Johannes Kepler in the Light of Recent Research

KSW = Krafft F. Meyer K. Sticker B. (eds), Internationales Kepler-Symposium Weil der Stadt 1971 (= Arbor scientiarum, Reihe a, Band i, Hildesheim, 1973).

KLC = Johannes Kepler—Werk und Leistung. Katalog der Ausstellung Linz 19 Juni bis 29 August 1971 (Linz, 1971).

KFR = Preuss E. (ed.), Kepler Festschrift 1971 (= Acta Albertina Ratisbonensia, Regensburg, 1971).

KVA = Vistas in astronomy (Kepler volume), xviii (1975).

See the bibliographies of Gingerich O. , Dictionary of scientific biography , vii (1973), 308–12 (but note that the references to Vistas in astronomy, xvi, should be to KVA), and List M. , “Bibliographia Kepleriana 1967–1975”, KVA, 955–1003.

Koestler A. , The sleepwalkers (London, 1968), 252.

“Die betrachtende Kreatur in trinitarischen Kosmos”, KFR, 64–98.

“Kepler's century”, KVA , 6. The “two Keplers” idea was opposed by Karl Rufus at a Symposium in 1930; see KVA, 278.

Elements of physical and geometrical astronomy (1726), Johnson reprint (London, 1972), i, 133–50.

Wilson C. , “Kepler's derivation of the elliptical path”, Isis, lix (1968), 5–25; Aiton E. J. , “Kepler's second law of planetary motion”, Isis, lx (1969), 75–90.

“Kepler's astrology and mysticism”, KVA, 402.

See Mahnke D. , Unendliche Sphäre und Allmittelpunkt (Halle, 1937), 142. Kepler's source may be located in Complementum theologicum, ch. 6.

Wilpert P. (ed.), Nikolaus von Kues: Werke . Reprint of 1488 ed. (Berlin, 1967), i, 299. De visione dei, ch. 6.

“Johannes Kepler—Homo iste”, KSW, 455.

ibid., 458.

Hammer F. , “Die Astrologie des Johannes Kepler”, Sudhoffs Archiv, lv (1971), 113–35.

List M. , “Das Wallenstein-Horoskop von Johannes Kepler”, KLC, 127–36.

Simon G. , “Kepler's astrology: The direction of a reform”, KVA, 446.

Beer A. , “Kepler's astrology and mysticism”, KVA, 412.

B. Sticker gives a good account of Kepler's theory of personality, KSW, 463–7.

Kepler Johannes , Selbstzeugnisse, tr. Hammer Esther (Stuttgart-Bad Cannstatt, 1971), 16–30.

Sticker , KSW, 467.

Simon , KVA, 447.

Fleckenstein J. O. , “Kepler and Neoplatonism”, KVA, 430.

Gerdes E. W. , “Keplers Theologisches Selbstverständnis und dessen Herkunft”, KSW, 360.

KGW = Kepler Johannes , Gesammelte Werke (Munich, 1937-), xvii, 187.

Rosen E. , “Kepler and the Lutheran attitude towards Copernicanism”, KVA, 318. See also Westman R. S. , “The comet and the cosmos: Kepler, Mästlin and the Copernican hypothesis”, in Dobrzycki J. (ed.), The reception of Copernicus' heliocentric theory (Dordrecht, 1972), 7–30, and Westman R. S. , “The Melanchthon Circle, Rheticus and the Wittenberg interpretation of the Copernican theory”, Isis, lxvi (1975), 165–93.

Gerdes E. W. , “Johannes Kepler as a theologian”, KVA, 339–40.

Hübner J. , “Naturwissenschaft als Lobpreis des Schöpfers”, KSW, 337.

ibid., 338–9.

ibid., 353.

Rosen , op. cit. (ref. 27), 324.

ibid., 337.

Hübner J. , “Kepler und Daniel Hitzler”, KLC, 73–80.

List M. , “Kepler und die Gegenreformation”, KFR, 51.

Hübner J. , “Kepler's praise of the Creator”, KVA, 374–5.

Hübner , op. cit. (ref. 29), 336.

