## Epitome astronomiae Copernicanae...

Linz; Linz; Frankfurt: Johann Planck; Johann Planck; Georg Tampach, 1618; 1620; 1621.

First edition, very rare first issue, and a superb copy, of the third of Kepler’s great trilogy of astronomical treatises, following *Astronomia nova* (1609) and *Harmonice mundi* (1619), in which he introduced his three laws of planetary motion. The *Epitome *“ranks next to Ptolemy’s *Almagest* and Copernicus’ *De revolutionibus* … [It] is the first systematic complete presentation of astronomy to introduce the ideas of modern celestial mechanics founded by Kepler … The title gives no inkling that Kepler had erected an entirely new structure on the foundation of the Copernican theory, that he had rescued the Copernican conception, at the time disputed and little believed, and helped it to break through by introducing his planet laws and by treating the phenomena of the motions physically” (Caspar, p. 297). “This work [the *Epitome*] would prove to be the most important theoretical resource for the Copernicans in the 17th century. Galileo and Descartes were probably influenced by it” (Britannica). Kepler “hypothesizes that force is needed to sustain motion and that hence some force must be acting on the planets. This force, he speculates, originates from the sun, can act over a vacuum, and may be magnetic. In contrast to many scientists of the time, Kepler believes much of space to be a vacuum” (Parkinson). “One important detail is Kepler’s extension of his first two planetary laws to all the other planets [they originally applied only to Mars] as well as to the moon and the four satellites of Jupiter” (*Johannes Kepler Quadricentennial Celebration*, University of Texas at Austin (1971), p. 77). The *Epitome* was in seven books. “The first three books covered spherical astronomy, the fourth through sixth planetary and lunar theory, and the seventh precession and related material … The spherical astronomy of the early books was unconventional chiefly in its heliocentric, or Copernican, interpretation of the diurnal rotation of the heavens, and in its account of the likely physical causes of this motion. The later books, however, described Kepler’s own theories: elliptical orbits, the area law, orbital planes passing through the center of the sun, and the various archetypal relations and physical forces underlying the structure and dynamics of the universe … This novel claim permeated the *Epitome* from beginning to end: astronomy was physics, and astronomical phenomena were best understood through mathematical study of their physical causes” (Stephenson, *Kepler’s Physical Astronomy* (1987), p. 139). “The theory of the moon is easily the most original part of the *Epitome *… a subject which had occupied Kepler since the 1590s but about which he had published little prior to the *Epitome*” (*ibid*., p. 140). Books I-III, IV and V-VII were originally issued separately and have their own title pages and imprints. Our copy has the first issue of Book IV, dated 1620, rather than the reissue of 1622 found in almost all copies of the *Epitome*. OCLC lists only four copies of the first issue of Book IV (none in US); only one has appeared at auction (the Richard Green copy, Christie’s, 17 June 2008, lot 208), and we know of only one other having appeared in commerce, which we handled several years ago, having acquired it from a private collector (who had himself acquired it from another collector some thirty years previously).

“The composition of the *Epitome* was closely intertwined with the personal vicissitudes of its author’s life. Although [Kepler] had been pressed for a more popular book on Copernican astronomy when his very technical *Astronomia nova* appeared, not until the spring of 1615 were the first three books ready for the printer. This part finally appeared in 1617 [but with imprint 1618], having been delayed a year because, even though he had previously signed a contract with an Augsburg publisher, Kepler wanted the work done by his new Linz printer. By that time his seventy-year-old mother had been charged with witchcraft, and the astronomer felt obliged to go to Württemberg to aid in her legal defence. Afterward, the writing of the *Harmonice mundi* interrupted progress on the *Epitome*, so that the second instalment, book IV, did not appear until 1620. The printing was barely completed when Kepler again journeyed to Württemberg, this time for the actual witchcraft trial. During pauses in the proceedings, he consulted with Maestlin at Tübingen about the lunar theory and arranged the printing of the last three books in Frankfurt. The publisher completed his work in the autumn of 1621, just as Kepler’s mother won acquittal after enduring the threat of torture.

