INDEX

Aaboe, Asger, 186

Abbott, E. A., 279

Abel, Niels Hendrik, 27, 120

Abscissa, 256

Abstraction, 15, 30 ff.

Acceleration, 294, 342, 352 ff.

centripetal, 350, 352 ff.

instantaneous, 365 ff.

in sinusoidal motion, 427

Adams, Oscar S., 186

Addition of ordinates, 442 ff.

Advancement of Learning, 283

Aesthetics, 24, 550

Age of Reason, 24 f., 240, 411 f.

Air, motion of, 438 ff.

Alberti, Leone Battista, 216, 229, 509

Alder, Henry L., 521, 540

Alexander the Great, 17, 153 f.

Alexandria, 17 ff., 136, 153

Alexandrian Greeks; see Greeks

Alexandrian library, 154

Algebra, 12, 17, 22 ff., 52 f., 253, 255, 478 ff.

as language, 94 ff.

of logic, 495 f.

modular, 487 ff.

of sets, 491 ff.

Algebraic transformations, 102 ff.

Al-Khowarizmi, 19

Almagest, 19, 158, 161, 192

Amplitude, 424

Analogy, 40 f.

Analysis, 24

Analytic geometry; see Coordinate geometry

Analytical Theory of Heat, 446

Anatomy, 202, 214

Angle, critical, 180

exterior, 127

interior, 127

Antiderivative, 389

Apollonius, 18, 19, 142, 148, 155, 329

Approximation, 71

Arabs, 19 ff., 27, 57, 96, 194, 198, 200

Archimedes, 18 ff., 155 ff., 228, 329, 455

Architecture, 37 f.

Area, 129, 131 ff., 366

by integration, 394 ff.

Aristarchus, 327

Aristotle, 15, 19, 47, 149, 194, 200, 228, 282, 286, 307

Arithmetic, 12, 20 f., 30 ff., 52 ff., 58 ff., 199, 478 ff.

modular, 484 ff.

Arithmetic mean, 502 f.

Armitage, Angus, 362

Ars Magna, 203

Art; see Mathematics as an art, Music, Painting

Associative axiom, 76 f., 479, 483, 492 f.

Astrology, 14, 199

Astronomy, 13 ff., 18, 23, 85, 124, 155, 157 f., 171 ff., 188 ff., 199, 253 f., 289, 326 ff.; see also Heliocentric theory, Ptolemaic theory

Athens, 15, 17

Atomic weight, 88 ff.

Atoms, 88 ff.

Augustine, Saint, 1, 9, 198

Average, 82 f., 502 ff.

Avogadro, A., 88

Axioms, 16, 26, 50 f., 75 ff., 126, 541 ff.

of Euclid, 126 f., 452 ff.

of physics, 324; see also Gravitation, Newton’s laws of motion, Parallelism

Babylonia, 12 ff., 17 ff., 31 ff., 45, 61, 68, 85, 96, 118, 171, 188, 199

Bacon, Francis, 1, 23, 280, 283

Bacon, Roger, 205

Ball, W. W. Rouse, 29, 93, 122, 152, 186, 208, 414

Barrow, Isaac, 336, 368

Base, 61, 85 ff.

Baseball arithmetic, 481 ff.

Baumgardt, Carola, 362

Bell, A. E., 305

Bell, Eric T., 29, 56, 249, 362, 414, 477, 498

Benade, Arthur H., 451

Bernoulli family, 24, 437

Bessel, Friedrich Wilhelm, 456

Binoculars, 181

Biology, 26, 83, 499 ff., 526; see also Anatomy, Eye

Blunt, Anthony, 230

Bohm, David, 540

Bolyai, John, 452, 456 ff.

Bonner, Francis T., 91, 305, 362, 480

Bonola, Roberto, 477

Boole, George, 495 f., 498

Born, Max, 540

Boyle, Robert, 281, 284

Boys, C. V., 152

Brahe, Tycho, 206, 327

Brianchon, Charles J., 242, 245 f.

