Prodromus Dissertationum Cosmographicarum, continens Mysterium Cosmographicum De Admirabili Proportione Orbium coelestium, deque causis coelorum numeri, magnitudinis, motuumque periodicorum genuinis & propriis, Demonstratum per quinque regularia corpora Geometrica … Addita est erudita Narratio M. Georgii Joachimi Rhetici, de Libris Revolutionum, atque admirandis de numero, ordine, & distantiis Sphaerarum Mundi hypothesibus, excellentissimi Mathematici, totiusque Astronomiae Restauratoris D. Nicolai Copernici. [Bound, as issued, with:] Pro suo Opere Harmonices Mundi Apologia adversus Demonstrationem Analyticam Cl.V.D. Roberti de Fluctibus …

Frankfurt: Erasmus Kempfer for Godefrid Tampach, 1621-1622.

Second, enlarged, edition of the Mysterium cosmographicum (first, 1596), Kepler’s first scientific book, “the first unabashedly Copernican treatise since De revolutionibus itself” (Gingerich in DSB), which laid “the foundation of his vast later astronomical work [and] immediately made him famous in scientific circles, and got him into contact with Galileo and Tycho Brahe” (Caspar). “Kepler maintained the basic ideas of the work of his youth throughout his life. In the dedication to the present edition he proudly points out his early achievement: ‘As if an oracle from the heavens had been dictated to me,’ he writes in fond memory. He realises that ‘almost all astronomical books which I have published since that time relate to one of the main chapters in this little book, representing an expansion, or an improvement upon it.’ Thus the present edition is especially suited to introduce Kepler’s thought: it offers the promising beginnings and the perfection – the beginnings as in the original text written by the young Magister, the perfection in the extensive annotations” (ibid.). In the Prodromus Kepler proposes his famous model of the planetary system according to which the celestial spheres carrying the orbits of the six known planets should circumscribe and inscribe a nested set of the five Platonic regular solids (cube, tetrahedron, octahedron, icosahedron and dodecahedron), which is spectacularly illustrated on the engraved plate. This system not only explained why there were exactly six known planets, it also predicted the relative diameters of their orbits; and of course it only made sense of the spheres carrying the orbits had a common center, in other words for a heliocentric universe. Although the model is erroneous, Kepler’s values for the relative diameters of the orbits are, in fact, within 5% of the true values. This edition presents the text of the first edition, which also included an Appendix containing a reprint of Rheticus’ Narratio prima (1540), the first publication of Copernicus’ heliocentric theory – the version here includes Kepler’s additional notes reflecting the development of his thinking in the intervening 25 years and references to his own works published during that period – and Kepler’s teacher Michael Maestlin’s account of Copernican planetary theory, De dimensionibus orbium et sphaerarum coelestium iuxta Tabulas Prutenicas, ex sententis Nicolai Copernici. The volume concludes with the first publication of Kepler’s Pro suo Opere Harmonices Mundi Apologia (with separate title page), a reply to Robert Fludd, the Oxford Rosicrucian, who had attacked Kepler’s theories on musical harmony.

Kepler’s first cosmological work was published shortly after his arrival in Graz. “Kepler’s fertile imagination hit upon what he believed to be the secret key to the universe. His own account, here greatly abridged, appears in the introduction to the resulting work, the Mysterium cosmographicum of 1596.

‘When I was studying under the distinguished Michael Maestlin at Tübingen six years ago, seeing the many inconveniences of the commonly accepted theory of the universe, I became so delighted with Copernicus, whom Maestlin often mentioned in his lectures, that I often defended his opinions in the students’ debates about physics. I even wrote a painstaking disputation about the first motion, maintaining that it happens because of the rotation of the earth. I have by degrees—partly out of hearing Maestlin, partly by myself—collected all the advantages that Copernicus has over Ptolemy. At last in the year 1595 in Graz when I had an intermission in my lectures, I pondered on this subject with the whole energy of my mind. And there were three things above all for which I sought the causes as to why it was this way and not another—the number, the dimensions, and the motions of the orbs.’

“After describing several false attempts, Kepler continues:

‘Almost the whole summer was lost with this agonizing labor. At last on a quite trifling occasion I came near the truth. I believe Divine Providence intervened so that by chance I found what I could never obtain by my own efforts. I believe this all the more because I have constantly prayed to God that I might succeed if what Copernicus had said was true. Thus it happened 19 July 1595, as I was showing in my class how the great conjunctions [of Saturn and Jupiter] occur successively eight zodiacal signs later, and how they gradually pass from one trine to another, that I inscribed within a circle many triangles, or quasi-triangles such that the end of one was the beginning of the next. In this manner a smaller circle was outlined by the points where the line of the triangles crossed each other.’