Gerdes , op. cit. (ref. 28), 340–50.

Schiffers N. , “Das Verhältnis von Theologie und Naturwissenschaft bei Kepler”, KSW, 332.

KGW, i, 23–24 and 285.

KGW , vi, 186–205. See Nitschke A. , “Keplers Staats- und Rechtslehre”, KSW, 409–24.

Westman R. S. , “Continuities in Kepler scholarship”, KVA, 62–63.

KGW, vi, 225.

Schiffers , op. cit. (ref. 39), 332–3.

Hübner , op. cit. (ref. 36), 381.

Schiffers , op. cit. (ref. 39), 333.

Gerlach W. , “Johannes Kepler; life, man and work”, KVA , 87. Also on the concept of harmony see Haase R. , “Fortsetzungen der Keplerschen Weltharmonik”, KLC , 61–72, Dickreiter M. , “Dur und Moll in Keplers Musiktheorie”, KLC , 41–50, and Klein U. , “Johannes Keplers Bemühungen um die Harmonieschriften des Ptolemaios und Porphyrios”, KLC, 51–60.

Westman , op. cit. (ref. 42), 61–62.

Burtt E. A. , The metaphysical foundations of modern science (2nd ed., London, 1932), 44–60.

Holton G. , “Johannes Kepler's universe; its physics and metaphysics”, American journal of physics, xxiv (1956), 340–5.

Koyré A. , La révolution astronomique (Paris, 1961), 119–458.

Westman , op. cit. (ref. 42), 63.

These papers have been reprinted (that of Mittelstrass in translation) in Studies in history and philosophy of science, iii (1972), 203–98. See also Russell J. L. , “Kepler and scientific method”, KVA, 733–45.

Mittelstrass J. , “Wissenschaftstheoretische Elemente der Keplerschen Astronomie”, KSW, 3–27.

ibid., 18–27.

ibid., 18.

ibid., 23.

Ibid.

ibid., 24–25. See also Haase R. , “Pansophia and mathesis universalis”, KVA, 528.

Westman R. S. , “Kepler's theory of hypothesis and the realist dilemma”, KSW, 29–54.

See Costabel P. , “Kepler and the Copernican model”, KVA, 218.

Westman , op. cit. (ref. 60), 44.

ibid., 45–50.

Buchdahl G. , “Methodological aspects of Kepler's theory of refraction”, KSW, 141–67.

ibid., 145.

ibid., 154.

ibid., 148.

ibid., 149.

ibid., 167.

See, for example, Contro W. S. , “Zur Kinematik der Planetenbewegung in Copernicus' Commentariolus”, Archive for history of exact sciences, vi (1970), 360–71.

Gingerich O. , “Kepler's place in astronomy”, KVA, 261–2. See also Krafft F. , “Physikalische Realität oder mathematische Hypothese”, Philosophia naturalis, xiv (1973), 243–75.

No part of celestial physics was more difficult for Kepler to explain than the lunar variation; see Thoren V. E. , “Kepler's work on the lunar theory”, KVA, 613–16.

Gingerich , op. cit. (ref. 71), 264.

ibid., 272–6.

ibid., 272. See also Gingerich O. , “The Mercury theory from antiquity to Kepler”, Actes du XIIe congrès international d'histoire des sciences (Paris, 1971), vol. 3A, 57–64 and Wilson C. , “The inner planets and the Keplerian revolution”, Centaurus, xvii (1973), 205–48.

An assessment of the accuracy of Kepler's terrestrial orbit has been made by Maeyama Y. , “On the order of accuracy of Kepler's solar theory”, KVA , 769–80. See also Maeyama Y. , “The historical development of solar theories in the late sixteenth and seventeenth centuries”, Vistas in astronomy, xvi (1974), 35–60.

Gingerich O. , “Kepler's treatment of redundant observations”, KSW, 307–14. On the determinations of the elements of the planetary orbits in the Leningrad manuscripts, see Bialas V. , “Die quantitative Beschreibung der Planetenbewegung von Johannes Kepler in seinem handschriftlichen Nachlass”, KFR, 99–140.

