Not Only in Latin, but also in Dutch, Chinese, Italian and German

Tonietti, Tito M.

doi:10.1007/978-3-0348-0675-6_2

Tito M. Tonietti⁵

Part of the book series: Science Networks. Historical Studies ((SNHS,volume 47))

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Abstract

The rules for music presented by Maurolico were predominant in texts written during the second half of the sixteenth century, and we have to consider them to represent orthodoxy in that period. Now the discussion about the division of the tone assumed the characteristics of controversies between continuous or discrete conceptions of the world, becoming its musical representation. We have followed these in their manifold variations, found in the cultures that were discussed in Part I.

But they most despise the low, grovelling populace when they

bring out their mathematics of triangles, squares, circles, and

other similar geometric figures, which then they lay the one on

the other, and mix up as in a labyrinth: at last they astonish the

idiots with several letters, arranged like an army in order of

battle, and subdivided in different companies.

But at last the preacher brought it thus far, that he could

demonstrate the whole Trinity to be represented by these first

rudiments of grammar, as clearly and plainly as it was barely

possible for a mathematician to draw a proof in the sand.

ErasmusErasmus from Rotterdam from Rotterdam, In praise of folly In praise of folly@In praise of folly , 204, 239.

Mark how one string, sweet husband to another, Strikes each in

each by mutual ordering; Resembling sire and child and happy

mother, Who, all in one, one pleasing note to sing.

ShakespeareShakespeare, William, Sonnet Sonnets, VIII.