“The proportion between the circles struck Kepler’s eye as almost identical with that between Saturn and Jupiter, and he immediately initiated a vain search for similar geometrical relations.

‘And then again it struck me: why have plane figures among three-dimensional orbits? Behold, reader, the invention and whole substance of this little book! In memory of the event, I am writing down for you the sentence in the words from that moment of conception: The earth’s orbit is the measure of all things; circumscribe around it a dodecahedron, and the circle containing this will be Mars; circumscribe around Mars a tetrahedron, and the circle containing this will be Jupiter; circumscribe around Jupiter a cube, and the circle containing this will be Saturn. Now inscribe within the earth an icosahedron, and the circle contained in it will be Venus; inscribe within Venus an octahedron, and the circle contained in it will be Mercury. You now have the reason for the number of planets.”

“Kepler of course based his argument on the fact that there are five and only five regular polyhedrons.

‘This was the occasion and success of my labors. And how intense was my pleasure from this discovery can never be expressed in words. I no longer regretted the time wasted. Day and night I was consumed by the computing, to see whether this idea would agree with the Copernican orbits, or if my joy would be carried away by the wind. Within a few days everything worked, and I watched as one body after another fit precisely into its place among the planets.’

“Astonishingly, Kepler’s scheme works with fair accuracy when space is allowed for the eccentricities of the planetary paths. Kepler was obliged to compromise the elegance of his system by adopting the second value for Mercury, which is the radius of a sphere inscribed in the square formed by the edges of the octahedron, rather than in the octahedron itself. With this concession, everything fits within 5 per cent—except Jupiter, at which ‘no one will wonder, considering such a great distance’ …

“Quixotic or chimerical as Kepler’s polyhedrons may appear today, we must remember the revolutionary context in which they were proposed. The Mysterium cosmographicum was essentially the first unabashedly Copernican treatise since De revolutionibus itself; without a sun-centered universe, the entire rationale of his book would have collapsed. Moreover, even the inquiry about the basic causes for the number and motions was itself a novel break with the medieval tradition, which considered the ‘naturalness’ of the universe sufficient reason …

“Furthermore, Kepler demanded to know how God the architect had set the universe in motion. He recognized that although in Copernicus’ system the sun was near the center, it played no physical role. Kepler argued that the sun’s centrality was essential, for the sun itself must provide the driving force to keep the planets in motion. This physical reasoning, which characterizes Kepler’s astronomy, makes its appearance in the latter part of the Mysterium cosmographicum. After announcing his celebrated nest of spheres and regular solids, which to him explained the spacing of the planets, he turned to the search for the basic cause of the regularities in the periods …

“Although the principal idea of the Mysterium cosmographicum was erroneous, Kepler established himself as the first, and until Descartes the only, scientist to demand physical explanations for celestial phenomena. Seldom in history has so wrong a book been so seminal in directing the future course of science” (Gingerich in DSB).

“At the instigation of a third party, Kepler appended a comparison of the “colossal difference” between his theory and that of Robert Fludd, the Oxford physician and Rosicrucian. The ensuing controversy at least illuminates the intellectual climate of the early 1600’s, when the new, quantitative mathematical approach to nature collided with the qualitative, symbolical, alchemical tradition. Fludd counterattacked in an arrogant, polemical pamphlet, to which Kepler replied in his Pro suo opere Harmonice mundi apologia (1622). The Apologia was appended to a reissue of his Mysterium cosmographicum [i.e., the Prodromus]. Although republished in a larger format, the 1596 text of Mysterium was unchanged. Numerous new footnotes called attention to the subsequent work, especially in the Harmonice mundi” (ibid.).

Folio (301 x 198 mm), pp. [iv], 163, with 5 leaves of plates: an engraving signed ‘Christophorus Leibfried. ff. Tübing: 1597’, and 4 large woodcut plates with letterpress headings and captions [Prodromus]; [2], 3-50 [Apologia]. Woodcut initials and woodcut diagrams in text, separate title pages to the Rheticus dated 1621 (but the register and pagination continuous) and to the ‘Apologia’, dated 1622 with large woodcut printer’s device. Contemporary limp vellum.

Item #5861

Price: $65,000.00

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