INDEX
Page references given in bold indicate illustrations.
abbreviators, discourse against, 151
Ackerman, James, 136
aerodynamics: and water flow, 33, 38, 58, 265, 267, 277–78
and bird flight, 186–87, 200–201, 252–53, 259–79, 269
compared to modern science, 265, 266, 267, 272, 278–79
and compressibility of air, 33, 252–54, 256, 266, 267, 278
and lift-to-drag ratio, 261–65
and mathematical reasoning, 261, 262, 263
and mechanical flight, 186, 251–54, 254, 255, 256, 256–60, 257, 260, 268, 272, 273, 274–76, 278–79
and pressure distribution, 262, 267, 278
and wind tunnel principle, 177, 261, 265, 278
air: as life-sustaining medium, 282, 298
mixed with blood, 284, 285, 286–87, 297, 298–99
Alberti, Leon Battista, 135, 218
algebra, 164, 169, 174, 175, 207
Alhazen (Ibn al-Haitham), 207
anatomy, human: and systemic thinking, 124, 125, 133–34, 284
and blood vessels, 25, 26, 29, 133, 145, 145, 212, 284, 285–88, 304, 305, 306–8
and bodily movement, 131, 133, 153–54, 211–14, 216, 225, 229, 233–34, 237, 240, 241
and bones, 130, 132, 133, 145, 212, 213, 228–31, 229, 230, 232, 233
and comparative anatomy, 133–34, 247–49, 250–51, 269, 272–73
compared to Alberti’s work, 218
compared to Vesalius’s work, 147–50
and critique of reductionism, 151
and dissections, 133, 144, 145, 217, 218, 219, 225–27, 234, 243, 245, 247, 248, 295, 304, 306, 314, 316
drawings related to, 128, 130, 131, 132, 133, 136, 137, 138, 143, 145, 145, 146, 147, 210, 212, 216–17, 220, 221, 224–25, 228–35, 229, 230, 232, 236, 237–41, 238, 242, 243, 243, 244, 245, 247–48, 248, 267, 305, 306, 306, 312
and female anatomy, 143, 143–44
geometry applied to, 131, 135, 137, 139, 141n, 142, 160, 234, 237
and hand, 132, 133, 231–33, 232
and harmonious relation, 136, 142–44, 150, 151
and heart, 134, 285–86, 287, 289–94, 292, 293, 295, 300, 312, plate 10
and integration of art and science, 217–19
and joints, 154, 213, 214, 228–29, 233–34
and Marcantonio della Torre’s work, 134
and mathematical reasoning, 131, 135, 139, 142, 235, 237
and mechanics, 131, 133, 153–58, 213, 234
medical texts used in, 144–45, 219, 221, 224
and muscles, 133, 145, 146, 154, 210, 212, 213, 214, 220, 233–35, 236, 237–40
and nervous system, 129, 131, 133, 135, 145, 211–12, 231, 240–41, 242, 243, 245, 291, 298
painting related to, 218
and plans for De figura umana, 133, 225
and proportion, 128, 135–42, 137
and spine, 214, 216, 230, 230–31, 243, 243
and tendons, 133, 154, 212, 213, 233–35, 237–40
text and figure relation in, 221, 224, 239
and Vitruvian man, 128, 139–42, plate 5
animal studies, 133–34, 136, 137, 138, 144, 243, 247–49, 250–51, 295, 315, 316. See also birds
antiquity, natural science in, 7–8
and anatomy, 144
and formation of the Earth, 86–87
and proportion, 135, 139–40, 141. See also Aristotelianism; Platonism
Arab natural philosophers, 87, 88, 144–45, 207
Archimedes, 162–64, 166–69, 189, 191
architecture, 24, 135, 136, 140, 324
contrasted with Platonism, 139
and Earth as living body, 26, 66
and four-element theory, 40, 66
and gravity, 40, 41, 174, 179, 192, 199
and human physiology, 283, 285
and motion, 173, 178–79, 181, 192
Aristotle: on animals, 108, 144
on bird flight, 252
on plants, 108
Arno river, 23, 71, 71, 73, 94, 95
artworks, Leonardo’s. See drawings; paintings
Avicenna (Ibn Sina), 87, 144–45, 219, 283, 284
beauty, quality of, 136, 137, 150
Bernoulli’s theorem, 35, 184, 262
Bertalanffy, Ludwig von, 311
Bertolini-Meli, Domenico, 173, 176
biology: and systemic thinking, 281, 282