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Notes

1.
Part I, Sect. 2.5.
2.
Part I, Sect. 6.7.
3.
Stevin 1966, pp. 428–429.
4.
Stevin 1966, pp. 426–427 and 440–441. ToniettiTonietti, Tito M. 2003b, pp. 226–228.
5.
Stevin 1966, p. 440.
6.
Stevin 1966, pp. 446–447.
7.
Stevin 1958, pp. 532–533.
8.
Stevin 1958, p. 738.
9.
Stevin 1966, p. 425.
10.
Stevin 1966, pp. 426–427.
11.
Emphasis in the text.
12.
Stevin 1966, pp. 426–429.
13.
DijksterhuisDijksterhuis, E.J. 1971, pp. 432–440. MinnaertMinnaert, M.G.J. 1970, pp. 48–49.
14.
Stevin 1966, pp. 429–433.
15.
Stevin 1966, pp. 436–437.
16.
Stevin 1966, pp. 456–459.
17.
Stevin 1966, p. 420. Even in the twentieth century, the editor of the manuscript, Adriaan D.FokkerFokker, Adriaan D., displayed a far greater tendency to censure towards StevinStevin, Simon’s avoidance of Pythagorean whole numbers, judging that he had acted “… haughtily and aggressively …”; StevinStevin, Simon 1966, p. 419. On the contrary, the Dutchman, Rudolf RaschRasch, Rudolf A. has recently provided us with more interesting details about the original pages of his earlier fellow-countryman, duly pointing out the influence that he had, more often than not in a negative sense, on BeeckmanBeeckman, Isaac, MersenneMersenne, Marin, DescartesDescartes, René and the two HuygensHuygens, Constantijn Huygens, Christiaan; RaschRasch, Rudolf A. 2008. See below, Sects. 9.1–9.3. Cf. BosBos, Henk G.M. 2004.
18.
Stevin 1958, pp. 501–503 and 738.
19.
StruikStruik, Dirk J. 1958, pp. 7–9.
20.
StruikStruik, Dirk J. 1958, pp. 463, 471 and 474.
21.
Struik 1958, p. 474.
22.
Struik 1958, p. 8.
23.
Minnaert 1970, p. 50.
24.
Part I Chap. 3.
25.
MinnaertMinnaert, M.G.J. 1970, pp. 47 and 50–51.
26.
NeedhamNeedham, Joseph, WangWang Ling & RobinsonRobinson, Kenneth Sirdwood 1962, p. 228.
27.
Needham & WangWang Ling & RobinsonRobinson, Kenneth Sirdwood 1962, pp. 220–228. ToniettiTonietti, Tito M. 2003b, pp. 234–237.
28.
Part I Sect. 3.2.
29.
ZhuZhu Zaiyu 1584, p. 20. NeedhamNeedham, Joseph, WangWang Ling & RobinsonRobinson, Kenneth Sirdwood 1962, p. 222. Chinese characters in Appendix D.
30.
Needham, WangWang Ling & RobinsonRobinson, Kenneth Sirdwood 1962, pp. 220–221.
31.
In China, where no Pythagorean prohibition of irrational numbers existed, the extraction of a root was seen as a kind of division; ToniettiTonietti, Tito M. 2006a; see above, Part I, Chap. 3.
32.
Zhu 1584, p. 8. NeedhamNeedham, Joseph, WangWang Ling & RobinsonRobinson, Kenneth Sirdwood 1962, p. 223. Chinese characters in Appendix D.
33.
Zhu 1596.
34.
Part I, Sect. 3.2.
35.
RobinsonRobinson, Kenneth Sirdwood 1980, p. 118. But we may note that he should have divided the diameters in the same proportion \(\root{12}\of{2}\) as the length, in order to obtain a good tempering also of the pipes; ToniettiTonietti, Tito M. 2003b, p. 240.
36.
Needham, Wang & RobinsonRobinson, Kenneth Sirdwood 1962, p. 214.
37.
ToniettiTonietti, Tito M. 2003b, pp. 231–232; see above, Part I, Sect. 3.2.
38.
Robinson 1980, p. 115; Chen 1999Chen Cheng-Yih (Joseph).
39.
See above in this section. ToniettiTonietti, Tito M. 2003b.
40.
Chen 1994.
41.
Tonietti 2003b.
42.
Part I, Sect. 6.5.
43.
Galileo Galilei 1996 II, pp. 671–680.
44.
Galileo GalileiGalilei, Galileo 1968, VI, p. 350 and XII, p. 436.
45.
Viviani 1891, 303. Cf. Galileo GalileiGalilei, Galileo 1968, XIX, p. 603. SettleSettle, Thomas B. 1996, pp. 30–31. Also in HuygensHuygens, Christiaan 1890, III, p. 473.
46.