Bronowski, J., 556

Brown, Lloyd A., 186, 435

Brunelleschi, 215

Bunim, Miriam, 230

Burtt, E. A., 305, 363

Bury, J. B., 556

Butterfield, Herbert, 305, 363

Byzantine Empire, 19, 21, 198, 200

Cajori, Florian, 208

Calculus, 24, 242, 253, 336, 365 ff.

history of, 409 ff.

of variations, 24

Calendar, 13, 124, 157 f., 199

Camera, 182

Cannizzaro, S., 88

Cantor, Georg, 462, 474

Cardan, Jerome, 22, 27, 119 f., 203, 205, 208, 255, 522

Carnot, L. N. M., 243

Carslaw, H. S., 477

Caspar, Max, 363

Casting out nines, 488 ff.

Catholic Church, 20, 198 ff., 206 f.

Cauchy, Augustin Louis, 411

Cause, 282 f.

Cavalieri, Bonaventura, 410

Cavallini, 210

Cesalpinus, Andrew, 204, 283

Chamberlin, W., 186

Chasles, Michel, 242

Chemistry, 89 ff., 155, 480

Childe, V. Gordon, 29

China, 12

Christianity, 19 f., 194, 198, 206, 227 f.

Cimabue, 210

Circle, 129, 156, 241, 254

equation of, 262 f.

Clagett, Marshall, 57, 195

Clark, Kenneth, 230

Clock, 254, 416, 433

Cohen, I. Bernard, 305, 363

Cohen, Morris R., 57, 540

Cole, Rex V., 230

Colerus, Egmont, 93, 122, 414

Columbus, Christopher, 136

Commutative axiom, 76 f., 483, 492 f.

Compass, 21, 201

Complex numbers, 26

Computers, 86 ff.

Condensation, 439

Cone, 241

Congruence, 129

arithmetic, 484 ff.

Conic sections, 142 ff., 241, 255; see also Ellipse, Hyperbola, Parabola

Conic Sections, 142

Construction problems, famous, 148

Coolidge, Julian L., 57, 230

Coordinate geometry, 22, 242, 250 ff.

Coordinates, 257, 308 ff.

Copernicus, Nicolaus, 21, 192, 206 f., 253, 326 ff., 551

Correlation, 516 ff.

Cosine, 159 ff.

Courant, Richard, 152, 498

Crombie, A. C., 208, 306

Cross ratio, 238, 247

Curve of an equation, 269 ff.

Curve fitting, 511 ff.

Curvilinear motion, 307

Cylinder, 156

Cylindrical surface, 465

Da Vinci, Leonardo, 202 ff., 208 f., 215 f., 225 ff., 229 f., 509

D’Alembert, Jean Ie Rond, 24, 411, 437

Dalton, John, 88

Dampier-Whetham, W.C.D., 195, 208, 306, 363

Dantzig, Tobias, 93

David, Edward E., Jr., 451

Davis, Philip J., 93

De Magnete, 283

De prospeitiva pingendi, 223

De Santillanà, Giorgio, 363

Decimal system, 85

Deduction, 30, 41 ff., 128

Deductive method, 45 ff., 128, 150

Deetz, Charles H., 186

Deferent, 192, 327

Definitions, 51

Della Francesca, Piero, 216, 229

Della Pittura, 216

Derivative, 375

Desargues, Girard, 234 ff., 239, 242, 244, 246, 248

Descartes, René, 22 f., 176, 205 ff., 240, 242, 250 ff., 255, 257, 273, 277 ff., 284 f., 288, 368, 476, 495, 523, 543

Description versus explanation, 288

Dialogue on the Great World Systems, 333

Dialogues Concerning Two New Sciences, 285, 307

Dido, problem of, 135

Differential equation, 24

Differential geometry, 24

Differentiation, 376

Dimensions, three, 273 ff.

four, 275 ff.

Diophantus, 18

Direct equation, 308

Directrix, 142 f.

Discourse on Method, 240, 252 f.

Discourses and Mathematical Demonstrations Concerning Two New Sciences, 285

Dispersion of data, 503 ff.

Displacement, 418

Distributive axiom, 78, 103 f., 483

Donne, John, 202

Drake, Stillman, 363

Dreyer, J. L. E., 195, 363

Duality, 242 ff.

Duccio, 210 ff.