and Aristotelianism, 67n
and Earth as a living body, 65–68, 157
and evolutionary theory, 249–50
and water as life-giving element, 17–18, 20, 21, 22, 63, 281, 282. See also anatomy, human; animal studies; botany; physiology, human
biomimicry, 260
birds, 134, 154, 186–87, 200–201, 251, 252–53, 259–79, plate 1
flying machines modeled on, 156, 186, 251–54, 254, 255, 256, 256–60, 257, 260, 324
blood: and Earth as living body, 25–26, 29, 66, 67
and plants’ sap, 27, 67, 124, 284
and water, 18, 25–26, 27, 29, 63, 67, 118, 284, 285
flow of, 18, 134, 284, 285–88, 294–304, 306–8, 311, 312
mixed with air, 284, 285, 286–87, 297, 298–99
blood vessels, 25, 26, 29, 133, 145, 145, 212, 284, 285–88, 304, 305, 306–8
body, human. See anatomy, human; physiology, human
bones, 66, 67, 130, 132, 133, 145, 212, 213, 228–31, 229, 230, 232, 233
Borgia, Cesare, 73
botany, 97–98
and systemic thinking, 31, 117–18, 124–25
compared to modern science, 112, 113, 116, 118, 119–20, 124–25
and lost manuscript, 31, 112–13
and plant morphology, 113–18, 115, 117
and plant physiology, 113–14, 118–25, 282, 284
and religious symbolism, 98, 102, 104
represented in Leonardo’s drawings, 62, 96, 97, 99, 99–102, 101, 105–7, 106, 107, 108, 109, plate 6
represented in Leonardo’s paintings, 80, 98, 100, 102, 104–5, 106, plate 2, plate 8
and seeds, 124–25
and spiral movement, 62, 98–102, 114
and Trattato della pittura, 112, 114, 115, 120, 121, 123
and vital sap, 31, 67, 113–14, 116–18, 120–23, 284
Bottazzi, Filippo, 125
Botticelli, Sandro, 98
brachial plexus, 243, 244, 245
Bramante, Donato, 33
branching patterns: in human anatomy, 118, 124
Brunelleschi, Filippo, 160
canals, 23–24, 43, 71, 73, 159, 196
Castelli, Benedetto, 46
chiaroscuro, 77
Christ, Leonardo’s representation of, 19, 20, 77, 104, plate 2, plates 7–8
Clagett, Marshall, 165
Codex Arundel: and botany, 105
and evolution, 250
and human physiology, 285
and mechanics, 164, 165, 176, 177, 189, 191, 192, 207
Codex Atlanticus: and aerodynamics, 33, 253, 266
and botany, 122
and element of air, 282
and fluid dynamics, 33, 38, 39, 55, 56
and flying machines, 258, 273, 274
and mechanics, 163, 164, 171, 175, 176, 177, 189, 190, 201, 202–3
Codex Leicester: and fluid dynamics, 40, 51, 51–52, 52
and hydraulic engineering, 32
and mechanics, 168, 168, 170–71, 186, 206
Codex Sul Volo, 154, 259, 260, 266, 267, 268–77, 272, 273, plate 1
Codex Trivulzianus: and aerodynamics, 253
Codices Forster, 176
Codices Madrid: and mechanics, 152, 158, 161, 166, 166–67, 167, 170, 171, 172, 172, 175, 183, 183, 185, 186, 195, 195–97, 197, 200
and water, 17
cognitive science, 131, 156, 318
communicating vessels, 171–72
comparative anatomy, 133–34, 247–49, 269, 272–73
complex systems, theory of, 10, 12, 22, 25, 311
conservation of energy, 181–84, 200, 208
Corte Vecchia, Leonardo’s workshop at, 4, 252, 254
Coulomb, Charles, 186
Deluge, biblical story of the, 82, 83
deluge drawings, 58–62, 59, 60, 61, 278
Descartes, René, 8, 113, 154, 155–56, 157, 181, 198
digestion, 214, 283, 288, 298, 308–11
disorder. See order and disorder, in nature
dissections, 133, 134, 144, 145, 217, 218, 219, 225–27, 234, 243, 245, 247, 248, 295, 304, 306, 314, 316
drawings, Leonardo’s: anatomical knowledge represented in, 128, 130, 131, 132, 133, 136, 137, 138, 143, 145, 145, 146, 147, 210, 212, 216–17, 220, 221, 224–25, 228–35, 229, 230, 232, 236, 237–41, 238, 242, 243, 243, 244, 245, 247–48, 248, 267, 269, 305, 306, 306, 312, plates 3–5, plates 9–10
