Giovanni Antonio Magini's “Keplerian” Tables of 1614 and Their Implications for the Reception of Keplerian Astronomy in the Seventeenth Century

TBOO = Dreyer J. L. E. (ed.), Tychonis Braha Dani opera omnia (Copenhagen, 1913–29).

JKGW = Caspar Max (eds), Johannes Kepler Gesammelte Werke (Munich, 1937–). In citations from these works, line numbers are given after the colon.

For an historiographical survey of the Scientific Revolution, see Cohen Floris H. , The Scientific Revolution (Chicago, 1994).

See, for example, Lindberg David C. and Westfall Richard S. (eds), Reappraisals of the Scientific Revolution (Cambridge, 1990), and Osler Margaret J. , Rethinking the Scientific Revolution (Cambridge, 2000).

Newton to Halley, 20 June 1686, in Turnbull H. W. (ed.), The correspondence of Isaac Newton, ii (Cambridge, 1960), 436.

Koyré Alexandre , The astronomical revolution: Copernicus-Kepler-Borelli, transl. by Maddison R. E. W. (Ithaca, 1973); Wilson Curtis , “Kepler's derivation of the elliptical path”, Isis, lix (1968), 4–25; and Stephenson Bruce , Kepler's physical astronomy (New York and Berlin, 1987).

Wilson Curtis , “Predictive astronomy in the century after Kepler”, in Taton R. and Wilson C. (eds), The general history of astronomy, ii: Planetary astronomy from the Renaissance to the rise of astrophysics, Part A: Tycho Brahe to Newton (Cambridge, 1989), 161–206; Applebaum Wilbur , “Keplerian astronomy after Kepler: Researches and problems”, History of science, xxxiv (1996), 451–504.

Russell J. L. , “Kepler's laws of planetary motion: 1609–1666”, The British journal for the history of science, ii (1964), 1–24. For a similar example, see Thoren Victor E. , “Kepler's second law in England”, The British journal for the history of science, vii (1974), 243–58.

The earliest numbering of “Kepler's laws” so far noticed is by Lalande in his Abrégé d'astronomie (Paris, 1774), 201, recorded by Gingerich Owen , “Five centuries of astronomical textbooks”, in Pasachoff Jay M. and Percy John R. (eds), The teaching of astronomy (Cambridge, 1990), 189–95, pp. 192–3. See also Wilson Curtis , “Kepler's laws, so-called”, H.A.D. news: The newsletter of the Historical Astronomy Division of the American Astronomical Society, no. 31 (May 1994), 1–2.

Voelkel James R. , The composition of Kepler's Astronomia nova (Princeton, 2001).

Wilson , “Predictive astronomy” (ref. 5).

On the historiographical appropriateness of replacing “reception” with “appropriation”, see Sabra A. I. , “The appropriation and subsequent naturalization of Greek science in Medieval Islam: A preliminary statement”, History of science, xxv (1987), 223–43.

Donahue William H. (transl.), Johannes Kepler: New astronomy (Cambridge, 1992), 286.

Ibid.

The “true” reference positions were calculated using the full series of terms from P. Bretagnon and G. Francou, VSOP87D (ftp://ftp.bdl.fr/pub/ephem/planets/vsop87/). Our C++ program matched the reference positions provided by Bretagnon and Francou to within 10^−10°. The published precision of the VSOP87 theory is 1″ for 4000 years before and after A.D. 2000. The parameters for the Ptolemaic theory were calculated using the method in Meeus Jean , Astronomical algorithms, 2nd edn (Richmond, Virginia, 1998), chap. 31. The Martian eccentricity was corrected for the vector sum with the Earth's line of apsides.

For biographical details, copies of Magini's correspondence, and a detailed bibliography of his works, see Favaro Antonio , Carteggio inedito di Ticone Brahe, Giovanni Keplero e di altri celebri astronomi e matematici dei secoli XVI e XVII con Giovanni Antonio Magini (Bologna, 1886). Although Favaro reprints the letters between Magini and Kepler, he does not discuss the tables in the Supplementum.

Magini G. A. , Novae coelestium orbium theoricae congruentes cum observationibus N. Copernici (Venice, 1589), signature b4v, translated in Rosen Edward , Three imperial mathematicians (New York, 1986), 99–100.

Magini to Kepler , 15 January 1610, JKGW, xvi, #548.

Kepler to Magini , 1 February 1610, JKGW, xvi, #551: 32–35.

Magini to Kepler , 23 February 1610, JKGW, xvi, #555: 51–53.

Magini to Kepler , 20 April 1610, JKGW, xvi, #569.

Kepler to Magini , 10 May 1610, JKGW, xvi, #573.

Magini to Kepler , 26 May 1610, JKGW, xvi, #576.

