|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Heath T. — A History of Greek Mathematics, Vol. 2 |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Pythagoras, motto 25 141
Pythagoras, Proclus on discoveries of 84—85 90 119 141 154
Pythagoras, theorem of Pythagoras 142 144—149
Pythagoras, theorem of Pythagoras, how discovered? 147—149
Pythagoras, theorem of Pythagoras, Pappus's extension ii. 369—371
Pythagoras, travels 4—5
Pythagoras, travels, story of bribed pupil 24—25
Pythagoreans 2 11 220
Pythagoreans, 'all things are numbers' 67—69
Pythagoreans, 'friendly' numbers 75
Pythagoreans, 'number' of an object 69
Pythagoreans, 'number' of an object, 'number in the heaven' 68
Pythagoreans, 1 is odd-even 71
Pythagoreans, 10 the 'perfect' number 75
Pythagoreans, a Pythagorean first taught for money 22
Pythagoreans, astronomical system (non-geocentric) 163—165
Pythagoreans, classification of numbers 72—74
Pythagoreans, construction of regular pentagon 160—162
Pythagoreans, definition of unit 69
Pythagoreans, definitions 166
Pythagoreans, discovered the incommensurable 65 90—91 154
Pythagoreans, discovered the incommensurable, with reference to  155 168
Pythagoreans, figured numbers 69
Pythagoreans, first cases of indeterminate analysis 80 91 96—97
Pythagoreans, first to advance mathematics 66
Pythagoreans, geometrical theorems attributed to 143—154
Pythagoreans, invented application of areas and geometrical algebra 150—154
Pythagoreans, oblong numbers 82—83 108 114
Pythagoreans, on order of planets ii. 242
Pythagoreans, quadrivium 11
Pythagoreans, side- and diameter-numbers giving approximations to 2 91—93
Pythagoreans, sum of angles of triangle =2R 135 143
Pythagoreans, theory of proportion only applicable to commensurables 153 155 167 216
Qay en heru, height (of pyramid) 127
Quadratic equation, numerical solutions ii. 344 ii. ii.
Quadratic equation, solved by Pythagorean application of areas 150—152 167 394—396 422—423
Quadratrix 2 23 171 182 218 219 225—230 ii.
Quadrivium of Pythagoreans 11
Quinary system of numerals 26
Quintilian ii. 207
Qusta b. Luqa, translator of Euclid 362 ii.
Rangabe, A.R. 49—50
Ratdolt, Erhard, first edition of Euclid 364—365
Reductio ad absurdum 372
Reductio ad absurdum, already used by Pythagoreans 168
Reduction (of a problem) 372
Reflection, equality of angles of incidence and reflection 442 ii. ii.
Refraction 6—7 444
Refraction, first attempt at a law (Ptolemy) ii. 294
Regiomontanus 369 ii. ii.
Regula Nicomachi 111
Rhabdas, Nicolas 40 ii. ii.
Rhind Papyrus, algebra in ii. 440—441
Rhind Papyrus, mensuration in 122—128
Right-angled triangle, inscribed by Thales in circle 131
Right-angled triangle, theorem of Eucl. I. 47
Right-angled triangle, theorem of Eucl. I., attributed to Pythagoras 142 144—145
Right-angled triangle, theorem of Eucl. I., supposed Indian origin of 145—146
Right-angled triangles in rational numbers, Diophantus's problems on ii. 507—514
Right-angled triangles in rational numbers, Indian examples 146
Right-angled triangles in rational numbers, Pythagoras's formula 80
Right-angled triangles in rational numbers, Pythagoras's formula, Euclid's 81—82 405
Right-angled triangles in rational numbers, Pythagoras's formula, Plato's 81
Right-angled triangles in rational numbers, triangle (3,4,5) known to Egyptians 122
Robertson, Abram ii. 27
Rodet, L. 234
Rodolphus Pius ii. 26
Rudio, F. 173 184 187—191 ii.
Rudolph of Bruges ii. 292
Ruelle, Ch.Em. ii. 538
Ruestow, F.W. ii. 309
Ruler-and-compasses restriction 175—176
Sachs, Eva 209n.
Salaminian table 48 50—51
Salinon ii. 23 ii.
Sar (Babylonian for  ) 28 ii.
Satapatha Brahmana 146
Savile, Sir H., on Euclid 360 369
Scalene, of an oblique , cone ii. 134
Scalene, of an odd number (Plato) 292
Scalene, of certain solid numbers 107
Scalene, of triangles 142
Schiaparelli, G. 317 330 ii.
Schmidt, W. ii. 308 309 310
Schoene, H. ii. 308
Schoene, R. ii. 308 317
Scholiast to Charmides 14 53
Schulz, O. ii. 455
Scopinas ii. 1
Se-qet, 'that which makes the nature' (of pyramid) = cotangent of angle of slope 127—128 130 131
Secondary numbers 72
Sectio canonis 17 215 444
Seelhoff, P. 75n.