botanical knowledge represented in, 62, 96, 97, 99, 99–102, 101, 105–7, 106, 107, 108, 109, plate 6
and collaboration with other artists, 99, 99–100
deluge, 58–62, 59, 60, 61, 278
exploded view in, 224, 231, 237, 238
and five Platonic solids, 135
flying machines represented in, 254, 254, 255, 256, 256–58, 257, 260, 260, 273
geological knowledge represented in, 64, 74, 75, 75, 76, 77, 90, 90, 94, 95
and grotesques, 135
mechanical knowledge represented in, 152, 158, 160, 162, 163, 166, 166, 167, 168, 168, 172, 172, 183, 185, 187, 191, 191, 193, 195, 195, 197, 197–98, 198, 203, 203, 205, 207, 208
physiological knowledge represented in, 285, 289–92, 292, 296, 300, 300, 304, 305, 306, 312, 313, 314, 315
self-portrait, 322
and studies for paintings, 99, 99–102, 101, 103, 105, 106
and water studies, 15, 16, 28, 29, 38, 39, 43, 43, 49–51, 50, 53, 54, 55–58, 56, 57, 59, 60, 61, 101, 197–98, 198, 267, 267, 278
in youth, 102
Dürer, Albrecht, 136
dynamic conception of nature, 8–9, 21, 32–33, 68, 99, 137, 139, 249, 281. See also aerodynamics; fluid dynamics
Earth: axial precession of, 88n
drawing of, 90
internal processes of, 87–94
as living body, 25–26, 65–68, 73, 95, 129, 133, 157, 249, 285
structure of, 88, 90–91. See also geology
and ecological design, 324–25
eddy, water. See vortex, water
Einstein, Albert, 199
Emboden, William, 80, 97, 98, 104, 105, 106, 107, 108, 110, 111, 112–13, 114, 116, 119–20, 122, 123, 124
embryology, 124–25, 135, 224, 312–14, 313, 315, 316–18, plate 9
energy, concept of, 181–82. See also conservation of energy
engineering: and geological observations, 65, 69, 73, 94
and hydraulic projects, 23–24, 31–32, 43, 71, 73, 159, 196, 324
Leonardo’s employment in, 31, 32, 43, 158, 196, 252
mechanical, 155, 158–62, 187, 200, 252, 258
and military projects, 73, 158–59, 196. See also machines; mechanics
entropy, 188
equilibrium: hydrostatic, 166–72, 167
static, 162–66
Eratosthenes, 86
Euler, Leonard, 35
evolutionary theory, 75, 249–50
fluid, 28, 33, 35, 37–39, 40, 41, 183–84
mechanical, 158, 162, 164, 166, 166, 168, 170, 171, 174, 185–86, 187, 193, 194, 202, 203, 204, 206, 208, 252, 254
exploded view, in Leonardo’s drawings, 224, 231, 237, 238
explosive phenomena, 202–3
Faraday, Michael, 199
Fasciculus medicinae (medical text), 219, 224
Fermat, Pierre de, 201
fetus, human. See embryology
Feynman, Richard, 34
flight, science of. See aerodynamics floods: and geological studies, 69, 74
and hydraulic projects, 23
represented in Leonardo’s drawings, 278
witnessed by Leonardo, 23. See also Deluge, biblical story of the
Florence: “anatomy of the artists” practiced in, 217–18
as center of Platonism, 139
Giotto’s campanile in, 251, 251
Leonardo’s activity in, 139, 154, 251, 259, 268, 271
fluid dynamics, 33–35
and comparison between air and water, 33, 38, 58, 265, 267, 277–78
and Aristotelianism, 40–41
and Bernoulli’s theorem, 35, 184, 262
and complexity theory, 22
and conservation of energy, 183, 183–84
and conservation of mass, 42–43
and continuity principle, 43, 45, 46
and distinction between flow and wave motion, 36–37
effect of gravity on, 39, 40, 153
and Euler’s work, 35
and experiments, 28, 33, 35, 37–39, 40, 41, 183–84
and flow visualization, 37, 38, 39, 39, 50, 51, 55, 58
and granular materials, 33
and Helmholtz’s work, 48
and mathematical reasoning, 31, 34–35, 39, 41, 42–43, 45, 48, 53, 58, 60
and Navier-Stokes equations, 34, 35
and Newton’s third law, 201
and perpetual motion, 187–88
