99
Ibid., p. 261.
100
Loc. cit.
101
Ibid., p. 262.
102
Prowe II, p. 389, and Ency. Brit. XIX-246d. Zinner (p. 262) gives the date of Rheticus' death as 1574.
103
Prowe I, 2, p. 387f.
Part III Chapter II. THE SYSTEM OF COPERNICUS
1
The first complete English translation was published in 1952 in the "Great Books of the Western World" series (Vol. 16, Chicago, transl. Charles Glenn Wallis).
2
Eng. Brit. II-584a.
3
Zinner, op. cit., pp. 273-8.
4
H. Dingle, The Scientific Adventure ( London, 1951), p. 74.
5
London, 1932, p. 26.
6
London, 1949, pp. 26-7.
7
London, 1939, p. 38.
8
Oxford, 1941, p. 182.
9
Earth
De revoluti-
onibus
Commentari-
olus
Diurnal rotation
1
1
Motions in longitude
3
1
Conic motion of earth's axis to account for its fixed direction in space * and for precession
1
1
Two rectilineal oscillations to account for (imaginary) fluctuations in the rate of precession and in the value of the obliquity†; resolved into circular motions each
4
– – 9
– – 3
Moon
Motions in longitude
3
3
Motion in latitude
1
1
– – 4
– – 4
Three Outer Planets
Motions in longitude 3 × 3 =
9
9
Oscillations in latitude resolved into 2 circular motions apiece, 3 × 2 =
6
6
– – 15
– – 15
Venus
Motions in longitude
3
3
3 oscillatory motions in latitude
resolved into 6 circular
motions
6
2
– – 9
– – 5
Mercury
Motions in longitude (includ-
ing one oscillatory motion)
5
5
Motions in latitude (as Venus)
6
2
– – 11
– – 7
– –
– –
48
34
* Copernicus thought with the ancients of the earth's axis as quasi-mechanically attached to the orbital ring (on the analogy of the moon turning always the same face to the earth) and therefore had to introduce a special motion to keep the axis parallel to itself in space.
†See below, p. 201, f.
The count refers to circles in general, that is to say, eccenters, epicycles, deferents, and cycloids to account for rectilineal oscillations.
Apart from the erroneous reference to 34 epicycles, I have nowhere seen a count made of the number of circles in De revolutionibus.
Incidentally, as Zinner has pointed out (op. cit., p. 187) even the famous count at the end of the Commentariolus is wrong as Copernicus forgot to account for the precession, the motions of the aphelia and the lunar nodes. Taking these into account, the Commentariolus uses 38 not 34 circles.
10
This was pointed out by A. Koyré, Nicolas Copernic Des Revolutions des Orbes Célestes ( Paris, 1934), p. 18 n.
11
Peurbach, Epitomae. In his Theoricae, which is a simplified popular exposure of the system, Peurbach only gives twenty-seven epicycles. Quoted by Professor Koyré (in a private communication to the author, 20.12. 1957).
12
The reasons why Copernicus had to increase the number of his circles are:
(a) to compensate for the abolition of Ptolemy's equants;
(b) to account for the imaginary fluctuation in the rate of precession and of the value of the obliquity;
(c) to account for the constant angle of the earth's axis;
(d) because he insisted on resolving rectilinear oscillations into circular motions – which Ptolemy, who was less of a purist, did not bother to do.
This made a total of 21 additional epicycles as against a gain of 13 (5 from the annual and 8 from the diurnal motion of the earth).
13
The editio princeps and the three subsequent editions ( Nuremberg, Basle, Amsterdam and Warsaw) were based not on Copernicus' manuscript but on the copy made of it by Rheticus, which differed from the manuscript in numerous details. Copernicus' original manuscript was only discovered in the 1830's in the library of Count Nostitz in Prague. Nevertheless the Warsaw edition of 1854 still followed the earlier ones, and only the Torun edition of 1873 took account of the discovery of the original.
14
Butterfield, op. cit., p. 30.
15
De revolutionibus, Lib. I, Cap. 9.
16
Ibid., Lib. I, Cap. 8.
17
H. M. Pachter, Magic into Science ( New York, 1951), pp. 26, 30.
18
Letter against Werner, Prowe II, p. 176 f. An English translation was published by Rosen, op. cit.
19
Rheticus, Ephemerides Novae ( Leipzig, 1950), quoted by Prowe II, p. 391.
20
The last observation of his own (an eclipse of Venus by the moon) which he used in the Revolutions was made in March 1529. The book went to the printers in 1542. During the intervening thirteen years, Copernicus continued to make observations and jotted down twenty-two results, but he did not use these in the Revolutions.
This enables us to determine the date of the completion of the manuscript with reasonable certainty. It must have been completed after 1529, since the Venus observation just mentioned is entered in the body of the text. It is unlikely that it was completed later than 1532, since observations made in that year are not entered into the text, but inserted on a separate leaf.
He continued to make corrections and alterations in subsequent years, but these were of a minor character.