Galileo GalileiGalilei, Galileo 1996, II, pp. 670 and 680. The sight is confounded, but the hearing is not, Galileo GalileiGalilei, Galileo seemed to say.
47.
PaliscaPalisca, Claude V. 1961 or GozzaGozza, Paolo 1989, or DrakeDrake, Stillman 1992, or Settle 1996.
48.
Galileo GalileiGalilei, Galileo 1968, V p. 325. Despite the misleading title, “Galileo and the Demise of Pythagoreanism”, and his use of commonplaces taken from others, who distorted and misinterpreted Vincenzio Galilei, even JordanJordan, William 1992 ended up by presenting only a Pythagorean Galileo Galilei.
49.
Galileo GalileiGalilei, Galileo 1964, pp. 5, 10, 17ff. At most, he could construct water-clocks. Cf. SettleSettle, Thomas B. Settle, Thomas B. 1996. Galileo GalileiGalilei, Galileo 1968, XI, p. 342. HoltonHolton, Gerald 1993, pp. 154–155 and 167–174. LundbergLundberg, Robert 1992, p. 219.
50.
Galileo GalileiGalilei, Galileo 1996, II, pp. 185–186. Cf. FeyerabendFeyerabend, Paul 1973, pp. 63–73; FeyerabendFeyerabend, Paul 1979, pp. 58–77.
51.
Galileo GalileiGalilei, Galileo 1996, I pp. 631–632.
52.
Galileo GalileiGalilei, Galileo 1996, II, pp. 27–28 and 260.
53.
Galileo GalileiGalilei, Galileo 1996, II, pp. 571, 707, 598–623. ToniettiTonietti, Tito M. 2004a, pp. 94–100.
54.
ToniettiTonietti, Tito M. 2002a.
55.
Galileo GalileiGalilei, Galileo 1996, I, p. 451 and II, p. 642.
56.
Galileo GalileiGalilei, Galileo, Dialogo sui massimi sistemi, “Ultima giornata”; in Galileo GalileiGalilei, Galileo 1996, II.
57.
Clavius S.I. 1589, p. 15.
58.
ToniettiTonietti, Tito M. 2006a, Chap. 4.
59.
See above, Part I, Chap. 3. ToniettiTonietti, Tito M. 2006a.
60.
Tonietti 2006a, Sect. 5.3.
61.
Part I, Chap. 3.
62.
Genesi, 28, 12.
63.
Tonietti 2006a, Sects. 4.1 and 4.3.
64.
Gernet 1982 and GernetGernet, Jacques 1989.
65.
Dudink 2001, p. 213. GernetGernet, Jacques 1982, passim.
66.
Part I, Sect. 3.6.2.
67.
Genesis, 3, 5.
68.
Tonietti 2006a, pp. 175–176. Galileo’s letter to Mons. Pietro DiniDini, Pietro of March 23rd, 1615. Galileo GalileiGalilei, Galileo 1968, V, p. 303. Cf. D’EliaDEliaPasquale@D’Elia, Pasquale 1947.
69.
Galileo GalileiGalilei, Galileo 1968, V, p. 370.
70.
FeyerabendFeyerabend, Paul 1985. StengersStengers, Isabelle 1989. HammondHammond, Frederick 1992. RedondiRedondi, Pietro 2004.
71.
ToniettiTonietti, Tito M. 2006a, Chap. 5.
72.
Tonietti 2006a, pp. 170–171.
73.
MartzloffMartzloff Jean-Claude 1981a, p. 34. ToniettiTonietti, Tito M. 2006a, pp. 182–197.
74.
Galileo GalileiGalilei, Galileo 1968, V, pp. 285 and 281–370. FeyerabendFeyerabend, Paul 1985, pp. 250–256. Cf. RedondiRedondi, Pietro 2004.
75.
Galileo GalileiGalilei, Galileo 1968, V, p. 356.
76.
Kepler 1619 [1969], V cap. III, 8, pp. 189–190. 1997, p. 411. The Italics are in the text.
77.
Kepler 1938, v. I, pp. 9, … and passim.
78.
With the permission of the emperor, but without that of the heirs.
79.
GeymonatGeymonat, Ludovico 1970, II, pp. 105–107 and 508–514.
80.
Tonietti 2004, pp. 665–669.
81.
Kepler 1619 [1969]; 1939; 1952; 1979; 1994; 1997. HoltonHolton, Gerald 1993, pp. 3–23.
82.
The golden section 1:x = x:(1 − x), indicating the whole as 1 and the larger part as x.
83.
(1 + x):1 = 1:x; that is to say, \(x = \frac{1} {1+x}\).
84.
In other words, it cannot be represented in a ‘rational’ manner, because \({x}^{2} = 1 - x; {x}^{2} + x - 1 = 0; x = (-1 + \sqrt{5})/2; x = 0, 6180339\ldots\).
85.
\(1 + 2 = 3\).
86.
1:2 \(\not =\) 2:3
87.
\(3 \times 1 = 2 \times 2 - 1\).
88.
\(\begin{array}{lll} &&5: 3\not =3: 2; 2 \times 5 = 3 \times 3 + 1 \\ & & 8: 5\not =5: 3; 3 \times 8 = 5 \times 5 - 1 \\ & & 13: 8\not =8: 5; 13 \times 5 = 8 \times 8 + 1 \\ & & 21: 13\not =13: 8; 21 \times 8 = 13 \times 13 - 1\\ & & \ldots \end{array}\)