and rates of flow, 39–40, 44–46
and Richardson cascade, 50
and viscosity (friction), 34, 35, 39, 41–42, 50, 153, 181, 186
and vortex motion, 22, 46–49, 47, 50, 51, 52, 52, 55, 60, 61–62, 101, 124, 281. See also hydrostatics; turbulence; water
flying machines, 156, 186, 251–54, 254, 255, 256, 256–60, 257, 260, 268, 272, 273, 274–76, 278–79, 324
form. See matter vs. form
four-element theory, 36, 40, 66, 88, 173
friction: and aerodynamics, 262
and fluid dynamics, 34, 39, 41–42, 153, 181
and geological erosion, 69
and human physiology, 285, 295, 296–97, 299, 307
and mechanics, 162, 181, 184–87, 195
Galen, 144, 145, 219, 283, 284, 288–89, 294–99, 303, 309, 313
Galileo Galilei, 5, 8, 41, 113, 174, 175–76, 179, 181, 193, 194, 195, 196, 198, 268
geology: and systemic thinking, 66, 133
and Aristotelianism, 66, 89, 91
and catastrophic events, 92–93
compared to modern science, 65, 68, 70, 75, 84, 89, 90, 93–94
and Earth as living body, 65–68, 73, 95, 129, 133
and Earth’s internal processes, 89–94, 95
and Earth’s shape and structure, 89–91, 90
and erosion, 21, 68, 69–70, 74, 77, 78–80, 86, 90, 91, 92, 94, 188
and Gaia theory, 68
and mountains, 69, 85–86, 89, 91, 92, 94
represented in Leonardo’s artworks, 20, 64, 65, 68, 74, 75, 75, 76, 77, 90, 90, 94, 95, 102, 320, plate 8
and sedimentation, 68, 70, 74, 75, 78, 80, 81, 82, 94
tectonic theory anticipated in, 89–93, 153, 180
and time, 65, 74–75, 77, 84, 94–95, 188, 189
and water as geological agent, 21, 66, 67, 68, 69–70, 74, 82, 83, 89, 90, 91, 92, 93, 94, 95, 153, 188
and weathering, 78–80, 188. See also Earth
geometry: and anatomy, 131, 135, 137, 139, 141n, 142, 160, 234, 237
and mechanics, 160, 161, 162, 163, 169, 173, 174, 175, 182, 191–92
and water flow, 42–43. See also proportion
Giacomelli, Raffaele, 252
Goethe, Johann Wolfgang von, 2, 8, 113, 249
golden section, 136
Gould, Stephen Jay, 70, 84, 91
grace, quality of, 211
gravity: Aristotelian concept of, 40–41, 174, 179, 192, 199
center of, 90–91, 92, 191–92, 214
and falling bodies, 192–96
modern theories of, 198–99
Greece, ancient, natural science in. See antiquity, natural science in; Aristotelianism; Platonism
grotesques, Leonardo’s drawings of, 135
Hamilton, William Rowan, 201
harmony, 136, 142–44, 150, 151
Harvey, William, 294, 295, 297, 298
Havel, Václav, 11
heart: action of, 214, 283–89, 293–94, 295, 299–303, 311–12
Aristotle’s conception of, 283
Avicenna’s conception of, 283
Galen’s conception of, 283, 288–89, 294
glass model of aorta of, 301
structure of, 134, 285–86, 287, 289–94, 292, 293, 295, 300, plate 10
heat, of human body, 283, 284, 285, 288, 295, 296–99, 303, 309, 312
Helen of Troy, 189
Helmholtz, Hermann von, 48
Helmont, Jan Baptista van, 119
Heraclitus, 33
herbals, Renaissance, 111
Heron of Alexandria, 44–45
Highmore, Nathaniel, 313n
Hildegard of Bingen, 110
Hippocrates, 219
holistic perspective, 7
in Leonardo’s work, 142–45, 147, 151
Hooke, Robert, 178
hormones, plant, 113, 118, 120, 122, 123, 124
horses, 136, 137, 138, 247–48, 248
humanism, Italian, 139
humors (vital fluids), 18, 26, 27, 113, 116, 157, 281, 284. See also vital spirits
Huygens, Christiaan, 177, 178, 207
hydraulic engineering, 23–24, 31–32, 43, 71, 73, 159, 196, 324
hydrodynamics. See fluid dynamics
impetus, theory of, 173, 179–81, 193, 196, 267, 270, 271
inclined-plane experiments, 41, 186, 193, 193–94, 208, 314
inertia, principle of, 179–81, 197, 208, 267
Ingenhouz, Jan, 120
Islam, natural philosophy cultivated in, 87, 88, 144–45, 207