Magini G. A. , Supplementum ephemeridum ac tabularum secundarum mobilum (Venice, 1614), 161–73.

Magini , Supplementum, 174–6.

Needled before publication by his correspondent the East Frisian pastor David Fabricius about the unsatisfactory nature of his calculation, Kepler testily retorted “Now, what more do you have that offends you? Is it because it cannot be calculated by a short cut? Nothing is lacking for us, my dear Fabricius, but geometry. Teach me geometrically to construct, square, and to cut ellipsoids in a given ratio, and straightaway I will teach you to calculate with the genuine hypothesis. So now, call upon those Dutch geniuses of yours to help me with this.” Kepler to Fabricius, 4 July 1603, JKGW, xiv, #262: 831–5.

Donahue (transl.), op. cit. (ref. 11), 181.

Kepler , Astronomia nova, ch. 56; Donahue (transl.), op. cit. (ref. 11), 543.

Consider the first example in Chapter 51. Kepler calculates the distances for two observations of Mars when the mean anomaly is around 87° — to be precise, 87;9,24 and 89;15. Since the two values are slightly different, he corrects the distance of the latter so that both calculated distances refer to the mean anomaly of 87;9,24. The observationally-determined distances are then 154,400 and 154,272. In the table in Chapter 56, Kepler gives the value for the distance at this mean anomaly calculated using the correct distance relation as 154,338. If we enter Magini's distance table with a mean anomaly of 87;9,24, it yields exactly 154,338.

Magini , Supplementum, 58.

TBOO, ii, 42–43, 50.

Magini , Supplementum, 53–57.

TBOO, ii, 44.

Magini , Supplementum, 177–9.

It is interesting to note that this method is one of the recipes for solving plane and spherical triangles that Tycho included in his compilation of methods for his assistants. It is actually the second of two methods for solving a plane triangle given two sides and the included angle, and the fact that it is labeled “A Shorter Solution” suggests that Tycho may not have been aware of it initially. See Brahe Tycho , Triangulorum planorum et sphaericorum praxis arithmetica, ed. by Studni&čka F. I. (Prague, 1886; reprinted Vaduz, 1984), fol. 6.

See Gingerich Owen , “Erasmus Reinhold and the dissemination of Copernican theory”, Studia Copernicana, vi (1973), 43–62, reprinted in Gingerich Owen , The eye of heaven: Ptolemy, Copernicus, Kepler (New York, 1993), 221–51.

Magini converts 8:30 Uraniburg to 8:41 for his meridian of Venice. This offset is, in fact, much too large. Kepler's value in the Rudolphine tables of a 2-minute difference between Uraniborg and Venice is much closer to the true value, and provides an interesting insight into Kepler's unsung work in geography.

Magini , Supplementum, 17. Magini's agreement should not be quite so exact. His solar theory yields a true longitude of 9,15;3,40 for this date and time, while the value he uses in the example is 9,15;3,4. His calculated position should be closer to 17;40,0 Cancer.

The middle values of the manuscript ephemeris agree to a minute of arc with Magini's tables, but the differences mount up toward each end. For 30 December 1582, the ephemeris value is over 4′ too low, and for 26 January 1583, it is close to 3′ too low. Therefore, the precise comparison with Kepler's computed values for the end points is somewhat problematic.

Kepler Johannes , “Preface to the Rudolphine tables”, JKGW, x, 40: 42–49, translated by Gingerich Owen and Walderman William in Quarterly journal of the Royal Astronomical Society, xiii (1972), 367.

See Gingerich Owen , “‘Crisis’ versus aesthetic in the Copernican Revolution”, Vistas in astronomy, xvii (1975), 85–95, reprinted in The eye of heaven (ref. 34), 193–204, p. 195. Note that the error curve there represents the difference of the true position from Magini's prediction, whereas here the error curve represents the difference of Magini from the true position, and therefore the curves are in opposite senses.

See Swerdlow N.M. and Neugebauer O. , Mathematical astronomy in Copernicus's De revolutionibus (New York, 1984), 83–84.

Kepler to Crüger Peter , 9 September 1624, JKGW, xviii, #993, 208.

Crüger to Kepler , 15 July 1624 (o.s.), JKGW, xviii, #990: 118–19.

Magini to Tycho , 20 February 1601, TBOO, viii, 401: 22–28.

Kepler to Magini , 1 June 1601, JKGW, xiv, #190: 158.

Kepler to Crüger , 9 September 1624, JKGW, xviii, #993: 405–7.

Kepler to Maestlin , 16/26 February 1599, JKGW, xiii, #133: 89–93.

Kepler Johannes , “Preface to the Rudolphine tables” (ref. 38), 369.

Donahue (transl.), op. cit. (ref. 11), 51.