Gingerich , op. cit. (ref. 77), 308. There was a systematic error in Kepler's reduction of Tycho's observations, owing to the inaccuracy of the solar theory, but this did not endanger his conclusions; see Wilson C. , “The error in Kepler's acronychal data for Mars”, Centaurus, xiii (1969), 263–8.

Wilson , op. cit. (ref. 10).

Maeyama , op. cit. (ref. 76), 770.

Kepler's work on the orbit of Mars was not invalidated by his ignorance of the perturbations of Mars by other planets; see Schmiedler F. , “Ueber die Störungen der von Kepler verwendeten Marsbeobachtungen”, KFR, 141–58, and Kovalevsky J. , “Kepler's laws and modern celestial mechanics”, KVA, 605–11.

Aiton , op. cit. (ref. 10).

See also Wilson C. , “How did Kepler discover his first two laws?”, Scientific American, ccxxvi (1972), 93–106; Wilson C. , “Kepler's ellipse and area rule”, KVA , 587–91; Krafft F. , “Nicolaus Copernicus and Johannes Kepler: New astronomy for old”, KVA , 287–306; Aiton E. J. , “The elliptical orbit and the area law”, KVA , 573–86; and Aiton E. J. , “Johannes Kepler and the astronomy without hypotheses”, Japanese studies in the history of science (in press).

On the significance of the harmonic law in relation to the Harmonice mundi as a whole, see Haase R. , “Marginalien zum 3. Keplerschen Gesetz”, KFR, 159–65.

Gingerich O. , “The origins of Kepler's third law”, KVA , 600. The account of the harmonic law given in Aiton E. J. , The vortex theory of planetary motion (London, 1972), 18–19, needs correction along the lines indicated here.

Gingerich , op. cit. (ref. 85), 596.

Krafft F. , “Johannes Keplers Beitrag zur Himmelsphysik”, KSW , 55–138. See also Krafft F. , “Kepler's contributions to celestial physics”, KVA, 567–72.

Danilov Y. A. and Smorodinskii Y. A. , “Kepler and modern physics”, KVA, 699–707.

A good account of Kepler's theory and the Platonic background is given by Krafft , op. cit. (ref. 87), 79–95. See also Duhem P. , The aim and structure of physical theory, tr. Wiener P. (Princeton, 1954), 220–52.

Aiton , op. cit. (ref. 85), 12–13.

Krafft , op. cit. (ref. 87), 94.

See Duhem P. , Etudes sur Léonard de Vinci (reprint: Paris, 1955), ii, 201–9. See also Aiton , op. cit. (ref. 85), 18. The interpretation of impetus as the formation of a physiological disposition is found in Luiz Coronel; see Duhem , op. cit., iii, 148–9.

Kepler J. , Somnium, tr. Rosen E. (London, 1967), 16.

Nobis H. M. , “Ropé und Nutus in Keplers Astronomie”, KFR, 244–65.

ibid., 261.

Krafft , op. cit. (ref. 87), 98.

ibid., 96–136.

Goldbeck E. , Keplers Lehre von der Gravitation (Halle, 1896).

Linnik V. P. , “Kepler's works in the field of optics”, KVA, 809–17.

Marek J. , “Johannes Kepler and the development of physical optics”, KSW, 215–27.

Chenakal V. L. , “Johannes Kepler's astronomical instruments”, KVA, 814–24.

ibid., 823–4. See also Prager F. D. , “Kepler als Erfinder”, KSW, 385–405.

Koelbing H. M. , “Kepler und die physiologische Optik”, KSW , 229–45, and Simon G. , “On the theory of visual perception of Kepler and Descartes”, KVA, 825–32.

Koelbing , op. cit. (ref. 103), 244. Kepler had some followers, however. Many of the plates in Scheiner's Rosa Ursina treat of the analogy between the eye and optical instruments; see Marek J. , “Kepler and optics”, KVA, 853.

Marek , op. cit. (ref. 100), 224–6.

Lohne J. A. , “Kepler und Harriot, Ihre Wege zum Brechungsgesetz”, KSW , 187–214. It is interesting to note that Kepler was the first to mark out the boundary surfaces of a physical beam, producing the cross-section of a ray of light whose geometry permits a search for the law of refraction governed by physical considerations, such as the relative densities of the media; see KSW, 254.