89.
Five was the Pythagorean number for marriage.
90.
Kepler 1619 [1969], III cap. XV par. VIII, pp. 76–77; 1997, pp. 241–242; translation slightly changed.
91.
Kepler 1619 [1969], III, pp. 7–9; 1997, pp. 137–139.
92.
Kepler 1619 [1969], III, pp. 13–15; 1997, pp. 147–150. Here species is misunderstood as “emanation”.
93.
Kepler 1619 [1969], III, p. 28; 1997, p. 165. Translation slightly changed.
94.
Kepler 1619 [1969], III, pp. 30–31; 1997, pp. 168–170. DickreiterDickreiter, Michael 1973, pp. 153–154.
95.
Kepler 1619 [1969], III, pp. 33–37; 1997, pp. 173–179. Here superstitione is translated as “fascination”.
96.
For Vincenzio’s tempered fourth, the table shows a printing error: 75,242 instead of 75,142, compared with the number 75,000 of the ratio 3:4.
97.
Kepler 1619 [1969], III, pp. 46–50; 1997, pp. 195–200. KeplerKepler, Johannes 2009, pp. 20–31.
98.
Kepler 1619 [1969], III, pp. 44, 58, 60, 85, V, pp. 233–234; 1997, pp. 189, 212, 215, 254, 476–478; passim.
99.
Kepler 1619 [1969], III, Chap. IX–XIV; 1997, pp. 200–237. DickreiterDickreiter, Michael 1973.
100.
Kepler 1619 [1969], III, p. 74; 1997, p. 236.
101.
Kepler 1619 [1969], III, p. 77; 1997, p. 240.
102.
Kepler 1619 [1969], III, p. 101; 1997, p. 276.
103.
Kepler 1619 [1969], IV, p. 109; 1997, p. 291.
104.
Kepler 1619 [1969], IV, pp. 114–117; 1997, pp. 298–302.
105.
Kepler 1619 [1969], IV, pp. 118–119; 1997, pp. 303–304. TangherliniTangherlini, Silvia 1974.
106.
Kepler 1992. KeplerKepler, Johannes 1997, pp. 308–309.
107.
Kepler 1619 [1969], IV, pp. 121–122; 1997, p. 308.
108.
Kepler 1619 [1969], IV, p. 131; 1997, p. 323.
109.
Kepler 1619 [1969], IV, p. 132; 1997, p. 325.
110.
Kepler 1619 [1969], IV, p. 133; 1997, p. 326.
111.
Kepler 1619 [1969], IV, p. 155; 1997, p. 355; translation different from ours.
112.
Kepler 1619 [1969], IV, p. 151; 1997, p. 350.
113.
In out great epoch, the Earth, considered as a single, complex living organism, has been resumed, and dubbed the ‘Gaia hypothesis’.
114.
Kepler 1619 [1969], IV, p. 162; 1997, pp. 365–366.
115.
Kepler 1619 [1969], IV, p. 163; 1997, p. 367; here Energeia has been translated as “activity”.
116.
Kepler 1619 [1969], IV, pp. 170–171; 1997, pp. 376–378 and pp. xxi–xxiii. Cf. KeplerKepler, Johannes 1984, pp. 87–90. Cf. CasparCaspar, Max 1993, pp. 76, 181–185 and passim.
117.
Kepler 1619 [1969], V, pp. 179, 181, 187; 1997, pp. 391, 396–397, 407.
118.
Kepler 1619 [1969], V, p. 189; 1997, p. 411.
119.
Kepler 1619 [1969], V, p. 194; 1997, p. 419.
120.
Kepler 1619 [1969], V, p. 198; 1997, p. 424; translation a little different.
121.
Kepler 1619 [1969], V, pp. 204, 207; 1997, pp. 435–436.
122.
Kepler 1619 [1969], V, p. 208, III pp. 64, 72, 75 and 84; 1997, pp. 441, 221, 234, 239 and 253.
123.
BorrenBorren, Charles van den 1944, p. 65 and passim.
124.
Kepler 1619 [1969], V, p. 208; 1997, p. 441. As I have done so far, at times I will modify the 1997 translation to make it closer to the Latin text, without continuing to point this fact out.
125.
The chords lend themselves to a modern harmonic interpretation as ‘hard’ major tonalities or ‘soft’ minor ones. However, this would be anachronistic, because KeplerKepler, Johannes referred to the Franco- Flemish polyphony that preceded the harmonic revolution of BachBach, Johann Sebastian and RameauRameau, Jean-Philippe: from the Greek-ecclesiastical modes to major and minor tonalities.
126.