human, 154, 213, 214, 228–29, 233–34
Jordanus de Nemore, 164
Keele, Kenneth, 155, 228, 233, 292, 303, 312, 313, 316, 321
Kemp, Martin, 68, 77, 84–85, 279, 320
kinematics. See motion
Laurenza, Domenico, 139, 141, 142, 144, 145, 147–51, 217, 221, 224, 228, 247, 256
Leibniz, Gottfried Wilhelm, 182
Lenoble, Robert, 179
Leo X, Pope, 318
Leonardo da Vinci, life of: certified as master painter, 99, 218
employed at Sforza court, 31, 32, 43, 158, 159, 218, 252
and employment as engineer, 31, 32, 43, 158, 196, 252
and flooding in Tuscany, 23
as member of painters’ guild, 218
and Pope Leo X’s ban on dissections, 318
and relations with Cesare Borgia, 73
and relations with Donato Bramante, 33
and relations with Brunelleschi, 160
and relations with Cardano, 160, 161
and renown as engineer, 196
as resident of Amboise, 318
as resident of Florence, 139, 154, 218, 251
as resident of Milan, 31, 77, 81, 131, 139, 154, 158, 189, 218–19, 251–52, 289, 312
as resident of Rome, 59, 252, 289, 312, 318
as student of Verrocchio, 19, 28, 99, 160, 217, plate 2
and visits to seashore, 36–37
and visit to Pavia, 160–61, 162
levers, 154, 161–66, 189, 190, 191, 200, 213
life. See biology linear relationships, 41, 168, 171, 175–78, 192–94, 268
living system, 9–10, 22, 25, 30, 68, 124, 143, 157, 282
Lovelock, James, 68
Lucretius, 87
lungs, 66, 214, 283, 288, 295, 296, 297
machines: development of, 158–62, 200
friction in, 185–86
human body compared to, 154–58
perpetual motion, 187–88. See also flying machines
macrocosm/microcosm relation: and biological processes, 18, 281, 282
difference of underlying forces in, 25, 153
and Earth as living body, 25, 66, 129
and proportion, 136
and qualitative form, 8
and water cycle, 25
Manuscript A: and fluid dynamics, 33, 45, 46–47, 47, 55
and geology, 66
and macrocosm/microcosm relation, 66
and mechanics, 161, 176, 179, 187, 187, 200, 204, 205, 207, 208, 208
Manuscript B: and botany, 123
and flying machines, 254, 255, 256, 256, 257, 258
Manuscript C: and mechanics, 161, 197, 198, 203, 203
and water, 281
Manuscript E: and bird flight, 266–67, 277–78
and mechanics, 165, 165, 176, 178, 181
and water, 17
Manuscript F: and aerodynamics, 271
and mechanics, 200
Manuscript G: and bird flight, 276
and botany, 105, 115, 119, 120, 282
Manuscript H, fluid dynamics in, 42, 50, 51
Manuscript I: and botany, 116
and water, 17
Manuscript K: and bird flight, 259, 266, 268
and water, 17
Manuscript L: and bird flight, 259
and water, 17
Manuscript M: and botany, 116, 117
and mechanics, 193
mathematics: and aerodynamics, 261, 262, 263
and anatomy, 131, 135, 139, 142, 235, 237
and fluid dynamics, 31, 34–35, 39, 41, 42–43, 45, 48, 53, 58, 60
and mechanics, 154, 160, 162, 163–64, 169, 173, 174, 175, 177, 182, 190, 193, 196, 198, 201, 207. See also algebra; calculus; geometry
matter vs. form, in Western science, 7–9, 113
Maxwell, James Clerk, 199
mechanics: Archimedean, 162–64, 166–69, 189, 191
and center of gravity, 191–92, 209
and communicating vessels, 171–72
and energy conservation, 181–84, 200, 208
and energy loss, 184–89, 195, 202, 208
and energy transfer, 202, 204, 206
and experiments, 158, 162, 164, 166, 166, 168, 170, 171, 174, 185–86, 187, 193, 194, 202, 203, 204, 206, 208, 252, 254
and force, 173, 174, 176, 178–79, 183, 190, 198–201
and friction, 162, 181, 184–87, 195
and Galileo’s work, 174, 175–76, 179
geometry applied to, 160, 161, 162, 163, 169, 173, 174, 175, 182, 191–92
and Hamilton’s work, 201