Dunnington, G.W., 477

Dürer, Albrecht, 216 ff., 509

Durrell, Clement V., 477

Earth, acceleration of, 350

circumference of, 136, 165

density of, 348

distance from moon, 171 f.

shape of, 352, 366

volume of, 348

Eastern Roman Empire; see Byzantine Empire

Easton, Stewart C., 208

Eclipse, 7, 174

Economics, 7, 24, 26, 33, 476

Egypt, 12 ff., 17 ff., 31 ff., 45, 68, 96, 118, 153 ff., 171, 188, 199

Einstein, Albert, 90, 549

Electricity, 25

Electromagnetic waves, 25; see also Radio

Elements of Euclid, 17, 125 ff., 142

Ellipse, 142 f., 222, 241, 253, 271, 328 ff., 334

equation of, 272 f.

Ellis, Havelock, 556

Energy, 33, 90

Enlightenment; see Age of Reason

Epicycle, 192, 327

Equation of a curve, 258 ff.

Equations, solution of, 106 ff., 255

first degree, 107

higher degree, 119 ff.

linear, 107

quadratic, 107 ff., 112 ff.

second degree, 107 ff., 112 ff.

Equator, 165

Equilibrium position, 418

Equivalent figures, 129

Eratosthenes, 136, 154, 157

Error curve, 507

Escape velocity, 401 ff.

Essay on Conic Sections, 239

Ethics, 24, 476

Euclid, 17 f., 19, 125 ff., 142, 154, 155 f., 200, 228, 329, 453

Euclid Vindicated from All Defects, 455

Euclidean geometry, 17 f., 25, 123 ff., 149 f., 159, 193 f., 247 f., 281 f., 395, 452 ff.

Eudoxus, 17, 125, 190

Euler, Leonhard, 24, 411, 437

Eves, Howard, 29, 93, 152, 414

Evolution, theory of, 452

Experimentation, 4, 40, 283 f.

Exponents, 96 ff.

Extrasensory perception, 537

Eye, 181 f., 234

Factoring, 104

Farrington, B., 195, 306

Fermat, Pierre de, 1, 22, 182 f., 240, 242, 250, 252, 255, 257, 277, 368, 522

Ferrari, Lodovico, 119

Fletcher, Harvey, 451

Focus, 142 ff.

Force, 33, 193

centripetal, 353

of gravitation, 326, 341 ff.

Foreshortening, 213, 221

Formula, 287 ff., 291

Fourier, Joseph, 445 f., 555

Fourier’s theorem, 446 ff.

Fraction, 62 ff.

Frank, Philipp, 477

Frequency distribution, 507

binomial, 533 f.

normal, 507

Frequency of sinusoidal motion, 425

Freund, John E., 521, 540

Function, 23, 290 ff.

linear, 299

periodic, 422

quadratic, 300

Fundamental tone, 448

Gade, John A., 363

Galen, 156, 204, 282

Galilei, Galileo, 23 ff., 205 ff., 240, 251, 254, 283 ff., 306, 307 ff., 325, 332, 334, 343, 363, 390, 412, 436 f., 499, 547, 549

Galois, Évariste, 27, 120

Galton, Sir Francis, 501, 517

Gamow, George, 93, 477, 540

Gases, 155

Gauss, Karl Friedrich, 25, 27, 455 ff., 549

Genetics, 83 f., 526

Geocentric theory; see Ptolemaic theory

Geographica of Eratosthenes, 157

Geographica of Ptolemy, 158

Geographical explorations, 200

Geography, 157 f., 332

Geometry, 12, 17 ff., 24, 32, 36, 123 ff., 199; see also Coordinate geometry, Euclidean geometry, Non-Euclidean geometry, Projective geometry

four-dimensional, 275 ff.

Geometry of Descartes, 253 f.

Germanic tribes, 20, 197

Ghiberti, 229, 509

Gibbon, Edward, 2

Gilbert, Wm., 283

Giotto, 213

Goethe, Johann Wolfgang, 2

Goldbach, Christian, 46

Graunt, John, 500

Gravitation, 294, 326 ff., 336, 341 ff., 360 f., 407 ff.

law of, 341, 547

Great circle, 169, 254

Greek art, 37

Greek science, 21, 138, 153 ff., 171 ff., 176, 187 ff., 281 ff., 288

Greeks, 2, 14 ff., 21, 23, 27, 31, 46 ff., 58 ff., 68 f., 96, 123 ff., 148 ff., 153 ff., 187 ff., 200, 203, 205, 213, 250, 452 f., 468 f.

