- The Latin edition: Kepler Johannes Gesammelte Werke von Dyck Walther Caspar Max Hammer F. List Martha Munich 1937–75 VI 287 368 19 vols (to date) this edition is cited hereafter as KGW. The German edition: translated by Max Caspar, Harmonice Mundi, Weltharmonik (Munich, 1939, reprinted 1971). The English edition: translated by Charles Glen Wallis, Great Books of the Western World, 54 vols (Chicago), 1952, XVI, 1005–85; this edition is cited hereafter as GBWW.
- Caspar , Max . 1959 . Kepler New York translated by C. Doris Hellman Also in paperback (New York, 1962) with slightly different pagination. First German edition in 1948.
- Kepler , Johannes . 1925 . Kosmische Harmonie 317 – 317 . Leipzig translated Harburger In this early German translation of the Harmonice Mundi there appears a fold-out folio sheet in which the interactions and interrelations of all four areas are cleverly displayed in a cryptic fashion.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. XI , 223 – 223 . Munich 19 vols (to date) Cited in Caspar (footnote 2), 271.
- Cassirer , Ernst . 1911 . Das Erkenntnisproblem in der Philosophie und Wissenschaft der Neueren Zeit Vol. I , 328 – 377 . Berlin 3 vols Caspar (footnote 2), 264–89. W. Pauli (translated by Priscilla Silz), The Influence of Archetypal Ideas on the Scientific Theories of Kepler is included in The Interpretation of Nature and the Psyche (New York, 1955), pp. 119–240.
- These three works were presented at the Kepler Symposium in Weil-der-Stadt in 1971 and have been reprinted together: Mittlestrass Jürgen Methodological Elements of Keplerian Astronomy Studies in the History and Philosophy of Science 1972 8 203 232 (translated by James Fearns) Robert S. Westman, ‘Kepler's Theory of Hypothesis and the Realist Dilemma’, Studies in the History and Philosophy of Science, 8 (1972), 233–64. Gerd Buchdahl, ‘Methodological Aspects of Kepler's Theory of Refraction’, Studies in the History, and Philosophy of Science, 8 (1972), 265–99.
- Aiton , Eric . 1975 . Johannes Kepler and Astronomy Without Hypothesis . Japanese Studies in the History of Science , 14 : 49 – 71 .
- Caspar . 1959 . Kepler 272 – 272 . New York translated by C. Doris Hellman This statement appears as a paraphrase of Kepler, but is in fact a translation from KGW (footnote 1), XI, 224. For alternative translations, see Pauli (footnote 5), 16–161, and E. W. Gerdes, ‘Johannes Kepler as Theologian’, Vistas in Astronomy, 18 (1975), 339–67 (pp. 355–6).
- Caspar . 1959 . Kepler 272 – 272 . New York translated by C. Doris Hellman 278
- See Guerlac Henry Copernicus and Aristotle's Cosmos Journal of the History of Ideas 1968 29 218 224 for an argument that would even include Copernicus.
- Hanson , Norwood Russell . 1961 . The Copernican Disturbance and the Keplerian Revolution . Journal of the History of Ideas , 22 : 169 – 184 . (pp. 182–3).
- Holton , Gerald . 1955 . Johannes Kepler's Universe: Its Physics and Metaphysics . American Journal of Physics , 22 : 340 – 351 . (p. 347).
- Caspar . 1959 . Kepler 273 – 273 . New York translated by C. Doris Hellman
- Caspar . 1959 . Kepler 271 – 271 . New York translated by C. Doris Hellman
- Heath , Thomas L. 1956 . The Thirteen Books of Euclid's Elements Vol. 3 , New York
- Heath . 1956 . The Thirteen Books of Euclid's Elements Vol. II , 96 – 96 . New York 3 vols.
