Tabulae Rudolphinae, quibus astronomicae scientiae, temporum longinquitate collapsae Resauratio continetur a Phœnice illo Astronomorum Tychone, ex illustri & generosa Braheorum in regno Daniae familia oriundo equite, primum animo concepta et destinata a anno Christi MDLXIV: exinde observationibus siderum accuratissimis, post annum praecipue MDLXXII, quo sidus in Cassiopeiae constellatione novum effulsit, serio affectata; variisque operibus, cum mechanicis, tum librariis, impenso patrimonio amplissimo, accedentibus etiam subsidiis Friderici II. Daniae Regis, regali magnificentia dignis, tracta per annos XXV, potissimum in insula freti Sundici Huenna, & arce Uraniburgo, in hos usus a fundamentis extructa: tandem traducta in Germaniam, in que aulam et nomen Rudolphi Imp. anno M D IIC. Tabulas ipsas, jam et nuncupatas, et affectas, sed morte authoris sui anno MDCI desertas, jussu et stipendiis fretus trium Imppp. Rudolphi, Matthiæ, Ferdinandi, annitentibus haeredibus Braheanis; ex fundamentis observationum relictarum; ad exemplum fere partium iam exstructarum; continuis multorum annorum speculationibus, & computationibus, primum Pragæ Bohemorum continuavit; deinde Lincii, superioris Austriæ metropoli, subsidiis etiam ill. provincialum adjutus, perfecit, absolvit, adq[ue] causarum & calculi perennis formulam traduxit Ioannes Keplerus, Tychoni primum a Rudolpho II. Imp. adjunctus calculi minister; indeq[ue] trium ordine Imppp. mathematicus: qui idem de speciali mandato Ferdinandi II. Imp. petentibus instantibusq[ue] haeredibus, opus hoc ad usus praesentium & posteritatis, … Cum privilegiis, Imp. & Regum rerumq[ue] publ. vivo Tychoni ejusq[ue] haeredibus, & speciali Imperatorio, ipsi Keplero concesso, ad annos XXX.

Ulm: Jonas Saur, 1627.

First edition, a copy with contemporary annotations, of this great scientific classic, “the chief vehicle for the recognition of his astronomical accomplishments” (DSB). “The tables are extraordinarily important, for they document in a unique way Kepler’s great contributions to astronomy” (Gingerich). This was Kepler’s last lifetime publication and his crowning achievement, “the foundation of all planetary calculations for over a century” (Sparrow). Kepler himself called the tables “my chief astronomical work” (Gingerich). “In 1601 Kepler was charged by the dying Tycho Brahe to complete his proposed Rudolphine tables of planetary motion, to be based upon Tycho’s great storehouse of observations. When the tables finally appeared twenty-six years later, Kepler excused the long delay in his preface, in which he cited not only salary and wartime difficulties, but also ‘the novelty of my discoveries and the unexpected transfer of the whole of astronomy from fictitious circles to natural causes, which were most profound to investigate, difficult to explain, and difficult to calculate, since mine was the first attempt’ (Gesammelte Werke 10, pp. 42-43; quoted in DSB). Kepler’s work was shaped not only by his Copernican bias and his discovery of the laws of planetary motion, but by the ‘happy calamity’, in 1618, of his initiation into logarithms, which enabled him to make the complex calculations necessary for determining planetary orbits. Kepler was thus able to take into account the relative heliocentric positions of the earth and planets, calculating these positions separately and combining them to produce the geocentric position; this yielded far more accurate positions than in previous tables, which had erred by as much as five degrees. This improvement constituted a strong endorsement of the Copernican system, and insured the tables’ dominance in the field of astronomy throughout the seventeenth century” (Norman). “The tables’ accuracy was strikingly demonstrated four years later. On 7 November 1631, when Kepler himself had been dead a year, the French astronomer Pierre Gassendi became the first observer in history to see Mercury crossing the face of the Sun, in fulfilment of a prediction by Kepler. Kepler’s tables were in error by only one-third of the solar diameter, whereas even the Copernican tables they had replaced were in error by thirty times that amount” (Hoskins, The Cambridge Concise History of Astronomy, pp. 110-111).

Provenance: Contemporary marginal annotations.

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 while 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 provincial mathematician and as a teacher at the Lutheran school there. 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).

“Kepler sent copies of his remarkable book to various scholars, including the most famous astronomer of the day, Tycho Brahe (1546-1601). Although unwilling to accept all these strange arguments, the Danish astronomer immediately recognized the author’s genius, and invited Kepler to visit him. However, the long journey was out of the question for the impecunious young man. Thus, wrote Kepler, ‘I ascribe it to Divine Providence that Tycho came to Bohemia.’ Tycho, fearing the loss of royal support by the King of Denmark, had in the meantime resolved to join the court of Rudolph II in Prague. Emperor Rudolph was a moody, eccentric man whose twin loves were the occult and his collection of curiosities. He was more than willing to support a distinguished astronomer whose accurate planetary positions could make horoscopes more accurate. Tycho arrived at Prague in 1599, and Kepler, forced out of Graz by religious controversy, joined him there the following January. To Kepler was assigned the analysis of the observations of Mars. The encounter between the young German theoretician and the famous Danish observer turned the course of astronomy … within two years Tycho had died and his full set of observations, although claimed by his heirs, fell into Kepler’s hands” (Gingerich). The first fruit of this legacy was Kepler’s discovery of his first two laws of planetary motion, published in 1609 in Astronomia Nova: that Mars moves in an elliptical orbit, and 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.