Gunpowder, 21, 201

Haldane, E. S., 279

Hall, A. R., 363

Halley, Edmond, 336, 338, 436, 500

Hamilton, Edith, 57

Hardy, G. H., 556

Harmonics of a musical sound, 448

Harrison, John, 433

Harvey, Wm., 204, 283

Heat, 24

Heath, Sir T. L., 152, 186

Hebrews, 14

Heliocentric theory, 21, 23, 253 f., 326 ff.

Hellenistic world; see Greeks

Helmholtz, Hermann von, 231, 448, 451

Heron, 139, 155

Hexagon, 241

Hubert, David, 25

Hindus; see India

Hipparchus, 18 f., 21, 158, 161, 165, 170, 190 ff., 282

Hippias, 125

Hippocrates, 125

Hofmann, J. E., 208

Holton, Gerald, 91, 306, 325, 363

Hooke, Robert, 254, 284, 338, 417, 433, 436 f., 440

Hooke’s law, 417, 429, 547

Huff, Darrell, 521

Huygens, Christian, 254, 284, 352, 368, 433, 436

Hyperbola, 142 f., 222, 241, 253

Hypersphere, 276

Idealization, 38 f.

Ideas of Plato, 34 ff.

Increment, 374

Indefinite integral, 389

India, 12, 19 ff., 27, 61, 72, 96, 200

Indirect method of proof, 128

Induction, 40 ff., 45

Inertia; see Mass

Infinite series, 24

Infinity, 236 f.

Instant, 368

Instantaneous rate of change, 367 ff.

Integer, 58 ff.

Integral, 389

as a limit, 404 ff.

Integration, 389

Intersection of sets, 492

Interval of time, 368

Invariant, 238, 247 f.

Ionia, 47, 188

Irrational numbers, 65 ff., 124

Isotope, 89 f.

Ivins, Wm. M., Jr., 231, 249

Jeans, Sir James, 57, 196, 363, 451

Johnson, Martin, 231

Jones, Burton W., 93

Jones, Sir Harold Spencer, 363

Kant, Immanuel, 476

Kasner, Edward, 414, 540

Kepler, Johannes, 21, 192, 206 f., 253, 283, 326 ff., 549

Kepler’s laws, 328 ff., 334 ff., 355 ff., 513, 548

Koyre, Alexandre, 363

Kuhn, Thomas S., 196, 363

La Hire, Philippe de, 242

Lagrange, Joseph Louis, 24, 411, 437

Langer, Susanne K., 498

Language of mathematics, 94 ff.

Laplace, Pierre Simon, 24, 522, 540

Latitude, 166 ff.

Law, 476

Lawson, Philip J., 231

Legendre, Adrien Marie, 24

Leibniz, Gottfried Wilhelm, 24, 206, 240, 242, 281, 366, 368, 375, 406 f., 410 ff., 495

Length of curve, 366

Lens, 181 f., 202, 254, 284

Leonardo da Vinci; see Da Vinci

Levinson, Horace C, 540

Life insurance, 500, 529 f.

Light, 2, 16, 24, 138 ff., 144 ff., 155, 193, 202, 215, 254, 284, 469 f.

reflection of, 138 f., 144 ff., 179, 381 f.

refraction of, 4, 155, 176 ff., 254, 381 f.

total reflection of, 179 f.

velocity of, 176

Limit, 372, 404 ff., 409 ff.

Line curve, 245

Line, equation of, 258 ff.

at infinity, 237

Lobachevsky, Nicholas I., 456 ff.

Logarithms, 22

Logic, 30 ff., 149 f., 495 f.

symbolic, 495 f.

Longitude, 158, 165 ff.

Lorenzetti, Ambrogio, 213

Loudness of a sound, 448 ff.

Luther, Martin, 201

Mac Curdy, Edward, 208

Magnetism, 25

Manning, H. A., 279

Map, 169, 254

Mariotte, Edmé, 284

Martini, Simone, 210

Mason, S. F., 363

Mass, 33, 340

of earth, 347

of sun, 351

Mastery of nature, 23, 280

Mathematical creation, 51 ff., 552

Mathematical logic, 495 f.