- Heath . 1956 . The Thirteen Books of Euclid's Elements Vol. II , 99 – 99 . New York 3 vols
- Until the nineteenth century, these were the only regular polygons that could be constructed in this fundamental fashion. In 1801, however, Gauss proved that if 2 N + 1 be a prime number (where N belongs to the set of integers), then regular polygons of sides 2 N + 1 can be inscribed in a circle employing only a compass and a rule. Thus is added to those here listed and implied, the figures of 17 sides (N=4), of 257 sides (N=5), etc. Max Caspar reflects on what challenges such new discoveries would have generated for Kepler and concludes that he would have received them with interest, but would have had little trouble in accommodating them. Caspar Kepler New York 1959 276 276 translated by C. Doris Hellman
- Heath , Thomas L. 1921 . A History of Greek Mathematics Vol. I , 402 – 402 . Oxford 2 vols
- This often told tale and its sources are discussed at length in Heath The Thirteen Books of Euclid's Elements New York 1956 III 1 5 3 vols
- Heath . 1956 . The Thirteen Books of Euclid's Elements Vol. III , 11 – 12 . New York 3 vols
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. VI , 323 – 323 . Munich 19 vols (to date) Cited in D. P. Walker, Studies in Musical Science in the Late Renaissance (London, 1978), p. 39.
- See Walker D.P. Kepler's Celestial Music Journal of the Warburg and Courtauld Institutes 1967 30 228 250 Also to be found in a slightly revised form in Walker (footnote 28), 34–62. For a more extensive analysis, see Michael Dickreiter, Der Musiktheoretiker Johannes Kepler (Bern and Munich, 1973).
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. VI , 99 – 99 . Munich 19 vols (to date) Cited in Walker (footnote 28), 42.
- Kepler introduces these geometric-musical relationships in 1596 in chapter 12 of the Mysterium Cosmographicum, and presents a full and detailed development in 1619 in a letter to Herwart von Hohenburg in 1599. For example: “The square of the sides of a triangle is to the square of the diameter as 3 to 4, i.e., ρητov (stated), and it subtends 1/3 or 2/3 of the circle; therefore this perfect λ'oγoσ (logos) gives rise to perfect harmony by fifths' KGW Gesammelte Werke von Dyck Walther Caspar Max Hammer F. List Martha Munich 1937–75 XIV 30 30 19 vols (to date)
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. VI , 175 – 176 . Munich 19 vols (to date) Cited in Walker (footnote 28), 53.
- Walker . 1978 . Studies in Musical Science in the Late Renaissance 57 – 57 . London
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. VI , 118 – 118 . Munich 19 vols (to date) The denominator of the fractions in each successive column is formed by adding the numerator and denominator of the preceding fraction. The numerator of the upper fraction is that of the preceding fraction, and the numerator of the lower fraction is the difference between numerator and denominator.
- Caspar . 1959 . Kepler 278 – 278 . New York translated by C. Doris Hellman
- Cassirer , Ernst . 1963 . The Individual and the Cosmos in Renaissance Philosophy Oxford (translated by Mario Domandi) First German edition in 1926. Caspar (footnote 2), 278–81. Pauli (footnote 5), 169–90.
- Beer , Arthur . 1975 . Kepler's Astrology and Mysticism . Vistas in Astronomy , 18 : 399 – 426 . Joachim Otto Fleckenstein, ‘Kepler and Neoplantonism’, Vistas in Astronomy, 18 (1975), 427–38. Gérard Simon, ‘Kepler's Astrology: The Direction of a Reform’, Vistas in Astronomy, 18 (1975), 439–48. The latter topic is developed in much more detail in Gérard Simon, Kepler: Astronome, Astrologue (Paris, 1979). Also F. Hammer, ‘Die Astrologie des Johannes Keplers’, Sudhoffs Archiv, 55 (1971), 113–35. See Eric Aiton, ‘Johannes Kepler in the Light of Recent Research’, History of Science, 14 (1976), 77–100, for other references.