“At Tycho’s death, Kepler received not only his observations but also his title of Imperial Mathematician. The chief duty of this post was to complete the great set of planetary tables originally envisioned by Tycho, to be based on his incomparable set of precisely determined positions and intended to provide much improved predictions. Kepler’s analysis of Mars could be considered the first step in this great undertaking. The discovery of the first two planetary laws had created an entirely new foundation for calculating the Rudolphine Tables. But since Kepler had derived these laws solely from the observations of Mars, he now had to demonstrate their validity for the other planets. Mercury created special difficulties, and the complex motion of the moon caused a great deal of trouble … The astronomer’s efforts to work on the tables were continually diluted by the time lost in trying to collect his salary, and by a variety of astronomical events. The most important of these was Galileo’s application of the telescope to the heavens, causing Kepler to take time out to write his Dissertatio cum Nuncio Sidereo – ‘Conversation with the Sidereal Messenger’ – of Galileo …

“In 1611 the political situation in Prague took an abrupt turn, ending Kepler’s exhilarating atmosphere of intellectual freedom. The gathering storm of the Counter-Reformation reached the capital, and brought about the abdication of Rudolph II. As warfare and bloodshed surged around him, Kepler sought refuge in Linz, where he was appointed provincial mathematician … The Linz authorities charged him first of all to ‘complete the astronomical tables in honor of the Emperor and the worshipful Austrian House, for the profit of … the entire land as well as also for his own fame and praise.’ After Rudolph’s death in 1612, his successor Matthias confirmed Kepler as court mathematician and agreed to his new residence away from Prague. But Kepler realized that as long as the Rudolphine Tables were unfinished, he would be tied to Linz. Thus the work on the tables became part of his fate …

“Meanwhile, another innovation completely altered Kepler’s original plan for the form of the tables – ‘a happy calamity,’ as he called it. In 1618 Kepler first saw John Napier’s epoch-making work on logarithms [through the intermediary of the Cursus mathematici practice (Cologne, 1618) by Benjamin Ursinus, which reproduced Napier’s tables] and was deeply impressed by it, recognizing how this new invention would simplify the time-consuming computations of astronomy. However, not content to adopt the new aid as he found it, during the winter of 1621-22 Kepler composed his own book on the subject. He exploited the new logarithms to solve two problems introduced for the first time by the novel form of the Rudolphine Tables. The first arises in the solution of what is now called Kepler’s equation. For a planet moving in an ellipse, under Kepler’s law of areas, there is no elementary way to find explicitly the position angle corresponding to a given time. However, the converse is easily calculated. Therefore he solved his equation for a set of uniformly spaced angles, which determine a set of non-uniformly spaced times. Kepler tabulated the logarithms of these intervals as a convenient means for interpolating to the desired times. The second important use of logarithms arises from the thoroughly heliocentric nature of the book. In previous planetary tables, the motions of the sun and planets were combined into a single procedure. In the Rudolphine Tables we must find separately the heliocentric positions of the earth and planet in question. To find the geocentric position of the planet, these two positions must be combined – essentially a problem of vector addition. Kepler facilitated this maneuver by tabulating the logarithms of the radius vectors of earth and planet, and by providing a convenient double-entry table for combining them.

“Kepler’s tables, unlike the modern Nautical Almanac, do not show the daily positions of the sun, moon, and planets. Instead, they contain general tables from which it is possible to work out a planet’s position for any time in the past or future. Besides the planetary data, Kepler included tables of logarithms, a catalogue of 1000 stars, and a list of the geographical longitudes and latitudes of a large number of cities. Approximately half the volume is made up of instructions for the use of the tables and numerical examples of their use.

“At long last, in 1624, Kepler completed his Rudolphine Tables in their new logarithmic form. The printing of the tables was very difficult because of wartime conditions. Linz offered no really suitable press, and circumstances in the city became increasingly unpleasant. Kepler’s lodgings were located on the city wall, and eventually he was obliged to open his house for the soldiers guarding the ramparts. To a correspondent he described the noise and smells of battle, but pointed out that he found solace in continuing his calculations. Finally, however, the printing was transferred to Ulm. Financing the book’s publication caused the astronomer much worry and trouble. A long trip to the imperial court in Vienna won some concessions for him, including an agreement to tax the city of Nürnberg for the arrears in his yearly allowance. Yet a visit to Nürnberg in 1625 was in vain, and he eventually decided to finance the work from his own pocket. Even this was not a simple operation, for Tycho’s heirs claimed both a share in the profits and also censorship rights …

“Because the Rudolphine Tables was in many ways the long-awaited climax to Kepler’s entire scholarly output, he proposed that this book, alone among his works, should have an appropriate frontispiece. His Tübingen friend Wilhelm Schickard (1592-1635) prepared a wash sketch of the proposed engraving. It showed the temple of Urania, modeled after the foyer of Tycho’s observatory, Stjerneborg, on the Danish island of Hven. On the ceiling of the temple was shown the geocentric Tychonic system, and within the building stood a series of notable astronomers, including Tycho himself. Kepler submitted the sketch to Tycho’s heirs, who at once objected. Their illustrious ancestor should be depicted more formally, they said, with his long ermine robe and the elephant medal around his neck, which he always wore while observing. (The medal was the highest award of the Danish monarchy.)

