Fritjof Capra (39 page)
Authors: The Science of Leonardo: Inside the Mind of the Great Genius of the Renaissance
Tags: #Science; Renaissance, #Italy, #16th Century, #Artists; Architects; Photographers, #Science, #Science & Technology, #Individual Artists, #General, #Scientists - Italy - History - to 1500, #Renaissance, #To 1500, #Scientists, #Biography & Autobiography, #Art, #Leonardo, #Scientists - Italy - History - 16th Century, #Biography, #History
1
. See Kemp (2004), pp. 38–40.
2
. See Keele (1983), p. 22.
3
. Ibid., p. 22.
4
. See Keele (1983), p. 22; Fazio Cardano was the father of the famous mathematician Girolamo Cardano, the founder of probability theory.
5
. See Laurenza (2004b), p. 40.
6
. See Ladislao Reti, ed.,
The Unknown Leonardo
, McGraw-Hill, New York, 1974, pp. 272–73.
7
. See Kemp (1981), p. 194.
8
. Quoted in Richter (1952), p. 322.
9
. See Chapter 7.
10
. For a discussion of the golden section and its connection with the Platonic solids, see Mario Livio,
The Golden Ratio
, Broadway Books, New York, 2002.
11
. Luca Pacioli,
De divina proportione
, Paganinum de Paganinis, Venice, 1509; fascsimile edition of the ms. in the Biblioteca Ambrosiana di Milano published by Fontes Ambrosiani XXXi, G. Biggiogero and F. Riva, eds., Milan, 1966.
12
. See Chapter 1.
13
. See Bramly (1991), pp. 294–95.
14
. Clark (1989), p. 146.
15
. See Hope (2001).
16
. Clark (1989), p. 149.
17
. The portrait, now in the Louvre, is also known as
La Belle Ferronière
.
18
. See Chapter 2.
19
. See Codex Leicester, folio 4r.
20
. See Chapter 1.
21
. See Bramly (1991), p. 308.
22
. See Chapter 2.
23
. Ludovico briefly regained possession of Milan in 1500 before being captured and taken to France as prisoner, where he remained until his death in 1508.
24
. See Keele (1983), p. 25.
25
. See Bramly (1991), p. 307.
26
. See Arasse (1998), p. 210.
27
. Ibid., p. 417.
28
. Kemp (1981), p. 218.
29
. See Bramly (1991), p. 310.
30
. The drawing is now in the Louvre; see Arasse (1998), p. 398.
31
. See Codex Atlanticus, folio 638vd.
32
. See Keele (1983), pp. 28–29.
33
. See also Chapter 2.
34
. Codex Leicester, folio 22v.
35
. See Keele (1983), p. 28.
36
. These rooms, with fading frescoes on their walls, may have been identified recently in a building in central Florence; see
International Herald Tribune
, January 19, 2005.
37
. See Arasse (1998), p. 448.
38
. See White (2000), pp. 208–9.
39
. See Keele (1983), pp. 30–32.
40
. See Bramly (1991), pp. 330–31.
41
. Ibid., p. 332.
42
. Codex Arundel, folio 272r.
43
. See Chapter 1.
44
. Codex Forster I, folio 3r.
45
. See Chapter 7.
46
. See Laurenza (2004b).
47
. Ibid., p. 96.
48
. See Bramly (1991), pp. 348–49.
49
. See Emboden (1987), pp. 62–65.
50
. See Chapter 1.
51
. See Kemp (1981), p. 270.
52
. See Bramly (1991), pp. 356–58.
53
. This bronze group,
Saint John the Baptist Preaching to a Levite and a Pharisee
, can still be seen above the Baptistery’s north door. The life-size statues do seem to exhibit Leonardesque features.
54
. Codex Arundel, folio 1r.
55
. Anatomical Studies, folio 154r.
56
. Ibid., folio 113r.
57
. Ibid., folio 69v.
58
. See Keele (1983), pp. 321–22.
59
. See Farago (2003).
60
. See Emboden (1987), p. 24.
61
. See Bramly (1991), pp. 370–71.
62
. See Laurenza (2004a), p. 87.
63
. See Emboden (1987), pp. 65–68.
64
. See Chapter 1.
65
. See Bramly (1991), pp. 385–86.
66
. See Chapter 9.
67
. Historians long believed that the dissections themselves got Leonardo into trouble with the pope. However, Domenico Laurenza has documented that there were no religious or ethical objections to dissections in Italy at the time. According to Laurenza, it was the clash between Leonardo’s Aristotelian view of the soul and Leo X’s Thomistic view that was at the root of the pope’s ban; see Domenico Laurenza, “Leonardo nella Roma di Leone X,”
XLIII Lettura Vinciana
, Biblioteca Leonardiana, Vinci, 2003.
68
. See Bramly (1991), pp. 384–85.
69
. See Chapter 1.
70
. Drawings and Miscellaneous Papers, vol. I, folio 67r.