Kepler 1619 [1969], V, p. 211; 1997, pp. 446.
127.
Kepler 1619 [1969], V, p. 212; 1997, pp. 446–448.
128.
Kepler 1619 [1969], V, p. 240; 1997, p. 486.
129.
Kepler 1619 [1969], V, p. 242; 1997, p. 489.
130.
Kepler 1997, p. 131.
131.
Kepler 1619 [1969], III, pp. 48 and 67; 1997, pp. 197 and 226.
132.
Kepler 1619 [1969], V, p. 247; 1997, p. 496.
133.
Kepler 1619 [1969], V, p. 245; emphasis in the text. KeplerKepler, Johannes 1955, v. XVII, p. 326. TangherliniTangherlini, Silvia 1974, p. 166. See above 8.2.
134.
Kepler 1619 [1969], V, p. 251; 1997, p. 503.
135.
Kepler 1619 [1969], V, pp. 249, 250, 251; 1997, pp. 500–502.
136.
Kepler 1619 [1969], V, pp. 249–251; 1997, pp. 130–131, 190, 390–391 and 499–503. StephensonStephenson, Bruce 1994, pp. 37–38 and 98–117.
137.
Kircher 1650.
138.
Kepler 1619 [1969], V, pp. 251–254; 1997, pp. 503–508. Baumgardt 1951, pp. 181–182. CasparCaspar, Max 1993, pp. 290–293. PauliPauli, Wolfgang 1955. AmmannAmmann, Peter J. 1967.
139.
Kepler 1619 [1969], IV, p. 106; 1997, p. 284.
140.
Kepler 1984, p. 117; cf. 137.
141.
Kepler 1984, pp. 67 and 75.
142.
Kepler 1984, pp. 15–22. CasparCaspar, Max 1993, pp. 351–353.
143.
Kepler 1984, pp. 22, 70, 97, 99, 107, 109.
144.
Kepler 1984, pp. 57, 102–105, 161.
145.
Kepler 1984, p. 161.
146.
Kepler 1984, p. 109.
147.
Kepler 1984, p. 83.
148.
See above, Volume I, Sect. 2.3, 6.2, 6.5.
149.
BaumgardtBaumgardt, Carola 1951, pp. 130–131.
150.
Kepler 1984, pp. 160 and 201.
151.
A scattered sentence between the Mysterium Mysterium cosmographicum@Mysterium cosmographicum Cosmographicum and De Stella Nova, quoted by Robert HalleauxHalleaux, Robert in KeplerKepler, Johannes 1975, p. 27.
152.
Kepler 1954, v. XVI, n. 493, pp. 154–165. Here he already wrote down some of those elements referring to music and sexual generation, in accordance with Fibonacci’s numbers, seen above in the Harmonices Harmonices Mundi Libri Quinque@Harmonices Mundi Libri Quinque mundi …. As regards the geometrical archetypes in God, in creation and in nature, see also KeplerKepler, Johannes’s letter to Christoph HeydonHeydon, Christoph of 1605. KeplerKepler, Johannes 1951, v. XV, n. 357, p. 235. Quotations also from Halleaux in the introduction to KeplerKepler, Johannes 1975, pp. 26–29.
153.
Kepler 1941, IV, pp. 275, 278, 279; KeplerKepler, Johannes 1975, pp. 73–74, 79–80.
154.
Kepler 1984, pp. 167–168. CasparCaspar, Max 1993, p. 204. As regards how KeplerKepler, Johannes wrote his books, see KoestlerKoestler, Arthur 1991, p. 309.
155.
Kepler 1984, pp. 180–181 and 187.
156.
Kepler 1619 [1969], III, p. 61; 1997, p. 217.
157.
Kepler 1997, pp. 163–164 and xxiii.
158.
Kepler 1619 [1969], V, p. 189. KeplerKepler, Johannes 1997, pp. 389–391, 411. CasparCaspar, Max 1940, pp. 462–484. Cf. CasparCaspar, Max 1993, pp. 91–96 and 264–290.
159.
Kepler 1997, pp. 489 and xvi–xxiv.
160.
Kepler 1997, pp. 498–500. CasparCaspar, Max 1993, pp. 228–232. Baumgardt 1951, pp. 27–28 and 118. In a letter dated August 4th, 1619, however, KeplerKepler, Johannes wrote that the Harmonices Harmonices Mundi Libri Quinque@Harmonices Mundi Libri Quinque mundi … had not been published yet. Baumgardt 1951, p. 141. As regards the extent of Kepler’s studies on PtolemyPtolemy, Claudius, see Stephenson 1994, pp. 98–117.
161.
Kepler 1997, pp. 219 and 239.
162.
Kepler 1619 [1969], “Dedicatio” [a–b]. Cf. KeplerKepler, Johannes 1997, p. 2. Here the translation is different: “non-inperturbato” was changed into “uninterrupted”. CasparCaspar, Max 1993, p. 288.
163.
