Aaboe, Asger, 186
Abbott, E. A., 279
Abscissa, 256
Acceleration, 294, 342, 352 ff.
instantaneous, 365 ff.
in sinusoidal motion, 427
Adams, Oscar S., 186
Addition of ordinates, 442 ff.
Advancement of Learning, 283
Age of Reason, 24 f., 240, 411 f.
Air, motion of, 438 ff.
Alberti, Leone Battista, 216, 229, 509
Alexander the Great, 17, 153 f.
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
Amplitude, 424
Analogy, 40 f.
Analysis, 24
Analytic geometry; see Coordinate geometry
Analytical Theory of Heat, 446
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.
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.
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
Atomic weight, 88 ff.
Atoms, 88 ff.
Avogadro, A., 88
Axioms, 16, 26, 50 f., 75 ff., 126, 541 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
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
Bessel, Friedrich Wilhelm, 456
Binoculars, 181
Biology, 26, 83, 499 ff., 526; see also Anatomy, Eye
Blunt, Anthony, 230
Bohm, David, 540
Bonner, Francis T., 91, 305, 362, 480
Bonola, Roberto, 477
Born, Max, 540
Boys, C. V., 152
Brianchon, Charles J., 242, 245 f.
Bronowski, J., 556
Brunelleschi, 215
Bunim, Miriam, 230
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
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
Chamberlin, W., 186
Chasles, Michel, 242
Childe, V. Gordon, 29
China, 12
Christianity, 19 f., 194, 198, 206, 227 f.
Cimabue, 210
equation of, 262 f.
Clark, Kenneth, 230
Cole, Rex V., 230
Columbus, Christopher, 136
Commutative axiom, 76 f., 483, 492 f.
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
Coordinate geometry, 22, 242, 250 ff.
Copernicus, Nicolaus, 21, 192, 206 f., 253, 326 ff., 551
Correlation, 516 ff.
Cosine, 159 ff.
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
Deductive method, 45 ff., 128, 150
Deetz, Charles H., 186
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
Duality, 242 ff.
Duccio, 210 ff.
Dunnington, G.W., 477
Durrell, Clement V., 477
Earth, acceleration of, 350
density of, 348
distance from moon, 171 f.
volume of, 348
Eastern Roman Empire; see Byzantine Empire
Easton, Stewart C., 208
Egypt, 12 ff., 17 ff., 31 ff., 45, 68, 96, 118, 153 ff., 171, 188, 199
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
Enlightenment; see Age of Reason
Equation of a curve, 258 ff.
Equations, solution of, 106 ff., 255
first degree, 107
higher degree, 119 ff.
linear, 107
second degree, 107 ff., 112 ff.
Equator, 165
Equilibrium position, 418
Equivalent figures, 129
Error curve, 507
Escape velocity, 401 ff.
Essay on Conic Sections, 239
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.
Eves, Howard, 29, 93, 152, 414
Evolution, theory of, 452
Experimentation, 4, 40, 283 f.
Exponents, 96 ff.
Extrasensory perception, 537
Factoring, 104
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.
centripetal, 353
Fourier’s theorem, 446 ff.
Fraction, 62 ff.
Frank, Philipp, 477
Frequency distribution, 507
binomial, 533 f.
normal, 507
Frequency of sinusoidal motion, 425
linear, 299
periodic, 422
quadratic, 300
Fundamental tone, 448
Gade, John A., 363
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
Gases, 155
Gauss, Karl Friedrich, 25, 27, 455 ff., 549
Geocentric theory; see Ptolemaic theory
Geographica of Eratosthenes, 157
Geographica of Ptolemy, 158
Geographical explorations, 200
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.
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.
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.
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
Heat, 24
Hebrews, 14
Heliocentric theory, 21, 23, 253 f., 326 ff.
Hellenistic world; see Greeks
Helmholtz, Hermann von, 231, 448, 451
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
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
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
Irrational numbers, 65 ff., 124
Isotope, 89 f.
Jeans, Sir James, 57, 196, 363, 451
Johnson, Martin, 231
Jones, Burton W., 93
Jones, Sir Harold Spencer, 363
Kant, Immanuel, 476
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
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
Leonardo da Vinci; see Da Vinci
Levinson, Horace C, 540
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
Line curve, 245
Line, equation of, 258 ff.
at infinity, 237
Lobachevsky, Nicholas I., 456 ff.
Logarithms, 22
symbolic, 495 f.
Lorenzetti, Ambrogio, 213
Loudness of a sound, 448 ff.
Luther, Martin, 201
Mac Curdy, Edward, 208
Magnetism, 25
Manning, H. A., 279
Mariotte, Edmé, 284
Martini, Simone, 210
Mason, S. F., 363
of earth, 347
of sun, 351
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.
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
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
Method, of exhaustion, 404
of increments, 372
Miller, Dayton C, 451
Mode, 502 f.
Mohammedans; see Arabs
Monge, Gaspard, 242 f.
Moody, E. A., 306
distance from earth, 171 f.
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
Musical instruments, 445, 447 ff.
Mydorge, Claude, 239
n-dimensional space, 26, 275 ff.
Navigation, 13, 22 f., 124, 253, 332, 335, 416
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
Origin, 256
Oscillatory motion, 417
Pacioli, Luca, 200 f.
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.
Pensées of Pascal, 240
Pentagon, 134
Pepys, Samuel, 2
Perimeter, 131 ff.
Period of a bob, 432
Periodic motion, 416 ff.
Periscope, 181
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
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
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
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.
Protestant Revolution, 22, 201
Provincial Letters, 240
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.
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
Raisz, E., 186
Randall, John H., Jr., 208, 289, 306, 556
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
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
Riemann, Bernhard, 25, 275, 461 ff.
Ripley, Julian A., Jr., 435
Roberval, Gilles P. de, 239
Rolle, Michel, 411
Roller, Duane H. D., 93, 306, 325, 363
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
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.
Similarity, 129
Sine, 159 ff.
Singer, Charles, 196
Singh, Jagit, 415
Sinusoidal functions, 418 ff., 436 ff.
Smith, David Eugene, 29, 57, 93, 122, 152, 186, 208, 415
Snell, Willebrord, 176
Social sciences, 7, 26, 33, 499 ff., see also Economics, Political theory
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
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.
Stevin, Simon, 284
Strong, E. W., 306
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
Tacitus, 197
Tangent, of an angle, 159 ff.
slope of, 380
Tartaglia, 8, 22, 119 f., 255, 284
Taylor, Lloyd Wm., 152, 186, 306, 364, 435, 451
Telescope, 147, 202, 254, 332 f.
Television, 25
Tensors, 26
The Harmony of the World, 330
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
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.
Vasari, Giorgio, 231
Velocity; see Speed
Venus, 174 f.
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
Western European civilization, 20 ff., 27
Whitehead, Alfred North, 10, 18, 122, 179, 306, 435, 546
Whole number, 58 ff.
Wiener, Philip, 415
Wolfe, Harold E., 477
Wood, Alexander, 451
Work, 397 ff.
Wren, Sir Christopher, 338
Young, John W., 249