (New York, Berlin, 1993), 400ff; Morelon , op. cit. (ref. 8), p. xix.

See Neugebauer , op. cit. (ref. 9); Goldstein B. R. , “On the theory of trepidation”, Centaurus, x (1965), 129–60; Dobrzycki J. , “Teoria precesji w astronomii średniowiecznej” [in Polish with English summary], Studia i materiały, C 11 (Wrocław, 1965), 3–47; Mercier R. , “Studies in the medieval conception of precession”, Archives internationales d'histoire des sciences, xxvi (1976), 197–220; Samsó J. , Las ciencias de los antiguos en al-Andalus (Madrid, 1992), 222ff.

Toomer G. J. , “A survey of the Toledan Tables”, Osiris, xv (1968), 5–174 (espec. pp. 118 ff).

See Chabás J. and Goldstein B. R. , “Andalusian astronomy: Al-Zīj al-Muqtabis of Ibn al-Kammād”, Archive for history of exact sciences (in press).

Rico y Sinobas M. , Libros del saber de astronomia del rey Don Alfonso X de Costilla (5 vols, Madrid, 1863–67), iv, 179; cf. Samsó J. , “Algunas notas sobre el modelo solar y la teoría de la precesión de los equinoccios en la obra astronómica de Alfonso X”, Acta hispanica ad medicinae scientiarumque historiam illustrandam, iv (1984), 81–114 (espec. p. 101).

Poulle E. , Les tables alphonsines (Paris, 1984); cf. i. North D. , “The Alfonsine tables in England”, in Prismata: Festschrift für Willy Hartner, ed. by Maeyama Y. and Salzer W. G. (Wiesbaden, 1977), 269–301.

Poulle E. , “The Alphonsine tables and Alphonso X of Castille”, Journal for the history of astronomy, xix (1988), 97–113; for some evidence that suggests otherwise, see now Goldstein B. R. Chabás J. , and Mancha J. L. , “Planetary and lunar velocities in the Castilian Alfonsine Tables”, Proceedings of the American Philosophical Society, cxxxviii (1994), 61–95.

Cf. Casanovas J. , “On the precession problem in the Alfonsine tables”, in De astronomia Alphonsi Regis, ed. by Comes M. Puig R. and Samsó J. (Barcelona, 1987), 79–87.

See Price D. J. , “A medieval footnote to Ptolemaic precession”, Vistas in astronomy, i (1955), 66.

See Mercier R. , “Studies in the medieval conception of precession”, Archives internationales d'histoire des sciences, xxvii (1977), 33–71 (espec. pp. 58–59).

Poulle E. , “Jean de Murs et les tables alphonsines”, Archives d'histoire doctrinale et littéraire du moyen âge, xlvii (1980), 241–71.

In another passage ( Poulle , op. cit. (ref. 23), 262), John of Murs attributes this value to “Alzophi et alii” (“al-Ṣūfī and others”), and attributes the value of 1°/66y to al-Battānī, which is in fact correct.

Poulle , op. cit. (ref. 23), 257–8.

Poulle , op. cit. (ref. 23), 25 8n.

North J. D. , “Just whose were the Alfonsine tables?”, Proceedings of the Fifth International Symposium on the History of Arabic Science, Granada 1992 (in press).

Poulle , op. cit. (ref. 23), 251.

North , op. cit. (ref. 27).

Poulle , op. cit. (ref. 23), 258.

Poulle , op. cit. (ref. 23), 262.

Almagest, vii.3 (transl. by Toomer G. J. , Ptolemy's Almagest (Berlin, New York, 1984), 338); Nallino C. , Al-Battānī sive Albatenii Opus astronomicum (3 vols, Milan, 1899–1907), i, 124, 292.