The statement in the dedication to Paul III that he withheld his work for "four times nine years" cannot be taken literally. (It is actually an allusion to Horace Epistle ad Pisonus.) He evidently brought the heliocentric idea back from Italy when he returned to Ermland in 1506 – which happens to be almost precisely four times nine years before he published the Revolutions; the details of the system must have been gradually taking shape in his mind between that earlier date and 1529. He was then in his middle fifties, and after that made no serious attempt to revise his theory.
21
De revolutionibus, Lib. III, Cap. 1-4. Misled by these data, Copernicus erroneously concluded that the rate of precession of the equinoxes was non-uniform, and sought to account for its imaginary fluctuations and the equally imaginary fluctuations of the obliquity of the ecliptic, b
y two independent oscillatory motions of the earth's axis.
22
De revolutionibus, Lib. III, Cap. 4.
23
Commentariolus, transl. Rosen, p. 57.
24
Ibid., p. 57 f.
He gives the same reason in the dedicatory preface to the Revolutions. Ptolemy's system, he explains there, agrees fairly well with the phenomena, but it violates "the first principle of uniformity of motion". Rheticus too, in the Narratio prima, keeps harping on the same subject: "You see that here in the case of the moon we are liberated from an equant by the assumption of this theory... My teacher dispenses with equants for the other planets as well..." (transl. Rosen, p. 135). "... My teacher saw that only on this [i.e. Copernicus'] theory could all the circles in the universe be satisfactorily made to revolve uniformly and regularly about their own centres, and not about other centres – an essential property of circular motion." ( Ibid., p. 137 ). (Non-uniform circular motion around a centre is] "a relation which nature abhors" ( ibid., p. 166 ).
25
De revolutionibus, Dedication to Pope Paul III.
26
Ibid., Lib. I, Cap. 5.
27
The pseudo- Plutarch De placiti philosophorum, from which Copernicus quoted the passage about Philolaus, Herakleides, etc., says, a few pages earlier (II, 24, quoted by Armitage, p. 88):
" Aristarchus places the sun among the fixed stars, and holds that the earth revolves round the sun."
In Copernicus' version on the manuscript of the Revolutions, this became transformed into:
" Philolaus perceived the mobility of the earth, and some say that Aristarchus of Samos was of the same opinion." ( Prowe II, p. 129.).
But even this watered-down tribute is crossed out in the manuscript. The name of Aristarchus actually occurs three times in the Revolutions (in Book III, chapters 2, 6 and 13), but these passages merely refer to his observations on the obliquity of the ecliptic and the length of the tropical year. The fact that Aristarchus fathered the heliocentric idea on which Copernicus built his system is nowhere mentioned.
Apart from the brief reference in the pseudo-Plutarch, Copernicus knew about Aristarchus' theory from the classic passage in Archimedes' Sand-reckoner (see above, Part One, ch. III, 3), which Regiomontanus, too, had specially marked (cf. Zinner, p. 178).
28
Averroes, Commentary on Aristotle's Metaphysics, quoted by Rosen, op. cit., p. 194 f.
29
De docta ignorantia (Basle, 1514).
30
Op. cit., II, 11, 12, quoted by Armitage, p. 89 f.
31
Ibid., p. 102seq. , quoted by Koyré, From the Closed World to the Infinite Universe ( Baltimore, 1957), p. 14 f.
32
Ibid., p. 105seq. , quoted by Koyré, pp. 20, 22.
33
Loc. cit.
34
Zinner, op. cit., p. 97.
35
Ibid., p. 100.
36
Ibid., p. 97.
36a
Cf. Prowe, I, 2, p. 480 ff.
37
Zinner, op. cit., p. 133.
38
Ibid., p. 152.
39
Loc. cit.
40
Ibid., p. 135. The daily rotation leaves the apparent movements of the firmament unaltered; the annual revolution should produce a small stellar parallax.
41
There is no direct evidence that Copernicus knew Calcagnini, but they were contemporaries at the small University of Ferrara, and Professor Antonius Leutus, who on 31 May, 1503, handed Copernicus the insignia of his doctor tide, was the godfather of Calcagnini.
42
Butterfield, op. cit., p. 29.
43
The semi-diameter of the earth was known to be approx. 4,000 miles and Copernicus believed the earth's distance from the sun to be approx. 1,200 semi-diameters ( De revolutionibus, Lib. IV, Cap. 21). Hence the diameter of the earth's orbit was believed to be 9.6 million miles.
44
The annual parallax was only proved in 1838 by Bessel.
45
De revolutionibus, Lib. I, Cap. 10.
46
Burtt, op. cit., p. 25.
47
De revolutionibus, Lib. I, Cap. 8.
PART FOUR
THE WATERSHED
Joannis Kepleri Astronomi Opera Omnia, ed. Ch. Frisch, 8 Vol., Frankofurti et Erlangae, 1858- 1871.
A modern collected edition of Kepler's work and correspondence, Johannes Kepler, Gesammelte Werke, ed. W. v. Dyck✠ and Max Caspar, in collaboration with Franz Hammer, was begun in 1938. Up to date ( March 1958), Volumes I to VII, IX, XIII to XVII are available. The texts are in the original Latin and medieval German.