“The first three books of this compendium deal mainly with spherical astronomy. Occasionally Kepler went beyond the conventional subject matter, considering, for example, the spatial distribution of stars and atmospheric refraction. Of special interest are the arguments for the motions of the earth; in describing the relativity of motion, he went considerably further than Copernicus and correctly formulated the principles later given more detailed treatment in Galileo’s *Dialogo* (1632). Because of these arguments, and as a result of the anti-Copernican furore stirred up by Galileo’s polemical writings, the *Epitome* was placed on the *Index Librorum Prohibitorum* in 1619 …

“Book IV opened with one of his favorite analogies, one that had already appeared in the *Mysterium cosmographicum* and that stressed the theological basis of his Copernicanism: The three regions of the universe were archetypal symbols of the Trinity – the center, a symbol of the Father; the outermost sphere, of the Son; and the intervening space, of the Holy Spirit. Immediately thereafter Kepler plunged into a consideration of final causes, seeking reasons for the apparent size of the sun, the length of the day, and the relative sizes and the densities of the planets. From first principles he attempted to deduce the distance of the sun by assuming that the earth’s volume is to the sun’s as the radius of the earth is to its distance from the sun. Nevertheless, his assumption was tempered by a perceptive examination of the observations. In their turn the nested polyhedrons, the harmonies, the magnetic forces, the elliptical orbits, and the law of areas also found their place within Kepler’s astonishing organization.

“The harmonic law, which Kepler had discovered in 1619 and announced virtually without comment in the *Harmonice mundi*, received an extensive theoretical justification in the *Epitome*, book IV, part 2, section 2. His explanation of the *P*∝*a*^{3/2} law [where *P *is the period of rotation of the planet in its orbit and *a* is its mean distance from the sun], was based on the relation

P ∝ (L x M)/(S x V),

where the longer the path length *L*, the longer the period; the greater the strength *S* of the magnetic emanation, the shorter the period (this magnetic ‘species,’ emitted from the sun, provided the push to the planet); the more matter *M* in the planet, the more inertia and the longer the period; the greater the volume *V* of the planet, the more magnetic emanation could be absorbed and the shorter the period. According to Kepler’s distance rule, the driving force *S* was inversely proportional to the distance *a*, and hence *L/S* was proportional to *a*^{2}; thus the density *M/V* had to be proportional to 1/*a*^{1/2} in order to achieve the 3/2 power law. Consequently, he assumed that the density (as well as both *M* and *V*) of each planet depended monotonically on its distance from the sun, a requirement quite appropriate to his ideas of harmony. To a limited extent he could defend his choice of *V* from telescopic observations of planetary diameters, but generally he was obliged to fall back on vague archetypal principles.

“The lunar theory, which closed book IV of the *Epitome*, had long been a preoccupation of its author. In Tycho’s original division of labor, Kepler had been assigned the orbit of Mars and [Christian] Longomontanus (1562-1647) that of the moon; but not long after Tycho’s death Kepler applied his own ideas of physical causes to the lunar motion. To Longomontanus’ angry remonstrance Kepler replied that it was not the same with astronomers as with smiths, where one made swords and another wagons. He believed that the moon would undergo magnetic propulsion from the sun as well as from the earth, but the complicated interrelations gave much difficulty. In 1616 Maestlin wrote to him:

‘Concerning the motion of the moon, you write that you have traced all the inequalities to physical causes; I do not quite understand this. I think rather that one should leave physical causes out of account, and should explain astronomical matters only according to astronomical method with the aid of astronomical, not physical, causes and hypotheses. That is, the calculation demands astronomical bases in the field of geometry and arithmetic …’

In other words, the circles, epicycles, and equants that Kepler had ultimately abandoned in his *Astronomia nova*.

“Kepler persisted in seeking the physical causes for the moon’s motion and by 1620 had achieved the basis for his lunar tables. The fundamental form of his lunar orbit was elliptical, but the positions were further modified by the evection and by Tycho’s so-called variation. Kepler’s lunar theory, as given in book IV of the *Epitome*, failed to offer much foundation for further advances; nevertheless, his very early insight into the physical relation of the sun to this problem had enabled him to discover the annual equation in the lunar motion, which he handled by modifying the equation of time.