Mathematical Principles of Natural Philosophy, 336 ff., 360 f.,

Mathematics, and art, 8, 37, 209 ff.

as an art, 8 ff., 550 ff.

and engineering, 23 ff., 110 f., 155 f., 475

and human beings, 27 f.

and nature, 16, 150, 187 ff., 205, 208 ff., 329, 359 ff., 412, 462 ff., 471 ff., 479 ff., 497 f., 542 ff.

nature of, 3 ff., 30 ff., 194, 471 ff., 541 ff.

prehistoric, 11

and science, 5 ff., 21, 23 ff., 46 ff., 110, 411, 462 ff., 473 ff., 547 ff.

and science compared, 33 ff., 110, 473 f.

and superstitions, 5

and theology, 2, 199 f., 331

Matrices, 26

Maxima and minima, 131 ff., 317, 366, 382 ff.

Maxwell, James Clerk, 25

Mazlish, B., 556

Mechanics, 289

Median, 502 f.

Medicine, 155 f.

Medieval civilization, 20, 39, 197 ff.

Medieval painting, 210

Medieval science, 198 ff., 281 ff., 288

Mendel, Gregor, 526

Mendeléev, Dimitri Ivanovich, 89

Méré, Chevalier de, 522

Mersenne, Marin, 239, 436 f.

Method, of exhaustion, 404

of increments, 372

Michelangelo, 229, 509

Microscope, 202, 254

Middle Ages, 2, 229

Miller, Dayton C, 451

Mode, 502 f.

Mohammedans; see Arabs

Monge, Gaspard, 242 f.

Moody, E. A., 306

Moon, 335, 344

distance from earth, 171 f.

motion of, 335, 339, 358 ff.

radius of, 172 f.

More, Louis T., 364

Moroney, M. J., 540

Mortimer, Ernest, 249

Motion, 193, 254, 287 ff., 293 ff., 365 f., 390 ff., 401 ff.

of a bob on a spring, 416 ff.

Museum of Alexandria, 154, 194

Music, 24, 193, 199, 436 ff.

Musical instruments, 445, 447 ff.

Mydorge, Claude, 239

n-dimensional space, 26, 275 ff.

Nagel, Ernest, 57, 540

Navigation, 13, 22 f., 124, 253, 332, 335, 416

Negative numbers, 20, 72 ff.

Neugebauer, Otto, 29, 57

Newman, James R., 364, 414, 498, 521, 540, 556

Newton, Sir Isaac, 2, 22 ff., 205 f., 240, 242, 251, 284, 289, 308, 335 ff., 366, 368, 375, 406 f., 409 ff., 417, 436, 455

Newtonian mechanics, 334 ff.

Newton’s laws of motion, 293 f., 310, 342, 547

Nichomachus, 18

Nicolo of Brescia; see Tartaglia

Noland, Aaron, 415

Non-Euclidean geometry, 25 f., 452 ff.

Normal probability curve, 505 ff., 530 ff.

Novum Organum of Bacon, 283

Number, concept of, 12 f., 15, 20, 30 ff., 58 ff.

Number mysticism, 59 f.

Ohm, George S., 447

Oison, Harry F., 451

On Burning Glasses, 148

On the Lever, 157

On the Motion of the Planet Mars, 328

On the Revolutions of the Heavenly Spheres, 327, 332

Optics; see Light

Ordinate, 257

Ore, O., 122, 208, 540

Origin, 256

Oscillatory motion, 417

Pacioli, Luca, 200 f.

Painting, 21, 204, 209 ff.

PanoFsky, Erwin, 231

Parabola, 142 ff., 222, 241, 253, 264, 311 ff., 334

equation of, 265 ff.

Paraboloidal mirror, 14 f., 147

Paragone of Leonardo, 229

Parallelism, 126, 236 f., 453 ff.

Parametric equations, 309

Parsons, Edward A., 186

Parthenon, 37

Pascal, Blaise, 1, 27, 206, 239 ff., 242, 245 f., 284, 410, 522, 554

Pascal’s triangle, 533 f.

Pearson, Karl, 501, 517

Pendulum, 254, 417

Pensées of Pascal, 240

Pentagon, 134

Pepys, Samuel, 2

Perimeter, 131 ff.

