20
Tertius Interveniens.
21
Harmonice Mundi, Lib. IV, Cap. I. G. W., Vol. VI.
22
Mysterium Cosmographicum, Cap. XXI, Notes 8 and II.
23
It is curious to note that no authority writing on Kepler seems to have noticed this stubborn omission of the word "ellipse"; perhaps because historians of science recoil from the irrationality of their heroes, as Kepler himself recoiled from the apparent irrationality of the elliptic orbits which he discovered.
24
Burtt, The Metaphysical Foundations of Modern Physical Science, London, 1932 (rev. ed.), p. 203. Burtt is a notable exception from the attitude referred to in the previous note.
25
Tertius Interveniens.
26
Mysterium Cosmographicum, Preface to the Reader.
26a
Ibid., Note 8.
Part IV Chapter III. GROWING PAINS
1
Letter to Friedrich, Duke of Wuerttemberg, 27.2. 1596. G. W., Vol. XIII, p. 50 ff.
2
G. W., Vol. XIII, p. 162 ff.
3
Letter to Maestlin, 11.6. 1598. G. W., Vol. XIII, p. 218seq.
4
"Horoscope." Cf. also Letter to Maestlin, 10.2. 1597, G. W., Vol. XIII, p. 104 seq.
5
Letter to Maestlin, 9.4. 1597, G. W., Vol. XIII, p. 113 seq.
6
Letter to Herwart, 9/10.4. 1599, G. W., Vol. XIII, p. 305 seq.
7
Letter to an anonymous woman, c. 1612, G. W., Vol. XVII, p. 39 seq.
8
Ibid.
9
Letter to Maestlin, 15.3. 1598, G. W., Vol. XIII, p. 185.
10
E. Reicke, Der Gelehrte, Monographien zur deutschen Kulturgeschichte, Vol. VII, Leipzig, 1900, p. 120.
11
G. W., Vol. XIII, p. 84 f.
12
G. W., Vol. XIII, p. 207.
13
Letter to Herwart, 16.12. 1598, G. W., Vol. XIII, p. 264 seq.
14
From the failure of his efforts, Kepler concluded that the parallax of the Polar Star must be smaller than 8', "because my instrument does not allow me to measure angles smaller than this. Hence the semi-diameter of the earth's orbit must be smaller than 1/500 of the semi-diameter of the sphere of the fixed stars." ( Letter to Herwart, G. W., Vol. XIII, p. 267 f.).
Copernicus assumed the mean distance of the earth from the sun = 1142 earth radii ( De revolutionibus, Lib. IV, Cap. 21). In round figures, the radius of the earth's orbit thus amounts to 1200 × 4000 = 4.8 million miles; and the minimum radius of the universe to 4.8 × 500 = 2400 million miles. Later on, however, in the Epitome, he enlarged the radius of the universe to sixty million earth radii, i.e. 24. 1010 miles. He arrived at this figure by assuming that the orbital radius of Saturn was the geometrical mean between the radius of the sun and the radius of the sphere of the fixed stars; and the radius of the sun to be fifteen times the radius of the earth. ( Epitome, IV, 1, O.O., VI, p. 332.)
15
Letter to Herwart, 16.12. 1598, loc cit. Kepler himself never accepted infinity. He believed that the fixed stars were all placed at almost exactly the same distance from the sun, so that their "sphere" (which, of course, he did not regard as real) was only "two German miles" in thickness. ( Epitome, IV, 1, O.O., VI, p. 334.)
16
Letter to Maestlin, 16/26.2. 1599, G. W., Vol. XIII, p. 289 seq.
17
Ibid.
18
For a profound analysis of the subjective elements in Newton's cosmology, see Burtt, op. cit.
19
Kepler's discoveries were not of the kind that "lie in the air"; the three laws were the result of a devious tour de force, and represent a rather exceptional "one-man show", as it were. Even Galileo failed to see their point.
20
Letter to Maestlin, 8.12. 1598, G. W., Vol. XIII, p. 249seq.
21
12.9. 1597, G. W., Vol. XIII, p. 131seq.
22
"Letter to Herwart, 16.12.1598", G. W., Vol. XIII, p. 264seq.
23
"Letter to Maestlin, 29.8.1599", G. W., Vol. XIV, p. 43seq.
24
"Letter to Maestlin, 22.11.1599", G. W., Vol. XIV, p. 86seq.