Kepler 1997, pp. 3–5. The idea is also found in LeibnizLeibniz, Gottfried Wilhelm; See Part II, Sect. 10.1.
164.
BaumgardtBaumgardt, Carola 1951, pp. 128–129. CasparCaspar, Max 1993, p. 306.
165.
Kepler 1619 [1969] “Dedicatio” [c–e]. Cf. KeplerKepler, Johannes 1997, pp. 3–5.
166.
CasparCaspar, Max 1993, passim. Baumgardt 1951, pp. 53–57 and 172–174.
167.
Letter to MästlinMastlinMichael@Mästlin, Michael dated December 12th/22nd, 1616; KeplerKepler, Johannes 1955, v. XVII, pp. 203–204. CasparCaspar, Max 1993, pp. 49–52, 77–118, 122, 188–189, 258–264, 359–360, … and passim. Baumgardt 1951, pp. 58–65, 101, 106–107.
168.
BaumgardtBaumgardt, Carola 1951, pp. 87, 90, 96, 129–131, 138, 163, 171, 174, 179, 189, 192–195. CasparCaspar, Max 1993, pp. 104, 109, 122–123, 141–142, 156–159, 188, 225, 356–357, 362–363, … and passim.
169.
Baumgardt 1951, pp. 112–113.
170.
BaumgardtBaumgardt, Carola 1951, pp. 133, 172–173. Cf. CasparCaspar, Max 1993, pp. 112–113, 148, 337, … passim.
171.
Baumgardt 1951, pp. 133–136 and 150. CasparCaspar, Max 1993, pp. 299, 307, 317, 335–337.
172.
Kepler 1619 [1969], III, pp. 51 and 98; 1997, 202, 272.
173.
Baumgardt 1951, pp. 133, 144–148, 189. CasparCaspar, Max 1993, pp. 220, 236 and 347.
174.
Kepler 1619 [1969], V, p. 241; 1997, p. 488. CasparCaspar, Max 1993, pp. 180–181 and 323.
175.
Kepler 1997, p. 452.
176.
Kepler 1619 [1969], V, p. 243; 1997, p. 491.
177.
Kepler 1619 [1969], V, pp. 245–248; 1997, pp. 493–498.
178.
CasparCaspar, Max 1993, pp. 68–69. KeplerKepler, Johannes 1984, pp. 68–69.
179.
CasparCaspar, Max 1993. Cf. Gingerich 1970.
180.
For example: BanvilleBanville, John 1993; KoestlerKoestler, Arthur 1991; Lombardi 2000.
181.
HindemithHindemith, Paul 1957/1961.
182.
In that area, and in that period, 38 poor women were sentenced to death for similar accusations. CasparCaspar, Max 1993, pp. 240–258. BaumgardtBaumgardt, Carola 1951, pp. 156–162. Banville 1993, pp. 154–156. LombardiLombardi, Anna Maria 2000, pp. 59–66.
183.
BaumgardtBaumgardt, Carola 1951.
184.
CasparCaspar, Max 1993, pp. 34–36 and 338–350. Baumgardt 1951, pp. 174 and 179.
185.
CasparCaspar, Max 1993, pp. 355–361. Baumgardt 1951, pp. 192–197.
186.
Baumgardt 1951, pp. 20, 24, 94, 112–117. CasparCaspar, Max 1993, p. 43. Walker 1967, pp. 243–245. Koestler 1991, pp. 231 and 236.
187.
NobleNoble, David F. 1994. In this book, which deals with the absence of female figures in the development of Western modern sciences, Kepler was not even mentioned, perhaps because he appeared to be such an exception for the author’s thesis.
188.
Baumgardt 1951, pp. 51 and 124. CasparCaspar, Max 1993, pp. 135–138.
189.
Barone 1989.
190.
Kepler 1984, p. 70.
191.
Donne 1969.
192.
Kepler 1963, v. VIII, pp. 135 and 461. CasparCaspar, Max 1993, p. 301. Bald 1970, pp. 338–365.
193.
DonneDonne, John 2002, pp. 44, 48, 52.
194.
Donne 2002, pp. 124 and 144.
195.
Donne 1969, pp. 101, 129, 139. BaldBald, R.C. 1970, passim. Only NicolsonNicolson, Marjorie 1940 and Edward RosenRosen, Edward in KeplerKepler, Johannes 1984, p. 70 have dwelt on Donne, the former in view of literary interests. Cf. Koestler 1991, p. 361. Cf. GingerichGingerich, Owen 1970, p. 306.
196.
Donne 1969, pp. xix–xxix.
197.
Donne 1969, pp. 12–19. Emphasis in the text.
198.
Donne 1969, p. 109.
199.
Donne 1969, pp. 6–7, 80–81, 102, xxx. Emphasis in the text
200.
CasparCaspar, Max 1993, pp. 252 and 256.
201.