Buchdahl , op. cit. (ref. 64).

Buchdahl points out that Kepler's reasoning is a complex mixture of all the various processes that have been formalized individually by philosophers; ibid., 163.

Harriot arrived at the sine law in 1602.

Buchdahl , op. cit. (ref. 64), 164–5.

ibid., 165, ref. 107.

Hofmann J. E. , “Ueber einige fachliche Beiträge Keplers zur Mathematik”, KSW, 261–84.

Belyi Y. A. , “Johannes Kepler and the development of mathematics”, KVA, 643–60; Belyi Y. A. and Trifunovic D. , “Zur Geschichte der Logarithmentafeln Keplers”, Schriftenreihe Geschichte Naturwissenschaft, Technik, Medizin, ix (Leipzig, 1972), 5–20 and Aiton E. J. , “Infinitesimals and the area law”, KSW, 285–305.

Belyi , op. cit. (ref. 113), 646.

Hofmann , op. cit. (ref. 112), 283–4. Whiteside D. T. , in his “Keplerian planetary eggs, laid and unlaid, 1600–1605”, Journal for the history of astronomy, v (1974), 1–21, has examined Kepler's research on Mars from the modern point of view, with particular reference to the limitations of Kepler's mathematical techniques.

Aiton , op. cit. (ref. 113), 292.

The similarity between the mathematical ideas of Nicholas and Kepler is very probably, as Westman and Schiffers suggest, of an external kind, stemming from a common Neoplatonic influence; see KSW, 317.

Hofmann , op. cit. (ref. 112), 270.

Costabel P. , “Kepler—mathematician and physicist”, KVA, 632.

ibid., 638.

Hofmann , op. cit. (ref. 112), 281.

Davis A. E. L. , “Systems of conics in Kepler's work”, KVA, 677.

ibid., 679.

Coxeter H. S. M. , “Kepler and mathematics”, KVA, 621–70.

Shafranovskii I. I. , “Kepler's crystallographic ideas and his tract The six-cornered snowflake'”, KVA, 861–76.

Belyi , op. cit. (ref. 113), 656; cf. Gingerich O. , in Dictionary of scientific biography , vii, 304.

D'Occhieppo K. F. , “Kepler, der zweite grosse Erneuerer der Astronomie” KLC, 87–98.

Bialas V. , “Eine doppelte Iterationsrechnung von Johannes Kepler und ihre Programmierung”, Nova Kepleriana, Neue Folge, Heft iii (1970), 5–30.

Bialas V. , “Data processing in the Rudolphine Tables”, KVA, 749–67.

Adam A. , “The Kepler-Schickart calculating machine”, KVA , 881–9; idem, “Die unerforschten Probleme in Keplers Werke”, KLC , 35–40, and Belyi , op. cit. (ref. 113), 658.

Sydow J. , “Kepler's homeland—Württemberg”, KVA , 135–8; Sutter B. , “Kepler in Graz”, KVA , 139–42; Horsky Z. , “Kepler in Prague”, KVA , 143–8; Hujer K. , “Kepler in Prague”, KVA , 149–54; Tursky H. , “Johannes Kepler in Linz”, KVA , 155–63; Specker H. E. , “Johannes Kepler and Ulm”, KVA , 165–76; Dobrzycki J. , “Kepler in Zagan”, KVA , 177–81; Färber S. , “Johannes Kepler and Regensburg”, KVA , 183–7. See also Gerlach W. and List Martha , Johannes Kepler, Dokumente zu Leben und Werke (Munich, 1971).

See Mikhailov A. A. , “Kepler's manuscripts”, KVA , 933–5, and Raskin N. M. , “The Kepler resources in the archives of the USSR Academy of Sciences”, KVA , 937–43. See also Caspar M. , Kepler, tr. Hellman C. Doris (London, 1959), 361–7.

See the colour plate, KVA, facing p. 1 and the photograph, KVA, 50.

Caspar , op. cit. (ref. 132), 367.