“Books V-VII of the *Epitome* dealt with practical geometrical problems arising from the elliptical orbits, the law of areas, and his lunar theory; and together with book IV they served as the theoretical explanation to the *Tabulae Rudolphinae*. Book V introduced what is now called Kepler’s equation,

*E *= *M* – *e* sin *E*,

where *e* is the orbital eccentricity, *M* is the mean angular motion about the sun, and *E* is an auxiliary angle related to *M *through the law of areas; Kepler named *M* and *E* the mean and the eccentric anomalies, respectively. Given *E*, Kepler’s equation is readily solved for *M*; the more useful inverse problem has no closed solution in terms of elementary trigonometric functions, and he could only recommend an approximating procedure …

“Book VI of the *Epitome* treated problems of the apparent motions of the sun, the individual planets, and the moon. The short book VII discussed precession and the length of the year. To account for the changing obliquity, Kepler placed the pole of the ecliptic on a small circle, which in turn introduced a minor variation in the rate of precession (one last remnant of trepidation); because he was not satisfied with the ancient observations, he tabulated alternative rates in the *Tabulae Rudolphinae*. Such problems, he proposed, could be left to posterity “if it has pleased God to allot to the human race enough time on this earth for learning these left-over things”” (Owen Gingerich in DSB).

Johannes Kepler (1571-1630) came from a very modest family in the small German town of Weil der Stadt and was one of the beneficiaries of the ducal scholarship; it made possible his attendance at the Lutheran *Stift*, or seminary, at the University of Tübingen where he began his studies in 1589. At Tübingen, the professor of mathematics was Michael Maestlin (1550–1631), one of the most talented astronomers in Germany, and a Copernican (though a cautious one). Maestlin lent Kepler his own heavily annotated copy of *De revolutionibus, **and so w*hile still a student, Kepler made it his mission to demonstrate rigorously Copernicus’ theory.

In 1594 Kepler moved to Graz in Austria to take up a position as teacher at the Lutheran school there, and as provincial mathematician. Just over a year after arriving in Graz, Kepler discovered what he thought was the key to the universe: ‘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.’ This remarkable idea was published in *Mysterium cosmographicum* (1596), “the first unabashedly Copernican treatise since *De revolutionibus*” (DSB).

In place of the tradition that individual incorporeal souls push the planets and instead of Copernicus’s passive, resting Sun, Kepler hypothesised that a single force from the Sun accounts for the increasingly long periods of motion as the planetary distances increase. A few years later he acquired William Gilbert’s *De Magnete* (1600), and he generalized Gilbert’s theory that the Earth is a magnet to the view that the universe is a system of magnetic bodies in which the rotating Sun sweeps the planets around by a magnetic force. This force, varying inversely with distance, was the major physical principle that guided Kepler’s struggle to construct a better orbital theory for Mars.

The great Danish astronomer Tycho Brahe (1546–1601) had set himself the task of amassing a completely new set of planetary observations. In 1600 Tycho invited Kepler to join his court at Castle Benátky near Prague. When Tycho died suddenly in 1601, Kepler quickly succeeded him as imperial mathematician to Holy Roman Emperor Rudolf II. The relatively great intellectual freedom possible at Rudolf’s court was now augmented by Kepler’s unexpected inheritance of a critical resource: Tycho’s observations. Without data of such precision to support his solar hypothesis, Kepler would have been unable to discover his ‘first law’, that Mars moves in an elliptical orbit. He published this discovery, together with his second or ‘area law’, that the time necessary for Mars to traverse any arc of its orbit is proportional to the area of the sector contained by the arc and the two radii from the sun, in *Astronomia nova*.

In 1611 Emperor Rudolf abdicated, and Kepler was forced to move to Linz where he was appointed district mathematician. The Linz authorities had anticipated that Kepler would use most of his time to work on and complete the astronomical tables begun by Tycho, but the work was tedious, and Kepler continued his search for the world harmonies that had inspired him since his youth. In 1619 his *Harmonice mundi*, which contained his third law, brought together more than two decades of investigations into the archetypal principles of the world: geometrical, musical, metaphysical, astrological, astronomical, and those principles pertaining to the soul. Eventually Newton would simply take over Kepler’s laws while ignoring all reference to their original theological and philosophical framework.

Barchas 1147; Carli and Favaro 76 and 92; Caspar 55, 69, 66; Cinti 60, 72, 67; Houzeau & Lancaster 11831; Lalande p. 205; Parkinson 70; Zinner 4662, 4820, 4870. See PMM 112.

8vo, pp. [xxviii], 417 [recte 409], [3, blank]; [ii], 419-622, [2, errata and blank]; [xii], 641-932, [16, index], with numerous woodcut diagrams in text and one folding printed table (first few leaves browned, occasional light browning elsewhere). Contemporary German blind-stamped pigskin with two metal clasps, blue edges, ‘A S A G’ and the date 1627 stamped in gilt on upper cover, manuscript title in upper spine compartment (small hole and some wear to upper spine compartment). A very fine copy.

Item #5189

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Price:
$195,000.00
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