25
"Maestlin to Kepler, 25.1.1600", G. W., Vol. XIV, p. 105seq.
Part IV Chapter IV. TYCHO DE BRAHE
1
J. L. E. Dreyer, Tycho Brahe, Edinburgh, 1890, p. 27. Dreyer's is the modern standard biography of Tycho. He also edited Tycho Opera Omnia.
2
Loc. cit.
3
OP. cit., p. 14.
4
To be precise, he used two threads, passing through two pairs of stars, and intersecting in the Nova.
5
Op. cit., p. 86 f.
6
An Itinerary written by Fynes Morison, etc., London, 1617, fol., p. 60, quoted by Dreyer, p. 89.
7
Dreyer, op. cit., p . 105.
8
Ibid, p. 262 n.
8a
His other, principal achievements were: improved approximations of the sun's and moon's orbits; discovery of the "moon's equation" (independently from Kepler); demolition of the Copernican belief in a periodic inequality in the precession of the equinoxes.
9
Ibid., p. 261.
10
Ibid., p. 249 f.
11
Ibid., p. 279.
Nicolai Raimari Ursi Dithmar si Fundamentum astronomicum, Strasburg, 1588.
13
The only differences between the system of Ursus and the Tychonic system were that in the former the daily rotation was attributed to the earth, in the latter to the fixed stars; and that different orbits were attributed to Mars.
14
"To Ursus, 15.11.1595", G. W., Vol. XIII, p. 48 f.
15
Nicolai Raimari Ursi Dithwar si de astronomicis Hypothesibus, etc., Prague, 1597.
16
"To Tycho, 13.12.1597", G. W., Vol. XIII, p. 154.
17
"Tycho to Kepler, 1.4.1598", G. W., Vol. XIII, p. 197seq.
18
21.4. 1598, G. W., Vol. XIII, p. 204 f.
19
19.2. 1599, G. W., Vol. XIII, p. 286 f.
20
The passage runs: "Some doctor stopped on his return journey from Italy in Gratz and showed me a book of his [Ursus'] which I hurriedly read in the three days for which I was permitted to keep it. I found in it ... certain golden rules which, as I remembered, Maestlin had frequently used in Tuebingen, and also the science of the sine and of the computation of triangles – subjects which, though generally known, were new to me ... for afterwards I found in Euclid and Regiomontanus most of what I had ascribed to Ursus."
21
G. W., Vol. XIV, p. 89seq.
Part IV Chapter v. TYCHO AND KEPLER
1
Dreyer, op. cit-, p. 279.
2.
"Letter to Herwart, 12.7.1600", G. W., Vol. XIV, p. 128seq.
3
Ca., p. 117.
4
"To Herwaft, 12.7.1600", G. W., Vol. XIV, p. 128seq.
5
Ca., p. 119.
6
"Tycho to Jessenius, 8.4.1600", G. W., Vol. XIV, p. 112seq.
7
April, 1600, G. W., Vol. XIV, p. 114seq.
7a
He had signed, however, a written undertaking to keep all information he obtained from Tycho "in highest secrecy", i.e. he could publish nothing without Tycho's consent.
8
9.9. 1600, G. W., Vol. XIV, p. 150seq.
9
9.10. 1600, G. W., Vol. XIV, p. 155seq.
10
28.8. 1600, G. W., Vol. XIV, p. 145seq.
11
F. Morison, op. cit.
12
Dreyer, op. cit.,
p. 386 f.
13
Quoted by Kepler in Astronomia Nova, I, Cap. 6.
Part IV Chapter VI. THE GIVING OF THE LAWS
1
ASTRONOMIA NOVA AITIO ΛOΓHTOΣ, sev PHYSICA COELESTIS, tradita commentariis DE MOTIBUS STELLÆ MARTIS, Ex observationibus, G. V. TYCHONIS BRAHE.
1a
Astronomia Nova, G. W., Vol. III, Preamble to the Table of Contents.
2
Ibid., II, Cap. 7.
3
Ibid., Dedication.
4
"It is inconceivable that a non-material force should be present in a non-body and should move through space and time," Ibid, I, Cap. 2.
5
Ibid., II, Cap. 14.
6
Ibid., II, Cap. 14.
7
At a later stage, however, he reverted to the Ptolemaic position.
8
Altogether, Tycho had observed ten oppositions, and Kepler himself two ( 1602 and 1604). The Tychonic data which he used were those for 1587, '91, '93, and '95.