Period of a bob, 432

Periodic motion, 416 ff.

Periscope, 181

Perspective, 210 ff., 232

focused, 215

optical, 211

terraced, 210

vertical, 211

Petty, Sir William, 500

Phidias, 37

Phillips, Melba, 91, 305, 362, 480

Philosophy, 7, 21, 24, 47 ff., 124, 252 f., 475, 545; see also Truth

Photograph, 234

π, 12, 68, 156

Pierce, John A., 451

Piero della Francesca; see Della Francesca

Pitch, 448 ff.

Plato, 2, 17, 30, 32 ff., 48, 50, 125, 199 f., 228, 476, 543

Playfair, John, 453

Poincaré, Henri, 25, 27, 477, 556

Point curve, 245

Point at infinity, 236 f.

Political theory, 7, 24, 26, 33, 476

Polyclitus, 35 f.

Polygon, 134; see also Pentagon, Quadrilateral, Rectangle, Square, Triangle

Polyhedron, 130

Poncelet, Jean Victor, 243 f.

Pope Julius II, 227

Poseidonius, 136, 157

Positional notation, 20, 61, 85 ff.

Poundal, 340

Praxiteles, 37

Precession of the equinoxes, 358

Prediction, 548

Premises, 41 ff.

Primary and secondary qualities, 285 f.

Prime numbers, 46

Principle of least time, 183, 254

Printing, 22, 201

Prism, 180

Probability, 26, 240, 253, 522 ff.

Projectile motion, 22 f., 201, 254 f., 284, 310 ff., 338 f., 366, 381

Projection, 216 ff., 232 ff., 419

Projective geometry, 21, 232 ff.

Proof, 39 ff., 45, 53 f.

Protestant Revolution, 22, 201

Provincial Letters, 240

Psychology, 24, 537

Ptolemaic theory, 158, 191 ff., 326 f.

Ptolemy, Claudius, 18 ff., 21, 155, 158, 161, 165, 170, 190 ff., 200, 228, 282

Ptolemy, Egyptian dynasty, 154 f.

Pyramids of Egypt, 13

Pythagoras, 17, 59, 65, 68, 228

Pythagorean theorem, 65 f., 161

Pythagorean triples, 65

Pythagoreans, 34, 59 ff., 65 ff., 125, 188 ff., 436

Quadrangle, 244

Quadratic formula, 116 f.

Quadrilateral, 134, 244

Quadrivium, 199

Qualitative knowledge, 156, 282

Quality of a sound, 448 ff.

Quantitative knowledge, 156, 288

Quetelet, L. A. J., 501, 509 f.

Radian, 423

Radio, 25, 147 f.

Raisz, E., 186

Randall, John H., Jr., 208, 289, 306, 556

Range, 316, 321

Raphael, 227 ff.

Rarefaction, 439

Rate of change, average, 367 ff.

instantaneous, 367 ff.

Reasoning, 3 ff., 15 ff., 39 ff., 149 ff; see also Logic

Rectangle, 131 ff.

Rectangular Cartesian coordinate system, 257, 274

Redfield, John, 451

Refraction, 176

Regular polyhedra, 129

Reichmann, W. J., 521, 540

Relativity, theory of, 90, 470 f.

Religion, 21, 34, 59, 206, 331 f.; see also Catholic Church, Christianity

and painting, 210 ff.

Renaissance, 2, 20, 202 ff., 209 ff., 248

Republic of Plato, 32

Resonator, 448

Rest position, 418

Rheticus, George Joachim, 551

Rhine, J. B., 537, 540

Riemann, Bernhard, 25, 275, 461 ff.

Ripley, Julian A., Jr., 435

Robbins, Herbert, 152, 498

Roberval, Gilles P. de, 239

Roessler, Edward B., 521, 540

Rolle, Michel, 411

Roller, Duane H. D., 93, 306, 325, 363

Romans, 18, 157, 194, 197

Root of an equation, 112

Rotation of the earth, 352 ff.

Russell, Bertrand, 9, 10, 208, 477, 556

Saccheri, Girolamo, 454 f., 461

Sambursky, S., 196

Sampling, 538 f.

Sarton, George, 196

Satellite, 354 f.