“He [Alfonso] determined [by observation] in his time the positions of the fixed stars, which he compared with their positions as accurately (veraciter) found by the ancients; he divided the time between them … and he found the amount of time [it took them] to move one degree;… in this way he found 1;22,40,53° in 100 years, and this motion is 0;0,49,28° per year…” (for the Latin text, see Poulle , op. cit. (ref. 23), 259). Is this a report of what John of Murs read in his source, or is it his reconstruction of what lay behind the parameters he found there? Note that according to the Parisian Alfonsine tables an accumulated precession of 17;8° corresponds to about 1236 years (the interval from the presumed epoch of Ptolemy's star catalogue, A.D. 16 (see Samsó J. and Castelló F. , “An hypothesis on the epoch of Ptolemy's star catalogue”, Journal for the history of astronomy, xix (1988), 115–20), to the epoch of the Alfonsine tables, A.D. 1252), but this yields an ‘average’ precession of about 0;0,49,54°/year, and not the value in John of Murs's text.

Toomer , op. cit. (ref. 15), 44.

Cf. North , op. cit. (ref. 27).

To be sure, it is Copernicus's geometrical argument that correctly ascribes the phenomenon of precession to the axis of the Earth, rather than to a motion of the stars. For further details, see Moesgaard K. P. , “The 1717 Egyptian years and the Copernican theory of precession”, Centaurus, xiii (1968), 120–38; Swerdlow N. M. and Neugebauer O. , Mathematical astronomy in Copernicus's De revolutionibus (2 vols, New York, Berlin, 1984), i, 129 ff.

Mercier , op. cit. (ref. 22), 60.

See Millás J. M. , Las tablas astronómicas del rey Don Pedro el Ceremonioso (Madrid, Barcelona, 1962), 190; Chabás J. , “Astronomia Hispanomusulmana: Las tablas de Barcelona” (in preparation: To appear in a volume edited by J. Samsó).

MS Vienna 5311 contains a number of astronomical treatises, including the Theorica planetarum by Campanus of Novara, and the explicit of that text (f. lOOr) is dated 13 Sept. 1356 ( Benjamin F. S. Jr , and Toomer G. J. , Campanus of Novara and medieval planetary theory (Madison, 1971), 98, 355). The latest date in the MS is 1428, and it appears in marginal comments above the headings of star lists on ff. 129v, 130r, and 131r; the Alfonsine tables are mentioned on f. 134va(last line). On f. 137r there are reports of some solar and stellar altitudes observed in Bologna in 1305–6, Montpellier in 1306, and Genoa in 1311–12, and we are also told that the longitude of Spica in 1306 was Lib 12;50°. It is then remarked that the corresponding entry for Spica in Ptolemy's star catalogue is Vir 26;40°, which leaves a difference of 16; 10°. According to this text, the epoch of Ptolemy's star catalogue is A.D. 141 (rather than A.D. 137 as in Toomer , op. cit. (ref. 32), 340; cf. North , op. cit. (ref. 27), n. 23), and this is 1165 years prior to 1306. The author of this note then divides 16; 10° by 1165 years, and he finds that 1° corresponds to 72 years “and a little more” (accurately 1°/72;4 years). He goes on to say that two ancient observations of Spica, by Timocharis, were separated by 12 years, and the increase in longitude between them was 0;10° (as indeed we read in Almagest, vii.3; Toomer , op. cit. (ref. 32), 336) which, he adds, is equivalent to 1°/72 years. Though it is not explicitly stated, the point would seem to be that precession has not changed since the earliest available observations that go back to the third century B.C.

See Swerdlow and Neugebauer , op. cit. (ref. 36), i, 147.

See Dobrzycki J. , “Astronomical aspects of the calendar reform”, in Gregorian reform of the calendar, ed. by. Coyne G. V. Hoskin M. , and Pedersen O. (Vatican City, 1983), 117–37 (espec. pp. 120 ff); Dobrzycki , op. cit. (ref. 14).

Rheticus gives a list of the accumulated precession according to Copernicus for various epochs, but does not compare these values with calculations based on the Alfonsine tables (see transl. by Hugonnard-Roche . (ref. 1), 95). For such a comparison, see the graph in Mercier , op. cit. (ref. 22), 48. By way of contrast, Rheticus does compare Copernicus's model for the motion of the solar apogee with the Alfonsine tables for this motion, arguing that Copernicus's model shows better agreement with what he takes to be observational data by various practitioners from Hipparchus to Copernicus (transl. by Hugonnard-Roche (ref. 1), 99–100, and 157, notes 56, 57).