To Explain the World: The Discovery of Modern Science (70 page)

complex numbers, 163

cone, volume of, 19

conic section, 40, 194, 235, 237

ellipse and, 318–19

parabolas and, 344–45

conservation of energy, 340–41

conservation of momentum, 197, 235, 362–63

Constantine I, emperor of Rome, 48, 49

Constantinople, 104, 253

constellations, 56–57Copernicus, Nicolaus, 72, 134, 141, 146, 307

Arabs and, 107, 117

astronomers’ reception of, 157–58

Descartes and, 204

Francis Bacon and, 201

Galileo and, 173, 177–79, 181–88

Kepler and, 162–63, 166–73, 255

Newton and, 237n, 251

planetary motion and, 48–49, 85–86, 90–91, 95, 117–18, 124, 141n, 148–63, 172, 228, 240

Ptolemaic theory and, 304–7, 325

relative sizes of planetary orbits and, 320–21

religious opposition to, 155–57, 181, 184–88, 213

Tycho’s alternative to, 158–61

Córdoba, 112, 114, 123

Cosimo II di Medici, 178

cosine, 296, 309, 313

cosmic rays, 263

counter-Earth, 78

Crease, R. P., 381

Cremonini, Cesare, 173, 180

Crombie, A. C., 137, 375

Ctesibius, 35, 41

cube, 10, 12, 17, 162, 163n, 275, 278–79

cubic equations, 109

Cutler, Sir John, 220

Cuvier, Georges, 265

Cyril of Alexandria, 50–51

d’Alembert, Jean, 248

Dalton, John, 11, 259

Damascus, 104, 117, 118

dark energy, 83, 165, 265

dark matter, 9, 264

Darwin, Charles, 24, 172, 200, 248, 265–66, 383

days of the week, 77n

De analysi per aequationes number terminorum infinitas
(Newton), 224

Dear, Peter, 125, 269, 373, 380

deduction, xv, 19–21, 132, 164, 189, 197, 201–3, 205, 247, 264–65, 289

deferents, 88–92, 93, 97, 110, 149, 150, 160, 180, 303–6, 324–24

Demetrius of Phaleron, 32

Democritus, 7, 11–14, 44, 46–47, 65, 110–11, 260

De Motu (On Motion)
(Galileo), 173

density

of Earth vs. water 240

Newton and, 232

De Revolutionibus
(Copernicus), 153–58, 183–84

derivative, 223

Descartes, René, 37, 40, 141, 194, 201, 202–14, 218, 223, 229, 236, 246, 248, 342, 346–48

Descartes’ law, 37, 207

Dialogue Concerning the Two Chief Systems of the World
(Galileo), 185–87, 193, 199

Dialogue Concerning Two New Sciences
(Galileo), 190, 193–94

Dicks, D. R., 373

Dietrich of Freiburg, 128, 209

diffraction, 205, 222

Diogenes Laertius, 4, 44, 57, 63

Dionysius II, of Syracuse, 10, 18

Diophantus, 40, 107

Dioscorides, 105

Dirac, Paul, 152, 261–62, 383

Discourse on Bodies in Water
(Galileo), 181, 190

Discourse on Light
(al-Haitam), 110

Discourse on Method
(Descartes), 203, 205, 212–13

displacement, 38–39, 292–93

DNA, 266

dodecahedron, 10, 12, 162, 163n, 275, 279

Dominicans, 127–30, 140

Donne, John, vii, 42

Doppler effect, 221

Doubts concerning Galen
(al-Razi), 111

Drake, S., 378, 379

Dreyer, J. L. E., 84

Droysen, Johann Gustav, 31

Duhem, Pierre, 99, 146, 260, 378

Duns Scotus (Johannes Scotus Erigena, John the Scot), 225

Earth

Aristotle on, 24–25, 49, 64–66, 70–71, 132, 143

axis of rotation, 58, 148, 152–53, 302

axis wobble of, 74–75

Copernicus on, 86, 95, 148–56

density of, 240

distance to Moon, 63, 66–68, 70, 72–73, 75, 83, 295–301

distance to planets, 149–50

distance to stars, 70

distance to Sun, 63, 66–68, 70, 75, 83, 90, 164, 295–301

epicycles of planets and, 303–7

Eratosthenes on, 75–76, 301–2

Galileo on, 184–88

Greeks on motion of, 10, 70–72, 79–86, 89, 153–54

Heraclides on, 89

     medieval Europe and motion of planets around, 124, 132, 136, 143

moon as satellite of, 178, 181, 363 (
see also
Moon)