and human anatomy, 131, 133, 153–58, 213, 234
and impact phenomena (percussion), 183, 200, 202–4, 205, 206–8
and Leibniz’s work, 182
and levers, 154, 161–66, 189, 190, 191, 200, 213
and linear relationships, 168, 171, 175–78, 192–94, 268
and mathematical reasoning, 154, 160, 162, 163–64, 169, 173, 174, 175, 177, 182, 190, 193, 196, 198, 201, 207
and Newton’s work, 174, 179, 182, 200, 209, 252
and Pascal’s principle, 169–72
and principle of least action, 201–2, 208
and pulleys, 154, 161, 165, 166, 168, 190, 200, 213, 258, 272
and pyramidal relationships, 175, 176
variables of, 174–76
and work, 200. See also motion
mechanistic philosophy, Leonardo’s organic approach contrasted with, 154–56, 157, 158
medical texts, 144–45, 219, 221, 224
Melzi, Francesco, 112
microcosm. See macrocosm/microcosm relation
Middle Ages, natural science in: and botany, 110–11
and medicine, 144
and proportion, 135
Milan: “anatomy of the doctors” practiced in, 217, 218–19
Aristotelianism taught in, 139
Leonardo’s activity in, 31, 77, 81, 131, 139, 154, 158, 189, 218–19, 251–52, 289, 312
military projects, 73, 94, 158–59, 196
Minot, Charles, 316
momentum, 181
Mondino de Luzzi, 145, 219, 284
morphology, plant, 113–18, 115, 117
Aristotelian concept of, 173, 178–79, 181, 192
and ballistic trajectories, 196–98, 209
circular, 177–78
and Descartes’s work, 181
of falling bodies, 192–96
and Galileo’s work, 175–76, 179, 181, 193, 194, 195, 196, 198
of human body, 131, 133, 211–14, 216, 225, 229, 233–34, 237, 240, 241
and impetus, 173, 179–81, 193, 196, 267, 270, 271
and inertia, 179–81, 197, 208, 267
and momentum, 181
and Newton’s work, 35, 179, 198, 200, 209, 252
and pendulum swing, xxvi, 194–95, 195, 196, 208
perpetual, 187–88
relativity of, 177, 208, 253, 265, 266, 278
spiral, 62–63, 98–102, 114, 124, 177–78
and Torricelli’s work, 198
and waves, 36–37. See also aerodynamics; dynamic
conception of nature
fluid dynamics
gravity
Mozart, W. A., 2
murals in Sforza Castle, 106–7
muscles, 132, 133, 145, 146, 154, 210, 212, 212, 213, 214, 220, 233–35, 236, 237–40
Navier-Stokes equations, 34
Needham, Joseph, 317
neptunism, geological theory of, 87, 88
nervous system, 129, 131, 133, 135, 145, 211–12, 231, 240–41, 242, 243, 245, 291, 298
Newton, Isaac, 1, 2, 3, 8, 35, 39, 113, 154, 174, 188, 198–99, 200, 209, 252
nonlinear dynamics, 34
Nuland, Sherwin, 234, 301–2, 316
O’Malley, C. D., 228, 235, 240, 302, 306
open systems, theory of, 12, 311
order and disorder, in nature, 188, 250
organic conception of nature: and anatomy, 136, 145, 150
and botany, 97, 99, 100, 113, 118, 124
contrasted with mechanistic conception, 154–56, 157, 158
and fluid dynamics, 17–18, 21, 22
Orr, David, 10–11
Ovid, 189
Pacioli, Luca, 135
paintings, Leonardo’s: anatomical knowledge represented in, 218, 251
botanical knowledge represented in, 80, 98, 100, 105, 106, plate 8
botanical symbolism in, 98, 102, 104
and collaboration with other artists, 80, 105
geological knowledge represented in, 20, 74, 77–80, 79, 94, 95, 102, 320, plate 8
and portrait of Prince Ludovico’s mistress, 31
religious signification in, 18–19, 20, 77, 98, 102, 104
states of mind registered in, 36, 216
by title: Annunciation, 251
Baptism of Christ, 19, plate 2
Last Supper, 4, 36, 189, 216, 252
Leda and the Swan, 62, 100–102, 101, 103, 106, 318, 319, 320, 321
Madonna and Child with Saint Anne, 19, 20, 74, 95, 211, 216, 318, plate 7
Mona Lisa, 19, 20, 95, 216, 318, 320–21, plate 11
Saint Jerome, 218