8a
"Letter to Herwart, 12.7.1600", G. W., Vol. XIV, p. 132 f.
9
Astronomia Nova, II, Cap. 18.
10
Ibid., II, Cap. 19.
11
Science and the Modern World, Cambridge, 1953 (reprint), p. 3.
12
Astronomia Nova, II, Cap. 20, III, Cap. 24.
13
Ibid., III, Cap. 22.
14
Loc. cit.
15
The observer on Mars went into action each time Mars returned to a given position in its orbit, i.e. had the same heliocentric longitude. Since the sidereal period of Mars was known, the times when this occurred could be determined, and the different positions which the earth occupied at these times could also be determined. The method yielded a series of triangles Mars-Sun-Earth: MSE 1, MSE 2, MSE 3, where the angles at S and E were known (from Tycho's data and/or from Kepler's previously established method of approximation). These yielded the ratios SE 1 /SM, SE 2 /SM, SE 3 /SM; and it was now a simple problem in geometry to determine the earth's orbit, (still assumed to be circular), its eccentricity, and the position of the punctum equans. The same method enabled him later on to determine the relative distances Mars-Sun for any observed geocentric longitude of Mars.
16
At the beginning of III, Cap. 33.
17
Table of Contents, summary of Cap. 32.
18
"At other places [not in the vicinity of aphelion and perihelion] there is a very small deviation..." The passage implies that the deviation is negligible. This is true of the earth's orbit, because of its small eccentricity, but not at all true of Mars, with its large eccentricity.
19
That Descartes derived his theory of vortices from Kepler is probable, but unproven.
20
Astronomia Nova, III, Cap. 40.
21
Loc. cit.
22
Loc. cit.
23
To sum up, the three incorrect assumptions are: (a) that the planet's velocity varies in inverse ratio with its distance from the sun; (b) the circular orbit; (c) that the sum of eccentric radii vectors equals the area. The erroneous physical hypotheses played only an indirect part in the process.
24
"Letter to Longomontanus, 1605", G. W., Vol. XV, p. 134 seq.
25
Astronomia Nova, IV, Cap. 45.
26
Loc. cit.
27
"Letter to D. Fabricus, 18.12.1604", G. W., Vol. XV, p. 78 seq.
28
"Letter to D. Fabricius, 4.7.1603", G. W., Vol. XIV, p. 409seq.
29
Letter to D. Fabricius, 18.12.1604.
30
Astronomia Nova, IV, Cap. 55.
31
Ibid., IV, Cap. 56.
32
Ibid., IV, Cap. 58.
33
1605; G. W., Vol. XV, p. 134seq.
34
Mysterium Cosmographicum, Cap. 18.
35
Cf. Insight and Outlook, London and New York, 1949.
35a
Astronomia Nova, Introduction.
36
Delambre, Histoire de l'Astronomie Moderne, Paris, 1891, Vol. I, p. 394.
37
"Third Letter to Bentley", Opera Omnia, London, 177985, IV, 380. Quoted by Burtt, op. cit., p. 265 f.
38
Thus, for instance, in Galileo Dialogue on the Great World Systems, it is Simplicius, the naïve Aristotelian, who says: "The cause [why bodies fall] is manifest, and everyone knows that it is gravity"; but he is promptly rebuked with: "You are out, Simplicius; you say that everyone knows that it is called gravity, and I do not question you about the name but about the essence of the thing. Of this you know not a tittle more than you know the essence of the mover of the stars in gyration." (Salusbury transl., ed. Santillana, Chicago, 1953, p. 250.)
39
10.2.1605; G. W., Vol. XV, p. 145seq.
40
Astronomia Nova, III, Cap. 33.
41
Ibid., III, Cap. 38.
42
Ibid., I, Cap. 6.
43
Max Caspar's introduction to his German translation of the Astronomia Nova, Munich and Berlin, 1929, p. 54.
Part IV Chapter VII. KEPLER DEPRESSED
1
"Letter to Heydon, October 1605", G. W., Vol. XV, p. 231seq.
2
"Letter to D. Fabricius, 1.10.1602", G. W., Vol. XIV, p. 263, seq.
2a
"Letter to D. Fabricius, February 1604", G. W., Vol. XV, p. 17seq.