- See Bowden Mary Ellen The Scientific Revolution in Astrology: The English Reformers, 1558–1686 Ann Arbor 1974 129 146 An unpublished doctoral dissertation in which the positive response of Sir Christopher Heyden and the negative response of Robert Fludd are discussed. The controversy with Fludd is also discussed in some detail in Pauli (footnote 5), 190–201.
- Pauli . 1955 . The Influence of Archetypal Ideas on the Scientific Theories of Kepler is included in The Interpretation of Nature and the Psyche 189 – 189 . New York
- A notable exception to this disclaimer occurs in De Stella Nova Das Wallenstein-Horoskop von Johannes Kepler Werk und Leistung Kepler J. Linz 1971 127 136 in which Kepler predicts on the basis of this dramatic new star a Christian victory over the Turks, some general conversion of Jews to Christianity, and political activity in general.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. VI , 246 – 246 . Munich 19 vols (to date) See also Pauli (footnote 5), 185.
- Caspar . 1959 . Kepler 279 – 279 . new York translated by C. Doris Hellman
- See List Martha Das Wallenstein-Horoskop von Johannes Kepler Werk und Leistung Kepler J. Linz 1971 127 136
- See North J.D. The Fortunes of Churches Centaurus 1980 24 181 211 (pp. 185–6). Also see Caspar (footnote 2), 153–6. The twelve signs of the Zodiac are divided into four groups of three signs each, that are called a ‘trigon’ or ‘triplicity’. Each of the trigons are associated with one of the four elements: air, earth, fire, or water. Successive conjunctions of Jupiter and Saturn take place about every 20 years and reoccur in the same trigon for about 240 years. Thus it takes four such periods or 960 years before the conjunction returns to the original point in a given trigon. In October of 1604, a new star appeared near such a conjunction as it was about to enter the trigon of fire. This latter event had taken place only ‘seven times since the creation of the world in a similar trigon of fire’, and to have it coincide with the birth of a new star made it an astrological event on a par with the star of Bethlehem.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 145 – 258 . Munich 19 vols (to date) In this work, Kepler opposes both authors as he puts forth his own essentially divergent point of view. Immediately following the title, there appears the following commentary: ‘A warning to sundry Theologos, Medicos, and Philosophos, in particular to D. Phillippus Feselius, that they should not, in their just repudiation of stargazing superstition, throw out the child with the bath and thus unknowingly act in contradiction to their profession’. See Pauli (footnote 5), 179–83, for a discussion of and selected translations from portions of this work.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 5 – 35 . Munich 19 vols (to date) For a recent English translation and commentary, see J. Bruce Brackenridge and Mary Ann Rossi, ‘Johannes Kepler's On the More Certain Fundamentals of Astrology, Prague 1601’, Proceedings of the American Philosophical Society, 123 (1979), 85–116. This article contains a foreword, notes, and analytical outline by the first-named author and a translation by the second. Copies of the translation and the notes can be obtained from the author of this article.
- Brackenridge and Rossi . 1979 . Johannes Kepler's On the More Certain Fundamentals of Astrology, Prague 1601 . Proceedings of the American Philosophical Society , 123 : 89 – 90 . This outline does not appear in Kepler's work, which simply contains the 73 theses in an undifferentiated sequence. The dangers and the advantages of imposing such an outline on a translation are obvious.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 12 – 12 . Munich 19 vols (to date) and Rossi (footnote 46), 91.
- Details of these calculations appear in Brackenridge Rossi Johannes Kepler's On the More Certain Fundamentals of Astrology, Prague 1601 Proceedings of the American Philosophical Society 1979 123 107 108
- Ptolemy . 1940 . Tetrabiblios 35 – 35 . London (translated by F. E. Robbins)
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 14 – 14 . Munich 19 vols (to date) and Rossi (footnote 46), p. 92.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 17 – 17 . Munich 19 vols (to date) and Rossi (footnote 46), p. 94.