Sawyer, W. W., 122, 152, 186, 249, 279, 306, 414, 498, 556

Schopenhauer, Arthur, 2, 53

Schrödinger, Erwin, 540

Scientific explanation, 282 f., 288

Scientific method, 281 ff., 337 ff., 359 ff.

Scott, J. F., 29, 152, 186, 279, 415

Sculpture, 37 ff.

Sears, Francis W., 186, 451

Section, 216 ff., 232 ff.

Similarity, 129

Sine, 159 ff.

Singer, Charles, 196

Singh, Jagit, 415

Sinusoidal functions, 418 ff., 436 ff.

Slope, 259 ff., 379 ff.

Smith, David Eugene, 29, 57, 93, 122, 152, 186, 208, 415

Smith, Preserved, 306, 364

Snell, Willebrord, 176

Social sciences, 7, 26, 33, 499 ff., see also Economics, Political theory

Socrates, 36, 50, 228

Sommerville, D. M. Y., 477

Sound, 16, 24, 155, 193, 436 ff.; see also Music

complex, 445 ff.

simple, 438 ff.

Sound wave, 440

Spectacles, 254

Speed, 287 ff.

instantaneous, 365 ff.

Spengler, Oswald, 556

Sphere, 129, 156, 222

equation of, 275 f.

and Riemannian geometry, 467 ff.

Spirit of Geometry, 240

Spring, 254

Spring constant, 429

Square, 132 ff.

Standard deviation, 504 f.

Statistics, 26, 499 ff.

Stevin, Simon, 284

Strabo, 136, 157

Strong, E. W., 306

Struik, Dirk J., 29, 57

Sullivan, John Wm. N., 364, 556

Summa of Pacioli, 202

Sun, density of, 351

distance from earth, 172

distance from Venus, 174 f.

mass of, 351

radius of, 173

Surface, equation of, 273 ff.

Sylvester, James Joseph, 26

Symbolism, 95 f., 255

Tacitus, 197

Tangent, of an angle, 159 ff.

slope of, 380

Tartaglia, 8, 22, 119 f., 255, 284

Taylor, Henry O., 57, 306

Taylor, Lloyd Wm., 152, 186, 306, 364, 435, 451

Telescope, 147, 202, 254, 332 f.

Television, 25

Tensors, 26

Thales, 17, 46, 125

The Harmony of the World, 330

Theorem, 46 f., 543 f.

Theory of numbers, 253, 490

Tides, 358

Torricelli, Evangelista, 240, 284

Total reflection of light, 180

Trajectory; see Projectile motion

Treatise on Painting of Leonardo, 216, 229

Triangle, 127 ff.

Trigonometric functions; see Sinusoidal functions

Trigonometric tables, 161 f.

Trigonometry, 18, 158 ff., 416 f, 441 ff.

Trivium, 199

Truth, 7, 17, 25, 149 ff., 206, 252, 281, 471 ff., 479 ff., 543

Tuning fork, 438 ff.

Turks, 200

Uccello, Paolo, 216, 229

Union of sets, 49.1

Universe, conceptions of, 188 f., 198 f.; see also Heliocentric theory, Ptolemaic theory

Valentin, Antonina, 208

Validity, 42

Vanishing line, 222

Vanishing point, 221 ff.

diagonal, 222 ff.

Variable, 287 ff., 291

Vasari, Giorgio, 231

Velocity; see Speed

Venus, 174 f.

Vesalius, Andreas, 204, 283

Vieta, Francois, 22, 118, 255

Voice, 450

Volume, 366

Von Bergeijk, Willem A., 451

Von Guericke, Otto, 284

Wallis, John, 368

Water power, 155

Weaver, Warren, 540

Wedberg, Anders, 57

Weierstrass, Karl, 27

Weight, 340, 343 ff, 353 f.

Western European civilization, 20 ff., 27

Whitehead, Alfred North, 10, 18, 122, 179, 306, 435, 546

Whole number, 58 ff.

Wiener, Philip, 415

Wightman, Wm. P. D., 364, 415

Wolf, Abraham, 306, 364, 521

Wolfe, Harold E., 477

Wood, Alexander, 451

Work, 397 ff.

Wren, Sir Christopher, 338

Young, Jacob W. A., 249, 477

Young, John W., 249

Zemansky, Mark, 186, 451

Zero, 20, 60 f.