3
"Greetings to the reader! I had intended to address thee, reader, with a longer preface. Yet the mass of political affairs which keep me more than usually busy these days, and the hasty departure of our Kepler, who intends to leave for Frankfurt within the hour, only left me a moment's time to write. But I thought nevertheless that I ought to address a few words to thee, lest ye should become confused by the liberties which Kepler takes in deviating from Brahe in some of his expositions, particularly those of a physical nature. Such liberties can be found in all philosophers since the world existed; and it in no way affects the work of the Rudolphine tables. [This refers to the planetary tables dedicated to Rudolph which Tengnagel had promised to produce, and never did.] You will be able to see from this work that it has been built on the foundations of Brahe ... and that the entire material (I mean the observations) was collected by Brahe. In the meantime, consider Kepler's excellent work ... as a prelude to the Tables and to the Observations to follow which, for the reasons explained, can only be published slowly. Pray with me to the Almighty and all-wise Lord for the rapid progress of this much desired work and for happier days.
Franz Gansneb Tengnagel,
In Campp. Counsellor of his Imperial Majesty."
4
G. W., Vol. XV, p. 131seq.
5
"D. Fabricius to Kepler, 20.1.1607", G. W., Vol. XV, p. 376seq.
6
30.10.1607, G. W., Vol. XVI, p. 71.
7
The writer is the Danzig astronomer P. Crueger, quoted in W. v. Dyck and M. Caspar Nova Kepleriana 4, Abhandlungen der Bayrischen Ak. d. Wiss. XXXI, p. 105seq.
8
Loc. cit.
9
Astronomiae Pars Optica, Dedication to Rudolph II, G. W., Vol. II.
10
"Letter to Besold, 18.6.1607", G. W., Vol. XV, p. 492.
10a
"Letter to Herwart, 10.12.1604", G. W., Vol. XV, p. 68 f.
11
"Letter to Herwart, 24.11.1607", G. W., Vol. XVI, p. 78seq.
12
"Letter to D. Fabricius, 11.10.1605", G. W., Vol. XV, p. 240seq.
13
Dissertatio cum Nuncio Sidero, G. W., Vol. IV, p. 281seq.
14
There has been some contro
versy on the question whether the title meant "messenger" or "message" – cf. Stillman Drake , Discoveries and Opinions of Galileo, New York, 1957, p. 19. Stillman Drake translates the title as The Starry Messenger; de Santillana (see below), as Sidereal Message (Dialogue) or Starry Message (The Crime of Galileo). I propose to use Messenger from the Stars, or Star Messenger for short.
Part IV Chapter VIII. KEPLER AND GALILEO
1
F. Sherwood Taylor, Galileo and the Freedom of Thought ( London, 1938), p. 1.
2
This is strictly true for small angles only, but sufficient for practical purposes of time-measurement. The correct law of the pendulum was discovered by Huygens. The candelabra still shown at the Cathedral of Pisa, whose oscillations are alleged to have given Galileo his idea, was only installed several years after the discovery.
3
His manuscript treatise De Motu, written about 1590, and privately circulated, certainly deviates from Aristotelian physics, but by subscribing to the entirely respectable theory of impetus which had been taught by the Paris school in the fifteenth century and by several of Galileo's predecessors and contemporaries. Cf. A. Koyré, Etudes Galileennes ( Paris, 1939).
4
About his technical treatise on the proportional compass, see below.
5
"Letter to Maestlin, September 1597", G. W., Vol. XIII, p. 140seq.
6
G. W., Vol. XIII, p. 130 f.
6a
Trattato della Sfera, Opere, Ristampa della Ediz. Nazionale ( Florence, 1929-39), Vol. II, pp. 203-255. Henceforth "Opere" refers to this edition, except when marked "Ed. F. Flora", which refers to the handier selection of works and letters in one volume, published in 1953.
7
Quoted by Sherwood Taylor, op. cit., p. 85.
8
G. W., Vol. XIII, p. 144seq.
9
G. W., Vol. XIV, p. 256.
10
Ibid., p. 441.
11
Ibid., p. 444 f.
12
It is surprising to read that Prof. Charles Singer attributes the discovery that the nova of 1604 had no parallax to Galileo, and moreover, passing in silence over Tycho's classic book on the nova of 1572, writes:
"New stars when previously noticed had been considered to belong to the lower and less perfect regions near the earth. Galileo had thus attracked the incorruptible and interchangeable heavens and had delivered a blow to the Aristotelian scheme, wellnigh as serious as the experiment on the tower of Pisa (sic)." (Ch. Singer, A Short History of Science to the Nineteenth Century, Oxford, 1941, p. 206.)