71
. The
Leda
was lost or destroyed in the early eighteenth century; see Bramly (1991), p. 465 n. 49.
72
. Arasse (1998), p. 462.
73
.
Trattato
, chapter 25.
74
. See Bramly (1991), p. 397.
75
. See Arasse (1998), p. 152.
76
. See Bramly (1991), p. 398.
77
. Ibid., p. 399.
78
. Quoted by Kemp (1981), p. 349.
79
. Quoted by Bramly (1991), p. 400.
80
. See Chapter 2.
81
. Quoted by Bramly (1991), p. 400.
82
. See Keele (1983), p. 41.
83
. See Introduction.
84
. See Chapter 7.
85
. Anatomical Studies, folio 113 r.
86
. Codex Atlanticus, folio 673 r.
87
. See Chapter 2.
88
. See Keele (1983), p. 40.
89
. See Chapter 2.
90
. Codex Trivulzianus, folio 27r.
91
. See Bramly (1991), pp. 406–7.
92
. Quoted by Bramly (1991), pp. 411–12.
93
. See Carlo Pedretti and Marco Cianchi,
Leonardo: I codici
, Giunti, Florence, 1995; see also Bramly (1991), p. 417.
94
. See Reti (1974).
CHAPTER
5
1
. Thomas S. Kuhn,
The Structure of Scientific Revolutions
, University of Chicago Press, 1962; see also Capra (1996), p. 5.
2
. See, e.g., George Sarton,
The Appreciation of Ancient and Medieval Science during the Renaissance
, University of Pennsylvania Press, Philadelphia, 1955; Marie Boas,
The Scientific Renaissance
, Harper & Brothers, New York, 1962.
3
. “Byzantine Empire” is the term commonly used to refer to the Greek-speaking Eastern Roman Empire during the Middle Ages. Its capital was Constantinople, today’s Istanbul.
4
. See Karen Armstrong,
Islam: A Short History
, Modern Library, New York, 2000, pp. 5–6.
5
. See Chapter 4.
6
. See Sarton (1955), p. 4.
7
. See Pedretti (1999), p. 83.
8
. Ibid., p. 91.
9
. See Chapter 39.
10
. Anatomical Studies, folio 139v.
11
. See George Sarton, “The Quest for Truth: A Brief Account of Scientific Progress during the Renaissance,” in Robert M. Palter, ed.,
Toward Modern Science
, vol. 2, Noonday Press, New York, 1961.
12
. See Chapter 4.
13
. See Kemp (1981), pp. 159–60.
14
. See Fritjof Capra,
The Tao of Physics
, Shambhala, Berkeley, 1975; 25th Anniversary Edition by Shambhala, Boston, 2000, pp. 55–56.
15
. See Capra (1996), p. 18.
16
. See Wilhelm Windelband,
A History of Philosophy
, published originally in 1901 by Macmillan; reprinted by The Paper Tiger, Cresskill, N.J., 2001, p. 149.
17
. See Chapter 9.
18
. See Chapter 8.
19
. See, Chapter 7.
20
. Sarton (1955), p. 171.
21
. Irrational numbers, e.g., square roots, cannot be expressed as ratios, or quotients, of integers.
22
.
Al jabr
refers to the process of reducing the number of unknown mathematical quantities by binding them together in equations.
23
. See Capra (1996), p. 114.
24
. See Sarton (1955), p. 52.
25
. See Capra (1982), p. 306.
26
. Ibid., p. 311.
27
. See Sarton (1955), p. 7.
28
. Ibid., pp. 169–70.
29
. Anatomical Studies, folio 136r.
30
. See Boas (1962), p. 131.
31
. See Chapter 3.
32
. See Chapter 4.
33
. See Kemp (1981), p. 323.
34
. See Emboden (1987), p. 141.
35
. See Chapter 4.
CHAPTER
6
1
. See, for example, Kuhn (1962).
2
. Quoted in Capra (1982), p. 101.
3
. For the classical work on Leonardian paleography, see Gerolamo Calvi,
I manoscritti di Leonardo da Vinci dal punto di vista cronologico storico e biografico
, Bramante, Busto Arsizio, 1982; first published in 1925, republished in 1982 with a foreword by Augusto Marinoni.
4
. A list of the scholarly editions of Leonardo’s Notebooks is given in the Bibliography on pp. 299–301.
5
. Codex Trivulzianus, folio 20v.
6
. Codex Forster III, folio 14r.
7
.
Trattato
, chapter 33.
8
. Codex Atlanticus, folio 323r.
9
. Ibid., folio 534v.
10
. Ms. E, folio 55r.
11
. See Introduction and Chapter 2.
12
. Clark (1989), p. 255.
13
. E. H. Gombrich, preface to
Leonardo da Vinci: Artist, Scientist, Inventor
, Catalogue of Exhibition at Hayward Gallery, Yale University Press, 1989.