The only serious modem work of biography is Max Caspar Johannes Kepler, Stuttgart, 1948.
Abbreviations
O.O. – Opera Omnia.
G.W. – Gesammelte Werke.
Ca. – Caspar's Biography.
Part IV Chapter 1. THE YOUNG KEPLER
1
O.O., Vol. VIII, p. 670seq., henceforth referred to as "Horoscope".
2
In 1945, a French unit was advancing on the town and started shelling it in the mistaken belief that the retreating German army had left a rearguard between its walls. At the critical moment a French officer whose name was given to me as Colonel de Chastigny – arrived at the scene, identified it as Kepler's birthplace, stopped the firing and saved Well from destruction.
3
"One of my ancestors, Heinrich, and his brother, Friedrich, were knighted ... in 143 0, by the Emperor [ Sigismond] on the bridge over the Tiber in Rome." (Letter from Kepler to Vincento Bianchi, 17 February, 1619; G. W., Vol. XVII, p. 321.) The Patent of Nobility is still extant, but the two Keplers knighted in 1430 were called Friedrich and Konrad, not Friedrich and Heinrich.
4
"Horoscope."
5
Ibid.
6
Ibid.
6a
Kretschmer, The Psychology of Men of Genius (transl. R. B. Cattell ), London, 1931.
7
I.e., placed very close to the sun.
8
O.O., Vol. V, p. 476seq.; henceforth referred to as "Memoir".
9
"Memoir." Cf. also letter to Herwart von Hohenburg. 9/10.4.1599, G.W. Vol. XIII, p. 305 ff.
10
"Horoscope."
11
Johannes Kepler in seinen Briefen, ed. Caspar and v. Munich Dyck and Berlin, 1930, Vol. I, p. 26.
12
"Memoir."
13
G.W., Vol. XIII, p. 19 f.
14
Tertius interveniens, G. W., Vol. IV, p. 145 seq.
15
De Stella nova in pede Serpentarii, G.W., Vol. I, p. 147seq.
16
Tertius interveniens.
17
De stella nova, Cap. 28.
18
Antwort auf Röslini Diskurs, G.W., Vol. IV, p. 99seq.
19
Ca., 108.
20
Tertius interveniens.
21
"Memoir."
21a
Antwort auf Röslini Diskurs, p. 127.
22
Tertius interveniens.
23
To Herwart, G.W., Vol. XIII, p. 305 ff.
Part IV Chapter II. THE "COSMIC MYSTERY"
1
Mysterium Cosmographicum(G.W.,Vol. I), Preface to the Reader.
2
Ibid., loc. cit.
3
Loc. cit.
4
Particularly striking is Kepler's advanced relativistic position in the first chapter of the Mysterium. For "metaphysical and physical" reasons, he says, the sun must be in the centre of the world, but this is not necessary for a formally correct description of the facts. Concerning the Ptolemaic and Copernican views of the apparent motion of the
fixed stars, he says: "It is sufficient that both should say (what both really say) that this phenomenon is derived from a contrasting motion between earth and sky." Regarding the annual revolution, he says that the universe of Tycho (where five planets revolve round the sun and the sun revolves round the earth) is pragmatically as legitimate as the Copernican. "Indeed, the proposition 'the sun rests in the centre' is too narrow, goes too far. It is sufficient to postulate more generally: 'the sun is the centre of the five planets.'"
5
In England, the significance of Copernicus was recognized earlier than on the Continent, mainly thanks to two works: firstly Thomas Digges' A Perfit Description of the Caelestiall Orbes according to the most aunciente doctrine of the Pythagoreans, latelye reuiued by Copernicus and by Geometricall Demonstrations approued, which he added, in 1576, to a new edition of his father Leonard Digges' Prognostication euerlasting; and secondly, Giordano Bruno La cena de le ceneri, which Bruno wrote during his English sojourn, and which was first published by Charlewood in London in 1584.
6
Cap. 13.
7
By inscribing Mercury's sphere not into the faces of the octahedron, as it ought to be done, but into the square formed by the four median edges. Cap. 13, Note 4.
8
Cap. 15.
9
Cap. 18.
10
Ibid., Note 8.
11
Cap. 20.
12
Ibid., Notes 2 and 3.
13
The law resulting from this first attempt was: R 1 : R 2 = P 1 : P 1 + P 2, where P 1, P 2 are the periods, R 1, R 2 the mean solar distances of two planets. The correct law ( Kepler's "Third Law") is, of course: R 1 : R 2 = P 1 2/3 : P 2 2/2.
14
Cap. 21.
15
Ibid., Note 7.
16
Ca., p. 78.
17
Mysterium Cosmographicum, Dedication of the 2nd Edition.
18
Astronomia Nova, summary of Cap. 45.
19
"Letter to Maestlin, 3".10. 1595. G. W., Vol. XIII, p. 33 ff.