The hypothesis that Donne may have drawn his inspiration directly from KeplerKepler, Johannes’s Somnium for his Ignatius, who likewise ended up on the Moon, seems unlikely to me. Note 8, added by KeplerKepler, Johannes to the Somnium … much later, says, “Fallor an author [sic!, auctor] Satyrae procacis, cui nomen Conclave Ignatianum, exemplar nactus erat [sic!, esset] huius opusculi; pungit enim me nominatim etiam in ipso principio.” [“I am not sure whether the author of an impudent satire, the title of which was Conclave Ignatianum, may by chance have come across a copy of this leaflet; he teases me by name, right from the beginning of the work.”] I prefer to maintain KeplerKepler, Johannes’s doubts. The relative dates and the limited circulation of a manuscript, which was only printed posthumously, make this possibility too complicated and too remote. Cf. Nicolson 1940 and Donne 1969, pp. 159–160.
202.
CasparCaspar, Max 1993, p. 128. Gingerich 1970, pp. 294–297.
203.
CasparCaspar, Max 1993, p. 136.
204.
Kepler 1954, v. XVI, pp. 205–206. Cf. CasparCaspar, Max 1993, p. 171. Translation slightly different.
205.
CasparCaspar, Max 1993, p. 255.
206.
CasparCaspar, Max 1993, pp. 336, 373–378. Banville 1993, pp. 176–180 and 150.
207.
Kepler 1619 [1969], IV, pp. 119–120. CasparCaspar, Max 1993, pp. 272 and 379. PauliPauli, Wolfgang 1955. TangherliniTangherlini, Silvia 1974.
208.
CasparCaspar, Max 1993, p. 380.
209.
CasparCaspar, Max 1993, p. 182.
210.
Kepler 1945, XIII, n. 113, p. 292. KeplerKepler, Johannes 1951, XV, n. 357, p. 232. CasparCaspar, Max 1993, p. 87. Koestler 1991, pp. 339–340. Banville 1993, pp. 127–129.
211.
KoestlerKoestler, Arthur 1991, pp. 369–370.
212.
See above, Sect. 10.2; ToniettiTonietti, Tito M. 2006a, Chap. IV, pp. 158–170.
213.
Kepler’s editors failed to identify the books implicitly quoted in the passage. Kepler 1993, v. XI 2, p. 513.
214.
Kepler 1993, v. XI 2, pp. 300–301.
215.
De Ursis 1612; entirely quoted and translated in D’EliaDEliaPasquale@D’Elia, Pasquale 1947, pp. 74–117, on pp. 105, 109, 107, 86, 62.
216.
Kepler 1969, v. X, pp. 7 and 21–22. The allegory of Magnetism is at the top on the right, holding in its hand also the needle of the magnetic compass. The one next to it shows the steelyard, which symbolises the way in that the sun has a stronger influence on the near planets, but less on the farther ones. This is followed, in order, by the Geometry of triangles, the numbers of Logarithms, the Telescope and lastly, the Physics of light.
217.
An eclipse of the sun actually took place on June 10th, 1630; Espenak 2008.
218.
Kepler 1993, v. XI 2, pp. 299–314. KeplerKepler, Johannes 1959, v. XVIII, n. 1055 pp. 309 and 534–535, n. 1122 pp. 416–417 and 562. Cf. CasparCaspar, Max 1993, pp. 331 and 350.
219.
D’Elia 1947, pp. 39–48. Pasquale D’EliaDEliaPasquale@D’Elia, Pasquale S.I., however, underestimated the persecution suffered by Galileo GalileiGalilei, Galileo, and attempted to find in the Society of Jesus some manifestations of sympathy for the Copernicans (though hidden, and ambiguous expressions, such as “… Dominum Galileum mathematicum tradat.” [“… Mr. Galileo is to be treated like a mathematician.”]). He covered up the expulsion of the Jesuits from China in 1616 in an appendix, even calling it a “pause”, pp. 71–72. Cf. SchuppenerSchuppener, Georg 1997. The Rudolphine Tables, which were a list of numbers, actually arrived in China. SzczesniakSzczesniak, Boleslaw 1949. HammerHammer, Franz 1950.
220.
CasparCaspar, Max 1993, p. 380.
221.
Kepler 1619 [1969], p. 36. KeplerKepler, Johannes 1997, pp. 66–69.
222.
Kepler 1619 [1969], I pp. 34–40; KeplerKepler, Johannes 1997, pp. 66–79.
223.