Saint John the Baptist, 62
Virgin of the Rocks, 19, 20, 31, 77–80, 79, 94, 98, 100, 102, 104–5, 106, plate 8. See also murals in Sforza Castle
Pascal, Blaise, 169–72
Pavia, Leonardo’s activity in, 160–61, 162
Pedretti, Carlo, 112
pendulum motion, xxvi, 194–95, 195, 196, 208
perception, 131
percussion (impact phenomena), 183, 200, 202–4, 205, 206–8
perpetual motion, 187–88
photosynthesis, 119–20
physics. See gravity; mechanics; motion
physiology, human: and aging, 306–8
and Earth as living body, 66–68, 157, 281, 285
and analogy with plant physiology, 284
and Aristotelianism, 283
and blood-air mixture, 284, 285, 286–87, 297, 298–99
and blood flow, 18, 134, 284, 285–88, 294–304, 306–8, 311, 312
and body heat, 18, 283, 284, 285, 288, 295, 296–99, 303, 309, 312
and digestion, 214, 283, 288, 298, 308–11
drawings related to, 285, 289–92, 292, 296, 300, 300, 304, 305, 312, 313, 314, 315
and embryology, 124–25, 135, 224, 312–14, 313, 314, 315, 316–18, plate 9
and friction, 285, 295, 296–97, 299, 307
and Galen’s work, 283, 284, 288–89, 294–99, 303, 309, 313
and Harvey’s work, 294, 295, 297, 298
and heart action, 214, 283–89, 293–94, 295, 299–303, 311–12
and heart structure, 285–86, 287, 289–94, 292, 293, 295, plate 10
and liver, 304, 305, 306–9, 317
and lung action, 214, 283, 288, 295, 296, 297
and macrocosm/microcosm relation, 66, 281, 282
and respiration, 214, 283, 288, 296
and vital spirits, 232, 283, 284, 285, 288–89, 295, 298–99, 302, 303, 309, 310, 312. See also anatomy, human
Piomelli, Ugo, 49
plants: as decorative motifs in art, 97–98
hormones in, 113, 118, 120, 122, 123, 124
medical properties of, 110, 111
morphology of, 113–18
photosynthesis in, 119–20
physiology of, 113–14, 118–25, 282, 284
religious symbolism of, 98, 102, 104. See also botany
plutonism, geological theory of, 87
Poincaré, Henri, 42
Pollaiolo, Antonio del, 217
Polyclitus, 135
Prigogine, Ilya, 311
printing press, 224
proportion, 135–42
Ptolemy, 86
pulleys, 154, 161, 165, 166, 168, 190, 200, 213, 258, 272
pyramidal relationships, 175, 176. See also linear relationships
qualities, science of, 8, 10, 139
Raphael, 1
reductionism, critique of, 151
relativity, general, Einstein’s theory of, 199
relativity of motion, 177, 208, 253, 265, 266, 278
religion, as theme in Leonardo’s artworks, 18–19, 20, 77, 98, 102, 104
Reti, Ladislao, 161
Richardson cascade, 50
Richter, Jean Paul, 105
Roberts, Jane, 107
rock cycle, 92
rock formations. See geology
Rome, ancient, natural science in. See antiquity, natural science in
Rome, in Renaissance period, Leonardo’s activity in, 59, 252, 289, 312, 318
Santerno river, 73
sap, in plants, 27, 31, 67, 113–14, 116–18, 120–23, 284
Saunders, J. B., 228, 235, 240, 302, 306
sculpture, 5, 84, 135–36, 160, 217, 251, 251
self-organizing systems, 68, 318
self-portrait, Leonardo’s, 322
Sforza Castle, Milan, Leonardo’s murals in, 106–7
Sforza court, Milan, Leonardo’s activity at, 31, 32, 43, 158, 159, 218, 252
Shakespeare, William, 2
skeleton. See bones
skull, human, 129, 130, 131, 135
solids, five Platonic, 135
soul, Leonardo’s doctrine of: and Aristotelianism, 153, 283
and brain as “seat of the soul,” 131, 241
compared to Cartesian doctrine, 156, 157
and Earth as living body, 67
and fetal development, 317–18
and integrative function, 156, 157
spine, human, 214, 216, 230, 230–31, 243, 243
spiral movement, 62–63, 98–102, 114, 124, 177–78
spiritual force and action, 199, 211–12, 240, 298
