INDEX abstraction: difference be tween ancient and mod ern, 5If; one-step abstrac tions and higher abstrac tions, 51; abstraction from possibility, 55, 57 (a char acteristic of modern mathe matics) abstractness, in rational thinking in general and in mathematics in particular, 48-58 Achilles and Patroclus, their relation, 356 act and potency in Aristotle, 165 Aeschylus, 6, 76, 303f (bio graphical sketch), 327 Agamemnon, 303 Agassi, Joseph (introduced the term "continuism"), 61n, 62, 70η, 74n, 77n, 93 Aguilonius, F., 297, 304 algebra: in the Renaissance, 38; rise of medieval a., 112f Alhazen, 97, 304, 369 Amontons, G., 225, 304 Ampere, A. M., 77, 102f, 305 (biographical sketch) Anatolius (St.) of Alexan dria, 13, 305 Anaxagoras: biographical sketch, 305f; 90, 367 Anaximander: biographical sketch, 306ff; 26, 88f, 308, 320, 366, 367 Anaximenes, 26, 88, 308, 320, 365, 366, 367 Anderson, C. D., 104f Anna Comnena, 70, 308 (bi ographical sketch) anti-Aristotelism in 17th cen tury, 67, 329 Anton, J. P., 161n, 167n apeiron in Anaximander, 88f, 307 Apollonius: biographical sketch, 309; his main fail ure, 189f; also 3, 30, 49, 54, 76, 83, 85, 110, 126, 139, 140, 328 applied mathematics, see mathematics; mathematicsto -a-purpose Aquinas (St. Thomas), 57, 67, 342 Archelaus, 367 Archilochus, 333 Archimedes: biographical sketch, 309ff; testimonials to his greatness, 33f; axiom of A., 35; the SandReckoner , 36, 310; disdain for philosophical niceties, 36, 94; mathematics in science, 47; space, 53f; Method, 76n; laws of A., 97, 116; algebra, 112f; mathematical physics, 144f; lever, 18 Iff; floating bodies, 184; general (con vex) curves, 222f; limits, 234; On Spirals, 281; Democritus , 320; achieve ments of Eudoxus, 325; also 4, 6, 27, 30, 31, 38, 49, 76, 83f, 85, 93, 110, 126, 139, 140, 158, 167f, 178, 328, 364 [373] INDEX Aristarchus, 310 Aristophanes, 96f (squaring of the circle), 280, 327, 364 (on Thales) Aristotle: biographical sketch, 31 Iff; on Timaeus, 16; poetry and Poetics, 19; origin of mathematics, 23f; Zeno's puzzles, 46; Py thagoreans, 46; symbols in logic, 50; absence of set theory in A., 56; created continuism, 61, 117; his torian, 65; astronomy, 86; Thales, 88, 364-68; homoeomery , 90; "created" Ionian school of monism, 118; Posterior Analytics, 122; on optics and har monics, 144; contradic tions and inconsistencies in Physica, 145f; on Time, 147f; his cosmology, 14849 ; Chance (tyche) and Fortuitous (Automaton), 150f; difference between chora (space) and topos (place) in A., 152f; topos in Physica, 153ff; physical system, 153, 160ff, 219; gravitational space, 154f; topos and chronos in Cate gories, 155f; matter, 156ff; his thermodynamical outlook, 159f; "Void" (kenon), 160; process-innature , 160-64, 219; kine sis, and its scope, 162ff; sense-perceptions, 163f; contraries, 165, 171; act and potency, 165, 177f; mathematical functions, 166f; the notion of "rela tion" (pros ti), 170; theory of topos, Π 2-75; finiteness of the universe (!cos mos), 175f; quality and quantity, 226; energy, 232; opposes Pythagorean space, 245; dimly an ticipates general space parameters, 246f; simul taneous time-scales, 251; Anaxagoras, 305f; apeiron of Anaximander, 307; Anaximenes , 308; sex sym bolism, 312; Democritus, 320f; Empedocles, 324; planetary system of Eudoxus , 325; ethics of Eudoxus , 326; ' Heraclitus, 334, 335; Hesiod, 335; squaring of the circle, 336; contempt for Melissus, 344f; in Oresme, 349f; comparison with Posidonius , 357; Pythagoras, 359; on Pythagorean nat ural philosophy, 36Of; cre ated the text-book figure of Thales, 364-68; Theophrastus , 368; Xenophanes , 370; Zeno, 371; also 4, 5, 6, 8, 28, 34, 37, 85, 92, 99f, 100, 124, 138, 235, 319, 324, 337, 357, 368 arithmetization of geometry, 229 "astrologer," 25n astronomy, 67ff; "saving the phenomena," 123ff Athenaeus, 34, 313 Augustine (St.), Ill [374] INDEX Bachet, G., 321 Bacon, Francis: definition of "philosopher," 313f; 62, 74 Bacon, Roger: biographical sketch, 314; 27, 71, 108, 187, 331 Bailly, J. S., 67ff, 314f Barrow, Isaac, 280 Bartholinus, E., 97, 315 Bernoulli, Daniel, 41 Bernoulli, James (Jacob), 41, 151, 276, 315 (biograph ical sketch), 352 Bernoulli, John, 41, 315 Bias of Priene, 333 "big-bang" theory (contem porary cosmogony), 252 Bloch, Marc (The Feudal So ciety, 1961), 39n Bochenski, J. M. (History of Formal Logic, 1962), 99 Boeckh, A., 70 Boetius, 357 Bohr, Niels, 6, 135, 315 (bi ographical sketch), 322f Boltzmann, L., 41, 128, 151, 315, 340, 353 Bolyai, J., 202 Bombelli, R., I l l Boole, G., 45, 101, 262 Born, M., 104, 323 Boyer, C. B., 40, 228 Boyle, R., 74, 225, 316, 343 Brahe, Tycho, 184 Brouwer, L. E. J., 287, 316 Burckhardt, J., 120, 316 Burkert, Walter, 14On...

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