CasparCaspar, Max 1993, pp. 59, 75, 144, 157, 161, 329, 339.
224.
CasparCaspar, Max 1993, pp. 45 and 183. KeplerKepler, Johannes 1997, p. xxi.
225.
GingerichGingerich, Owen 1970, p. 297.
226.
Gingerich 1991, pp. 60 and 63.
227.
Stephenson 1994, pp. 8, 11, 249 and 251.
228.
Stephenson 1994, pp. 126–127.
229.
Stephenson 1994, p. 141.
230.
In the Epitome astronomiae copernicanae Epitome Astronomiae Copernicanae@Epitome Astronomiae Copernicanae , the angle at which the Sun was observed from the Earth was 720 parts of 360^∘, that is to say, half a degree; this was the same whole number 720, the smallest, with which musical ratios were to be distributed into two octaves. 720 was also the same fraction of 360^∘ at which the Moon could be seen. This allowed the copy of God on Earth, the measurer that is to say man, to observe a total eclipse of the Sun, and to invent astronomy. KeplerKepler, Johannes 1953, v. VII pp. 277–279. Kepler 1619 [1969], III p. 45–46; KeplerKepler, Johannes 1997, pp. 192–193. Cf. Koyré 1966, p. 295. In CasparCaspar, Max’s edition, KeplerKepler, Johannes made reference to “Book III”, Chap. VI, of the Harmonices Harmonices Mundi Libri Quinque@Harmonices Mundi Libri Quinque mundi …, whereas “720” is found in Chap. VII. The printing error is remaining for a long time.
231.
Stephenson 1994, pp. 13 and 120.
232.
Stephenson 1994, pp. 117 and 141.
233.
Kepler 1949, v. XIV, n. 128 pp. 7–16; n. 130, pp. 21–41; n. 132, pp. 43–59.
234.
Stephenson 1994, pp. 90–91.
235.
Kepler 1949, v. XIV, pp. 13–15 and 459. DickreiterDickreiter, Michael 1973, pp. 76–77 and 130.
236.
Kepler 1949, v. XIV, pp. 29. DickreiterDickreiter, Michael 1973, p. 130.
237.
Kepler 1949, v. XIV, pp. 50–51. DickreiterDickreiter, Michael 1973, pp. 126–127.
238.
Warrain 1942.
239.
Koyré 1966, p. 308.
240.
Holton 1993, pp. 3–23.
241.
Koestler 1991.
242.
Walker 1967, pp. 238–239; Walker 1989a, pp. 72–73. Perhaps for the same reason, our English musicologist treated Vincenzio GalileiGalilei, Vincenzio as a Pythagorean, while on the contrary, this Tuscan lutenist was rather on the side of AristoxenusAristoxenus, as we have seen above in Sect. 6.7 of Part I.
243.
Kepler 1955, v. XVII p. 52. DickreiterDickreiter, Michael 1973, pp. 123–138.
244.
Kepler 1619 [1969], III p. 85; 1997, p. 254. DickreiterDickreiter, Michael 1973, pp. 145–146.
245.
DickreiterDickreiter, Michael 1973, p. 158.
246.
The approximation of Vincenzio GalileiGalilei, Vincenzio appears to be very good, because 18/17 equals 1.05882, compared with the root 1.05946 that is obtained from Table 8.3 of Zhu ZaiyuZhu Zaiyu.
247.
Kepler 1940, v. VI, p. 388. DickreiterDickreiter, Michael 1973, p. 159.
248.
Kircher 1650, pp. 376 and 378. DickreiterDickreiter, Michael 1973, pp. 193–194.
249.
DickreiterDickreiter, Michael 1973, pp. 197–198.
250.
GeymonatGeymonat, Ludovico 1970, v. II pp. 105–107 and 506–514.
251.
See Sect. 6.4 of Part I.
252.
Tangherlini 1974.
253.
Lombardi 2000, passim.
254.
Kepler 1619 [1969], V p. 197; 1997, p. 423.
255.
Kepler 2009, pp. 21, 24, 28–29. Cf. KeplerKepler, Johannes 1619.
256.
For different points of view, see GozzaGozza, Paolo 2000.

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Tito M. Tonietti

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Tonietti, T.M. (2014). Not Only in Latin, but also in Dutch, Chinese, Italian and German. In: And Yet It Is Heard. Science Networks. Historical Studies, vol 47. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0675-6_2

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