Star of Bethlehem, botanical drawing of, 62, 96, 101, plate 6
Steno, Nicolas, 70n
Stoics, natural philosophy of, 86
Strabo, 86
stratigraphy, 70n
sun, life-sustaining power of, 282, 284
systematic approach, 6, 136, 161, 197, 218, 252, 281
systematic experiments and expositions, 40, 41, 81, 129, 158, 190, 204, 231, 233, 254
systematic studies, 218
systemic thinking, ix–x, 4, 5, 6, 7–9, 11, 13, 84, 117, 151, 185, 196, 208, 249, 323
systemic conception of life, 25
systemic understanding of life, xii, 10
systems science, 8
systems view of life, x
tectonic theory, 89–93, 153, 180
tendons, 66, 132, 133, 154, 212, 213, 233–35, 237–40
thermodynamics, laws of, 184–85, 188, 208, 250
time: and biological evolution, 249, 250
and geological processes, 65, 74–75, 77, 84, 94–95, 188, 189, 249
and irreversible processes, 188–89, 208
Titian, 147
topological thinking, 42, 48, 73, 142
Torre, Marcantonio della, 134
Torricelli, Evangelista, 198
Trasimene, lake, 73
Trattato della pittura, 93, 112, 114, 115, 115, 120, 121, 123, 142
turbulence: and air flow, 58–62, 59, 60, 261, 263, 267, 281
and blood flow, 18, 285, 295, 296, 297, 299, 300, 300, 301, 303
drawings related to, 49–53, 50, 51, 52, 53, 54, 56, 57, 59, 60, 61
experiments related to, 37–38
and water flow, 22, 33–35, 37–38, 49–62, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 281
Tuscany, Leonardo’s activity in, 65, 295. See also Florence
uniformitarianism, geological theory of, 84
velocity, angular vs. linear, 177–78
Verrocchio, Andrea del, 19, 28, 99, 160, 217, plate 2
Vesalius, Andreas, 147–50, 148, 149, 150
viscosity, 34, 35, 39, 41–42, 50, 153, 181, 186
vision, 131
visualization, flow, 37, 38, 39, 39, 50, 51, 55, 58
vital spirits, 232, 283, 284, 285, 288–89, 295, 298–99, 302, 303, 309, 310, 312
Vitruvian man, 128, 139–42, plate 5
vivisection, 133n, 294–95, 309
vortex, water, 22, 46–49, 47, 50, 51, 52, 52, 55, 60, 61–62, 101, 124, 281
vulcanism, geological theory of, 87
water: and air flow, 33, 38, 265, 267, 277–78
and blood, 18, 25–26, 27, 29, 30–31, 63, 67, 118, 284, 285
and analogy with plants’ sap, 27, 31, 117–18, 124
distillation of, 18, 28, 29, 285
and Earth as a living body, 25–26, 29, 67, 285
geological significance of, 21, 66, 67, 68, 69–70, 74, 82, 83, 89, 90, 91, 92, 93, 94, 95, 153, 188
as humor, 18, 26, 27, 157, 281, 284
incompressibility of, 33, 39, 42
jets of, 49, 50, 50, 55–57, 197–98, 198, 209
as medium for biological processes, 17–18, 20, 21, 22, 63, 281, 282
religious significance of, 18–19, 20
represented in Leonardo’s drawings, 15, 16, 28, 29, 38, 39, 43, 43, 49–51, 50, 53, 54, 55–58, 56, 57, 59, 60, 61, 101, 197–98, 198, 267, 267, 278
represented in Leonardo’s paintings, 18–20
and water cycle, 24–31, 67, 284–85
and waterfalls, 55–58, 56, 57. See also fluid dynamics
wave motion, 36–37
Windsor Collection: and anatomical drawings, 130, 132, 133, 137, 138, 143, 143, 145, 146, 216n, 220, 221, 228, 229, 230, 232, 233, 236, 237, 238, 239, 241, 242, 243, 244, 247, 248, 269, 269, plates 3–4, 9–10
and anatomical notes, 151
and botanical drawings, 106, 106, 107, 107, plate 6
and deluge drawings, 59, 59–62, 60, 61
and embryological drawings, 312, 314, 315, 316, plate 9
and geological drawings, 75, 75, 76
and physiological drawings, 285, 289–92, 292, 300, 300, 304, 305, 312
and representations of bodily movement, 214, 214, 215
and water studies, 17, 29, 43, 49–51, 50, 52, 53, 53, 54, 55–58, 56, 57
wind tunnel, 177, 261, 265, 278
Wren, Christopher, 199
Zöllner, Frank, 137