motion around Sun, debated, 89, 95, 143

Newton and ratio of masses of Sun and, 239

orbit of, circular vs. elliptical, 53, 59, 91, 152

orbit of, eccentricity, 167, 324

orbit of, Kepler on, 162, 166–67

orbit of, speed, 59, 152

precession of orbit, al-Zarqali measures, 113–14

Ptolemy on motion of planets around, 88–92, 94–95, 143, 324–25

Pythagoreans on motion of, 72, 78, 151, 153–54

relative speed of Jupiter and, 221–22

rotation of, 70–71, 85–86, 108, 134–36, 148, 151, 153–54, 241, 246

shape of, Descartes and, 204

shape of, equatorial bulge, 153

shape of, flat, 65, 78

shape of, oblate, 241, 246

shape of, spherical, 49, 63–66

sidereal period and, 171

size of, 53, 63, 65n, 67–68, 70, 75–76, 107–9, 228n, 301–2, 311–13, 362

tides and, 184–85

earth, as element, 6, 10, 12, 64–66, 259

Easter, date of, 60–61

eccentricity, 167–69, 317–19, 324

eccentrics, 87–88, 91–95, 98, 112, 142, 151–53, 166, 169, 254

eclipses

lunar, 59, 63–64, 94, 298

planets, 94

solar, 4, 63, 66–67, 72–73, 83, 94, 298

ecliptic, 57, 73–74, 177

Ecphantus, 153

Egypt, xiv, 1, 4, 7, 31–33, 46, 55, 104–5, 116.
See also
Alexandria

Einstein, Albert, 34, 172, 204n, 222–23, 248–53, 260–61

electromagnetism, 250, 257–64

electrons, 9, 34, 180, 247, 257, 260–64

electroweak theory, 263–64

elementary particles, 9, 11, 14, 21, 180, 247, 249, 262–63, 267

elements

alchemists on, 11

Aristotle on, 10, 64–66

chemical, identified, 11, 259

Greeks on four, 6, 10, 12

medieval Europe and, 125

Plato on, 10, 18, 45

Elements
(Euclid), 15, 17–19, 35, 47, 51, 69, 126, 223, 232, 275, 285

Elizabeth I, queen of England, 170, 257

ellipses, 40, 167, 235, 255, 316–19

foci of, 167, 316, 318

parabola and, 343

elliptical orbits of planets, 117–18, 167, 231, 324–28

Empedocles, 6–7, 10, 12, 45, 111

empiricism, 132–33, 201–2, 253

Encke’s comet, 250

Epicurus of Samos, 22, 46, 48

epicycles, xv, 87, 91n, 98, 254

Arabs and, 110, 112, 117

Copernicus and, 151–53, 182

equal-angles and equants and, 324–25

inner and outer planets and, 303–7

Kepler and, 166

medieval Europe and, 141–42

Ptolemaic model and, 88–95, 97–98, 149–53, 155, 168, 254–55

Tycho and, 160

Epitome of Copernican Astronomy
(Kepler), 168

Epitome of the Almagest
(Regiomontanus), 141

equal-angles rule, 36–37, 208–10, 221, 290

equal-area rule, 168–69, 231, 323–28

equant, 87, 92–95, 117, 151–52, 166, 169, 254, 323–28

equinoxes, 58, 60–61

precession of, 74–75, 107, 118, 153, 241–42, 244, 248

Eratosthenes, 51, 75–76, 107, 301–2

ether, 10, 258

Euclid, 15, 17–19, 35, 37, 47, 51, 69, 105, 119, 126, 206, 210, 223, 232, 272, 275–77, 285

Euctemon, 59–60, 81, 152

Eudoxus, 18–19, 51, 80–87, 95, 97, 142

Euler characteristic, 278

Europa, 177–78

Europe, medieval, 1, 105, 124–43

scientific revolution and, 253

Eusebius, bishop of Caesarea, 58

evolution, 24, 164–65, 265–66

experiment, xv, 255

Aristotle and, 29

Descartes and, 204, 208–9, 213

development of, 189–202

Galileo and, 192–94, 200, 213

Greeks and, 24, 29, 35, 69

Huygens and, 195–97

hypothesis and, 213

medicine and, 41–43

medieval Europe and, 133, 137

Newton and, 218–19

prediction and, 146

explanation, description vs., xiii, 99

falling bodies

Aristotle and, 25–29, 51, 64–66, 71, 129, 133, 173, 190

da Vinci and, 202

Descartes and, 204

Earth’s rotation and, 135

experiments with inclined planes, 192–94, 200, 339–43

falling drops, 33, 288–89

Galileo and, 173, 190–94, 200, 213, 240, 339–46

Greeks and, 25–27, 33

Huygens and, 195–96, 342

mean speed theorem and, 140

medieval Europe and, 135–37, 140

Moon’s orbit and, 228–30, 235, 242, 361–62

Newton and, 190, 225–26, 228–30, 235, 242, 245

Oresme and, 136–37

terminal velocity and, 25–26, 286–88

thrown objects (projectile), 27, 51, 71, 133–35, 156, 161, 170, 194, 342–46

Tycho and, 161

Fantoli, A., 378

Faraday, Michael, 258

Fermat, Pierre de, 37, 208, 221, 331, 348, 358

fermions, 263

field concept, 21, 250, 262

fine-tuning, 82–83, 85–86, 89–90, 149–51, 155, 255

Finocchiaro, M. A., 378

fire

Boyle and, 200

as element, 6, 10, 12, 64, 259

Lavoisier and, 259

first mover, doctrine of, 26

first principles, 27, 97

Fitzgerald, Edward, 109

floating and submerged bodies, 38–39, 181, 291–94