“The frontispiece in its final form was a great elaboration over the trial sketch. Ten of the temple’s 12 zodiacal columns are visible; their rich variety depicts the increasing elegance of astronomy. Those at the back, merely rough-hewn logs, represent the most ancient traces of the science. Nearby stands a Chaldean observer who, for want of an instrument, uses his fingers to measure the angular separations of the stars. The Greek astronomers Hipparchus and Ptolemy appear beside brick columns adorned with instruments of the times. Copernicus, seated beside an Ionian column, engages in spirited conversation with Tycho, who stands in his magnificence by an elaborate and splendid Corinthian pillar. The Danish astronomer points to the Tychonic system inscribed on the ceiling, and his Latin comment to Copernicus may be loosely translated, ‘How about that?’ Surrounding the dome of the temple appear six goddesses, each recalling an important idea of Kepler. To the far right stands Magnetica, with her lodestone and compass, reminding us of the magnetic forces that Kepler believed to control the planets. Next is Stathmica, goddess of the law of the lever and balance; the sun at the fulcrum reminds us that this is a form of Kepler’s law of areas. The third divinity is Geometria, with her mathematical compass, square, and tablet bearing the Keplerian ellipse. The next figure is Logarithmica, who holds in her hands rods in the ratio of one to two, while emblazoned on her halo is the natural logarithm of ½. The fifth goddess holds a telescope, and the sixth a globe with its shadow, reminding us of Kepler’s two books on optics: Dioptrice (1611) and Astronomiae Pars Optica (1604). Above the temple hovers the imperial eagle, generously dropping golden coins from his beak for the support of astronomy. A few of the coins even manage to fall to the foundations of the temple where, in the left panel, we see Kepler himself, calculating by candlelight. And here is a marvelous personal touch, for prominently on the worktable sits a replica of the dome of the temple of Urania. In his subtle and uncensored fashion, Kepler reminds us that although Tycho may have built the most splendid column, the temple of Urania would never have been finished without Kepler himself laboring far into the night!

“Kepler personally oversaw the printing and•worked almost daily with the typesetters. One thousand copies were printed, an enormous edition for a 17th-century science book … Kepler’s tables enabled him to predict the transit of Mercury over the disk of the sun on November 7, 1631, a phenomenon never previously observed. He did not live to see the prediction fulfilled, for he died on November 15, 1630, at Regensburg, where he had gone on yet another effort to collect his back salary. However, this transit of Mercury was actually witnessed by the astronomer Pierre Gassendi at Paris … In 1665, J. B. Riccioli related that the tables of Ptolemy, Copernicus, and Longomontanus each erred by about five degrees in predicting this transit, whereas Kepler missed by less than 10 minutes of arc! The overwhelming evidence of this crucial experiment convincingly established the power of the Rudolphine Tables. In this almost forgotten way, the geocentric world view was broken and the heliocentric system, together with Kepler’s laws of planetary motion, triumphed” (ibid.).

Initial sales of the work were disappointing and, having moved from Ulm to Sagan in 1629, Kepler decided to enhance the book by adding a set of directions for using the tables for astrological purposes – this was the Sportula genethliacis missa (present in this copy), printed in 1629. A very few copies have in addition an appendix (in quarto format) by Kepler’s son Jacob Bartsch (1600-1633), published in Sagan in 1629, in which Bartsch suggests that logarithmic tables more accurate than those in the Tabulae Rudolphinae can be found in Ursinus’ Trigonometria cum magno logarithmorum canone (1624) and in his own Tabulae manuales, completed by 1629 but not published in full until 1700 (this appendix is extremely rare).

Folio (342 x 228mm), pp. [xvi], 12, [3], 1-40, [1], 42-119, [1, blank], with engraved allegorical frontispiece by Georg Köler of Nuremberg after Kepler depicting Hipparchus, Ptolemy, Copernicus, Brahe, and Kepler gathered in the Temple of Urania, numerous woodcut diagrams in text (margin of k3 folded in, with a contemporary marginal extension and parts of the first letters of the marginal notes supplied in contemporary manuscript, a little marginal worming to prelims, not affecting text, a single small wormhole in lower blank margin penetrating about a third of the way through, not touching text). Contemporary half-pigskin and rose blind-ruled paper-covered boards (binding worn with some loss of the paper on both covers, pigskin very rubbed). Quarter morocco clamshell.

Item #5639

Price: $95,000.00

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