Seleucus ii. 3
Semicircle, angle in, is right (Thales) 131 133—137
Senkereh, Tables 28 29
Senti, base (of pyramid) 127
Serenus ii. 519—526
Serenus, on section of cone ii. 522—526
Serenus, on section of cylinder ii. 519—522
Sesostris (Ramses II) 121
Sexagesimal system of numerals and fractions 28—29
Sexagesimal system of numerals and fractions, sexagesimal fractions in Greek 44—45 59 61—63 233 ii.
Sextius 220
Sicily 8
Simon, M. 200
Simplicius, commentary on Euclid 358 ii.
Simplicius, extract from Eudemus on Hippocrates's quadrature of lunes 171 182—199
Simplicius, on Antiphon 221—222
Simplicius, on Eudoxus's theory of concentric spheres 329
Simplicius, on mechanical works of Archimedes ii. 24 ii.
Simson, R., edition of Euclid's Data 421
Simson, R., edition of Euclid's Elements 365 369
Simson, R., on Euclid's Porisms 435—436
Simson, R., restoration of plane loci of Apollonius ii. 185 ii.
Simus of Posidonia 86
Sines, tables of ii. 253 ii.
Sinus rectus, sinus versus 367
Smith, D.E. 49 138n.
Solids, five regular, all five investigated by Theaetetus 159 162 212 217
Solids, five regular, content of ii. 335 ii.
Solids, five regular, discovery attributed to Pythagoras or Pythagoreans 84 141 158—160 168
Solids, five regular, discovery attributed to Pythagoras or Pythagoreans, alternatively (as regards octahedron and icosahedron) to Theaetetus 162
Solids, five regular, Euclid's constructions for 415—419
Solids, five regular, Pappus's constructions ii. 368—369
Solids, five regular, Plato on 158—160
Solon 4 48
Sophists, taught mathematics 23
Sosigenes 316 329
Soss = sussu = 60 (Babylonian) 28 ii.
Speusippus 72 73 75 ii.
Speusippus, on Pythagorean numbers 76 318
Speusippus, on the five regular solids 318
Sphaeric 11—12
Sphaeric, earlier text-book presupposed in Autolycus 349—350
Sphaeric, Sphaerica of Menelaus ii. 252—253 260 261—273
Sphaeric, Sphaerica of Theodosius ii. 245 246—252
Sphaeric, treatises on, by Autolycus and Euclid 348—352 440—441
Sphere-making 18
| Sphere-making, Archimedes on ii. 17—18
Spiric sections ii. 203—206
Sporus 226
Sporus, criticisms on quadratrix 229—230
Sporus, duplication of cube 266—268
Square numbers 69
Square numbers, 8 times a triangular number +1 = square 84 ii.
Square numbers, any square is sum of two triangular numbers 83—84
Square numbers, formation by adding successive gnomons (odd numbers) 77
Square root, extraction of 60—63
Square root, extraction of, ex. in sexagesimal fractions (scholiast to Euclid) 63
Square root, extraction of, ex. in sexagesimal fractions (Theon) 61—62
Square root, extraction of, method of approximating to surds ii. 51—52 ii. ii. ii.
Ssade, Phoenician sibilant became 900 32
Stadium of Zeno 276—277 281—283
Star-pentagon, or pentagram, of Pythagoreans 161—162
Stereographic projection (Ptolemy) ii. 292
Stevin, S. ii. 455
Strabo 121 ii. ii.
Strato ii. 1
Subcontrary (=harmonic) mean, defined 85
Subtraction in Greek notation 52
Surds see "Approximations"
Surds, Theaetetus's generalization 203—204 205 209 304
Surds, Theodorus on 22—23 155—156 203—209 304
Surface-Loci 219 ii.
Surface-Loci, Euclid's 439—440 ii. ii.
Surya-Siddhanta ii. 253
Sussu = soss (Babylonian for 60) 28 ii.
Synesius of Cyrene ii. 293
Synthesis 371—372
Synthesis, defined by Pappus ii. 400
Syracuse 8
Table of chords 45 ii. ii.
Taittiriya Samhita 146
Tannery, P. 15 44 87 89 119 132 180 182 184 188 196n. 232 279 326 440 ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. ii. 546 ii. ii. ii.
Teles on secondary education 21
Teos inscription 32 34
Tetrads of Apollonius 40
Tetrahedron, construction 416 ii.
Tetrahedron, volume of ii. 335
Thabit b. Qurra, of Apollonius's Conics V-VII ii. 127
Thabit b. Qurra, of Archimedes's Liber assumptorum ii. 22
Thabit b. Qurra, of Menelaus's Elements of Geometry ii. 260
Thabit b. Qurra, of Ptolemy ii. 274—275
Thabit b. Qurra, translator of Euclid 362 363
Thales 2 4 67
Thales, astronomy 137—139 ii.