- Ptolemy . 1940 . Tetrabiblios 35 – 39 . London (translated by F. E. Robbins) There is also in antiquity an astrometeorological concern for the colour of the planet; i.e., Mars heats because it is red. Kepler is to expand on this type of optical explanation.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 18 – 18 . Munich 19 vols (to date) and Rossi (footnote 46), 94–5.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 18 – 18 . Munich 19 vols (to date) and Rossi (footnote 46), 95.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 18 – 18 . Munich 19 vols (to date) and Rossi (footnote 46), 95.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 19 – 20 . Munich 19 vols (to date) and Rossi (footnote 46), 95.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 20 – 20 . Munich 19 vols (to date) and Rossi (footnote 46), 95–6.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 21 – 22 . Munich 19 vols (to date) and Rossi (footnote 46), 96–7.
- For example Pauli The Influence of Archetypal Ideas on the Scientific Theories of Kepler is included in The Interpretation of Nature and the Psyche New York 1955 180 182 commenting on the astrological influence of stars, states that ‘only their light rays can be regarded as effective’ and ‘it is the planets … which (through the intermediary of light) are effective vehicles of astrological influence’. See also Fleckenstein (footnote 38), 429–30, in which he refers to ‘angles formed by the light rays’. The latter is correct, although the role of light could be misconstrued. In Pauli, however, it appears that the distinction between the physical and archetypal cause is missing.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 22 – 22 . Munich 19 vols (to date) and Rossi (footnote 46), 97.
- This reference to ‘five-sidedness’ relates to the pentagon and its internal golden section with its ability to replicate itself. Thesis 43 continues to discuss what is and is not transferred between ‘trees and apples’ and concludes with a reference to ‘the inborn beauty of five-sidedness’. One can observe the natural pentagram in an apple by cutting it in half normal to its axis; i.e. as one would cut a grapefruit. Literally the ‘quintessence’ of the apple can be observed as the seeds of its replication nestle in the natural pentagram of the seed pod of the apple. See figure 2 and Heath The Thirteen Books of Euclid's Elements New York 1956 III 440 440 3 vols. and 27
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 23 – 23 . Munich 19 vols (to date) and Rossi (footnote 46), 98.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 27 – 27 . Munich 19 vols (to date) and Rossi (footnote 46), 100.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 31 – 31 . Munich 19 vols (to date) and Rossi (footnote 46), 102.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 22 – 22 . Munich 19 vols (to date) and Rossi (footnote 46), 97.
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 42 – 42 . Munich 19 vols (to date)
- KGW . 1937–75 . Gesammelte Werke Edited by: von Dyck , Walther , Caspar , Max , Hammer , F. and List , Martha . Vol. IV , 27 – 27 . Munich 19 vols (to date) and Rossi (footnote 46), 100.
- Bowden . 1974 . The Scientific Revolution in Astrology: The English Reformers, 1558–1686 122 – 122 . Ann Arbor
- Caspar . 1959 . Kepler 281 – 281 . New York translated by C. Doris Hellman
- Koyré , Alexander . 1973 . The Astronomical Revolution Edited by: Maddison , R.E.W. London, Paris, Ithica p. 387, n. 55. First French edition in 1961.
- Caspar . 1959 . Kepler 281 – 281 . New York translated by C. Doris Hellman ‘Two Keplers, so to speak, face each other’, and Koyre (footnote 74), 120. ‘Johann Kepler is a veritable Janus’. It is only when taken from context, however, that such statements support such a view.
- See Sticker Bernhard Johannes Kepler Homo Iste Vistas in Astronomy 1975 18 55 55 Also Gérard Simon (footnote 38), 449. ‘If…Kepler is a veritable two-faced Janus, he is this first of all in that the modern face and the archaic face of his genius are vigorously inseparable’.
Annals of Science
Volume 39, 1982 - Issue 2