Thales, definition of number 69
Thales, geometrical theorems attributed to 130—137
Thales, introduced geometry into Greece 128
Thales, measurement of distance of ship from shore 131—133
Thales, measurement of height of pyramid 129—130
Thales, one of Seven Wise Men 128 142
Thales, predicted solar eclipse 137—138
Theaetetus 2 119 170
Theaetetus, investigated regular solids 159 162 212 217
Theaetetus, on irrationals 209—212 216—217
Theaetetus, on surds 22—23 155 203—204 205 209 304
Themistius 221 223 224
Theodorus of Cyrene, on surds 22—23 203—209 304
Theodorus of Cyrene, taught mathematics 22—23
Theodosius ii. 245—246
Theodosius, no trigonometry in ii. 250
Theodosius, other works ii. 246
Theodosius, Sphaerica 349—350 ii.
Theologumena arithmetices 96 97 318
Theon of Alexandria, commentary on Syntaxis 58 60 ii. ii.
Theon of Alexandria, edition of Euclid's Elements 360—361 ii.
Theon of Alexandria, examples of multiplication and division 58 59—60
Theon of Alexandria, extraction of square root 61—63
Theon of Alexandria, of optics 441 ii.
Theon of Smyrna 12 72 73 74 75 76 79 83 87 ii.
Theon of Smyrna, forms of numbers which cannot be squares 112—113
Theon of Smyrna, on 'side-' and 'diameter-numbers' 91—93 112
Theon of Smyrna, treatise of ii. 238—244
Theophrastus 158 163
Theophrastus, on Plato's view of the earth 315
Theudius 320—321
Theuth, Egyptian god, reputed inventor of mathematics 121
Thevenot, M. ii. 308
Thrasyllus 97 176 177 ii. ii.
Thucydides ii. 207
Thymaridas, 'rectilinear' = prime numbers 72
Thymaridas, definition of unit 69
Timaeus of Locri 86
Tittel ii. 300 301 304
Tore (or anchor-ring), sections of (Perseus) ii. 203—206
Tore (or anchor-ring), use by Archytas 219 247—249
Tore (or anchor-ring), volume of (Dionysodorus and Heron) ii. 218—219 ii.
Torelli, J. ii. 27
Transversal, lemmas relating to quadrilateral and transversal (Pappus) ii. 419—420
Transversal, Menelaus's theorem for spherical and plane triangles ii. 266—270
Triangle, spherical, propositions analogous to Euclid's on plane triangles ii. 262—265
Triangle, spherical, sum of angles greater than two right angles ii. 264
Triangle, theorem about sum of angles Pythagorean 135 143
Triangle, theorem about sum of angles Pythagorean, Geminus and Aristotle on 135—136
Triangular numbers 15 69
Triangular numbers, 8 times triangular number +1 = a square 84 ii.
Triangular numbers, formation 76—77
Trigonometry ii. 5 ii. ii. ii. ii. ii.
Trisection of any angle, Pappus on ii. 385—386
Trisection of any angle, solutions 235—244
Tschirnhausen, E.W. 200
Tycho Brahe 317 ii. ii.
Tzifra (=0) ii. 547
Ukha-thebt (side of base in pyramid) 126 127
Unit, definitions (Pythagoreans, Euclid, Thymaridas, Chrysippus) 69
Usener, H. 184 188
Valla, G., translator of extracts from Euclid 365
Valla, G., translator of extracts from Euclid, and from Archimedes ii. 26
van Roomen, A. ii. 182
Van Schooten, F. 75n. ii.
Venatorius, Thomas Gechauff, ed. princeps of Archimedes ii. 27
Venturi, G. ii. 308
Vieta 200 223 ii. ii. ii. ii.
Vigesimal system (of numerals) 26
Vincent, A.J.H. 50 436 ii. ii. ii.
Vitruvius 18 147 174 213 ii. ii.
Vitruvius and Heron ii. 302—303
Viviani, V. ii. 261
Vogt, H. 156n. 203n.
von Braunmuehl, A. ii. 268—269n. ii. ii.
Wescher, C. ii. 309
Wilamowitz-Moellendorff, U. v. 158n. 245 ii.
Xenocrates 24 319
Xenocrates, upheld 'indivisible lines' 181
Xenocrates, works on Numbers 319
Xenophon, on arithmetic in education 19
Xylander (W. Holzmann) ii. 454—455 ii.
Yahya b. Khalid b. Barmak ii. 274
Zamberti, B., translator of Euclid 365 441
Zeno of Elea 271—273
Zeno of Elea, arguments on motion 273—283
Zeno of Sidon on Eucl. I. 1 359 ii.
Zenodorus ii. 207—213
Zero in Babylonian notation 29
Zero in Babylonian notation, O in Ptolemy 39 54
Zeuthen, H.G. 190 206—209 210—211 398 437 ii. ii. ii. ii. ii. ii.
Zodiac circle, obliquity discovered by Oenopides 138 174 ii.
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå