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Heath T. Ч A History of Greek Mathematics, Vol. 2
Heath T. Ч A History of Greek Mathematics, Vol. 2

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Ќазвание: A History of Greek Mathematics, Vol. 2

јвтор: Heath T.

язык: en

–убрика: »стори€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1921

 оличество страниц: 586

ƒобавлена в каталог: 07.05.2008

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ѕредметный указатель
'Abdelmelik al-Shirazi      ii. 128
'Aganis', attempt to prove parallel-postulate      358 ii.
'Attic' (or 'Herodianic') numerals      30Ч31
'Friendly' numbers      75
'Geometrical harmony' (Philolaus's name for cube)      85Ч86
'Herodianic' (or 'Attic') numerals      30Ч31
'Heron the Younger'      ii. 545
'Horizon', use in technical sense by Euclid      352
'Linear' (of numbers)      73
'Linear' loci and problems      218Ч219
'Oblong' numbers      82Ч83 108 114
'Oblong' numbers, gnomons of      82Ч83
'Odd' number defined      70Ч71
'Odd' number defined, 'odd-even', 'odd-times-odd', numbers      71Ч74
'Odd' number defined, 1 called 'odd-even'      71
'Paradoxes' of Erycinus      ii. 365Ч368
'Perfect' numbers      74Ч75
'Perfect' numbers, 10 with Pythagoreans      75
'Perfect' proportion      86
'Phaenomena' = observational astronomy 17      322 349
'Piremus' or 'peremus' in pyramid      126 127
'Plane' loci      218
'Plane' problems      218Ч219
'Platonic' figures (the regular solids)      158 162 294Ч295 296Ч297
'Side' and 'diameter-numbers'      91Ч93 112 153 308 380 ii.
'Solid' loci and problems      218 ii.
'Solid' loci and problems, Solid loci of Aristaeus      438 ii.
'Solid' numbers, classified      106Ч108
'Stadium,' 1/60th of 30∞      ii. 215
'Stigma,' name for numeral $\varsigma$, originally [ (digamma)      32
'Treasury of Analysis'      421 422 439 ii.
abacus      46Ч48
Abraham Echellensis      ii. 127
Abu 'l Fath al-Isfahani      ii. 127
Abu 'l Wafa al-Buzjani      ii. 328 ii. ii.
Abu Bekr Muh. b. al-Hasan al-Karkhi      see "al-Karkhi"
Abu Nasr Mansar      ii. 262
Achilles of Zeno      275Ч276 278Ч280
Adam, James      305Ч307 313
Addition in Greek notation      52
Adrastus      ii. 241 243 244
Aeetius      158Ч159 163 ii.
Agatharchus      174
Ahmes (Papyrus Rhind)      125 130 ii.
Akhmim, papyrus of      ii. 543Ч545
Al-Chazini      ii. 260Ч261
Al-Fakhri, by al-Karkhi      109 ii.
Al-Hajjaj, translator of Euclid      362
Al-Hajjaj, translator of Ptolemy      ii. 274
Al-Kafi of al-Karkhi      111
Al-Karkhi, on sum of $1^{3}+2^{3}+...+n^{3}$      109Ч110 111 ii. ii.
al-Ma'mun, Caliph      362
al-Mansur, Caliph      362
Albertus Pius      ii. 26
Alexander Aphrodisiensis      184 185 186 222 223 ii. ii.
Alexander the 'Aetolian'      ii. 242
Alexeieff      ii. 324Ч325n.
Algebra, beginnings in Egypt      ii. 440
Algebra, epanthema of Thymaridas      94Ч96
Algebra, geometrical      150Ч154
Algebra, geometrical, application of areas (q.v.)      150Ч153
Algebra, geometrical, scope of geometrical algebra      153Ч154
Algebra, hau-calculations      ii. 440Ч441
Algebra, Pythagorean      91Ч97
Alhazen, problem of      ii. 294
Allman, G.J.      134 183
Almagest      ii. 274
Alphabet, Greek, derived from Milesian      33Ч34
Alphabet, Greek, derived from Phoenician      31Ч32
Alphabet, Greek, quasi-numerical use of alphabet      35Ч36n.
Alphabetic numerals      31Ч40 42Ч44
Amasis      4 129
Amenemhat      I 122 III
Ameristus      140 141 171
Amyclas (better Amyntas)      320Ч321
Amyntas      320Ч321
an-Nairizi, comm. on Euclid      363 ii. ii. ii.
Analemma of Diodorus      ii. 287
Analemma of Ptolemy      ii. 286Ч292
Analysis, absent from Euclid's Elements      371Ч372
Analysis, already used by Pythagoreans      168
Analysis, defined by Pappus      ii. 400
Analysis, supposed invention by Plato      291Ч292
Anatolius      11 14 97 ii. ii.
Anaxagoras, centrifugal force and centripetal tendency      172Ч173
Anaxagoras, explanation of eclipses      7 162 172
Anaxagoras, geometry      170
Anaxagoras, in Erastae      22 174
Anaxagoras, moon borrows light from sun      138 172 ii.
Anaxagoras, on perspective      174
Anaxagoras, tried to square circle      173 220
Anaximander      67 177
Anaximander, astronomy      139 ii.
Anaximander, distances of sun and moon      139
Anaximander, introduced gnomon      78 139 140
Anaximenes      ii. 244
Anchor-ring      see "Tore"
Anderson, Alex      ii. 190
Angelo Poliziano      ii. 26
Angle 'of a segment' and 'of a semicircle'      179
Angle, 'angle of contact'      178Ч179 ii.
Anharmonic property, of arcs of great circles      ii. 269Ч270
Anharmonic property, of straight lines      ii. 270 ii.
Anthemins of Tralles      243 ii. ii. ii. ii. ii.
Antiphon      184 219 221Ч222 224 271
Apastamba-Sulba-Sutra      145Ч146
Apelt, E.F.      330
Apelt, O.      181n. 182
Apices      47
Apollodorus, author of Chronica      176
Apollonius of Perga      ii. 1 ii.
Apollonius of Perga, 'general treatise'      ii. 192Ч193 ii.
Apollonius of Perga, 'General treatise', on book I of Euclid      358
Apollonius of Perga, arithmetic, 'tetrads'      40
Apollonius of Perga, arithmetic, continued multiplications      54Ч57
Apollonius of Perga, astronomy      ii. 195Ч196
Apollonius of Perga, astronomy, A. and Tycho Bralie      317 ii.
Apollonius of Perga, astronomy, on epicycles and eccentrics      ii. 195Ч196 ii.
Apollonius of Perga, astronomy, trigonometry      ii. 253
Apollonius of Perga, comparison of dodecahedron and icosahedron      419Ч420 ii.
Apollonius of Perga, conics      ii. 126Ч175
Apollonius of Perga, conics, conics obtained from oblique cone      ii. 134Ч138
Apollonius of Perga, conics, conics obtained from oblique cone, asymptotes      ii. 148Ч149
Apollonius of Perga, conics, conics obtained from oblique cone, construction of normals      ii. 166Ч167
Apollonius of Perga, conics, conics obtained from oblique cone, focal properties (central conics)      ii. 156Ч157
Apollonius of Perga, conics, conics obtained from oblique cone, harmonic properties      ii. 154Ч155
Apollonius of Perga, conics, conics obtained from oblique cone, new names, parabola      150 167 ii.
Apollonius of Perga, conics, conics obtained from oblique cone, normals as maxima and minima      ii. 159Ч167
Apollonius of Perga, conics, conics obtained from oblique cone, number of normals through point      ii. 163Ч164
Apollonius of Perga, conics, conics obtained from oblique cone, prime property equivalent to Cartesian equation (oblique axes)      ii. 139
Apollonius of Perga, conics, conics obtained from oblique cone, propositions giving evolute      ii. 164Ч165
Apollonius of Perga, conics, conics obtained from oblique cone, rectangles under segments of intersecting chords      ii. 152Ч153
Apollonius of Perga, conics, conics obtained from oblique cone, tangents      ii. 140Ч141
Apollonius of Perga, conics, conics obtained from oblique cone, transformation of coordinates      ii. 141Ч147
Apollonius of Perga, conics, text      ii. 126Ч128
Apollonius of Perga, conics, text, arabic translations      ii. 127
Apollonius of Perga, conics, text, characteristics      ii. 132Ч133
Apollonius of Perga, conics, text, prefaces      ii. 128Ч132
Apollonius of Perga, determinate section      ii. 180Ч181
Apollonius of Perga, duplication of cube      262Ч263 ii.
Apollonius of Perga, on cochlias      232 ii.
Apollonius of Perga, on cochlias, 'sister of cochloid'      225 231Ч232
Apollonius of Perga, on cochlias, on irrationals      ii. 193
Apollonius of Perga, on cochlias, on the burning-mirror      ii. 194 ii.
Apollonius of Perga, on contacts      ii. 181Ч185
Apollonius of Perga, on contacts, three-circle problem      ii. 182Ч185
Apollonius of Perga, Plane Loci      ii. 185Ч189
Apollonius of Perga, sectio rationis      ii. 175Ч179
Apollonius of Perga, sectio spatii      ii. 179Ч180 ii. ii.
Application of areas      150Ч153
Application of areas, method attributed to Pythagoras      150
Application of areas, method attributed to Pythagoras, equivalent to solution of general quadratic      150Ч152 394Ч396
Approximations to $\pi$      232Ч235 ii. ii.
Approximations to $\surd 2$ (by means of 'side-' and 'diameter-' numbers)      91Ч93
Approximations to $\surd 2$ (Indian)      146
Approximations to $\surd 3$ (Archimedes)      ii. 51Ч52
Approximations to $\surd 3$ (Ptolemy)      45 62Ч63
Approximations to cube root (Heron)      ii. 341Ч342
Approximations to surds (Heron)      ii. 323Ч326 ii. ii.
Apuleius of Madaura      97 99
Archibald, R.C.      425n.
Archimedes      3 52 54 180 199 202 203n. 213 217 224Ч225 229 234 272 ii.
Archimedes, arithmetic, approximations to $\surd 3$      ii. 51Ч52
Archimedes, arithmetic, octads      40Ч41
Archimedes, arithmetic, octads, fractions      42
Archimedes, arithmetic, octads, value of $\pi$      232Ч233 234 ii.
Archimedes, astronomy      ii. 17Ч18
Archimedes, astronomy, on Aristarchus's hypothesis      ii. 3Ч4
Archimedes, astronomy, sphere-making      ii. 18
Archimedes, conics, propositions in      438Ч439 ii.
Archimedes, cubic equation solved by conics      ii. 45Ч46
Archimedes, on Democritus      180 327
Archimedes, on Democritus, equality of angles of incidence and reflection      ii. 353Ч354
Archimedes, on Democritus, equality of angles of incidence and reflection, integral calculus anticipated      ii. 41Ч42 61 62Ч63 74 89Ч90
Archimedes, on Democritus, Lemma or Axiom of A.      326Ч328 ii.
Archimedes, on Democritus, on semi-regular solids      ii. 98Ч101
Archimedes, on Democritus, triangle, area in terms of sides      ii. 103
Archimedes, on Democritus, trisection of any angle      240Ч241
Archimedes, traditions      ii. 16Ч17
Archimedes, traditions, engines      ii. 17
Archimedes, traditions, general estimate      ii. 19Ч20
Archimedes, traditions, mechanics      ii. 18
Archimedes, works, catoptrica      444 ii.
Archimedes, works, cattle-problem      14 15 ii. ii. ii.
Archimedes, works, character of      ii. 20Ч22
Archimedes, works, character of, lost      ii. 23Ч25 103
Archimedes, works, character of, works extant      ii. 22Ч23
Archimedes, works, liber assumptorum      ii. 101Ч103
Archimedes, works, measurement of a circle      ii. 50Ч56 ii.
Archimedes, works, mechanical works, titles      ii. 23Ч24
Archimedes, works, mechanical works, titles, plane equilibriums      ii. 75Ч81
Archimedes, works, on conoids and spheroids      ii. 56Ч64
Archimedes, works, on floating bodies      ii. 91Ч97
Archimedes, works, on floating bodies, problem of crown      ii. 92Ч94
Archimedes, works, on spirals      230Ч231 ii. ii.
Archimedes, works, on the sphere and cylinder      ii. 34Ч50
Archimedes, works, quadrature of parabola      ii. 85Ч91
Archimedes, works, sand-reckoner      ii. 81Ч85
Archimedes, works, text      ii. 25Ч27
Archimedes, works, text, editions      ii. 27
Archimedes, works, text, MSS      ii. 26
Archimedes, works, the method      ii. 20 21 22 27Ч34 ii. ii.
Archytas      2 170 212Ч216 ii.
Archytas, mechanics      213
Archytas, no mean proportional between n and n+1      90 215
Archytas, on means      85 86
Archytas, on music      214
Archytas, solution of problem of two mean proportionals      214 219 245 246Ч249 334 ii.
Argyrus, Isaac      224n. ii.
Aristaeus of Croton      86
Aristaeus, comparison of five regular solids      420
Aristaeus, solid Loci (conics)      438 ii. 118Ч119
Aristarchus of Samos      43 139 ii. ii.
Aristarchus of Samos, anticipated Copernicus      ii. 2Ч3
Aristarchus of Samos, date      ii. 2
Aristarchus of Samos, fractions in      43
Aristarchus of Samos, numbers in      39
Aristarchus of Samos, other hypotheses      ii. 3 4
Aristarchus of Samos, treatise on sizes and distances of Sun and Moon      ii. 1 3 4Ч15
Aristarchus of Samos, treatise on sizes and distances of Sun and Moon, trigonometrical purpose      ii. 5
Aristonophus, vase of      162
Aristophanes      48 161 220
Aristotelian treatise on indivisible lines      157 346Ч348
Aristotherus      348
Aristotle      5 120 121
Aristotle, arithmetic, on Pythagoreans and numbers      67Ч69
Aristotle, arithmetic, on the gnomon      77Ч78 83
Aristotle, arithmetic, reckoning by tens      26Ч27
Aristotle, arithmetic, reckoning by tens, why 1 is odd-even      71
Aristotle, arithmetic, reckoning by tens, why 2 even and prime      73
Aristotle, astronomy, Pythagorean system      164Ч165
Aristotle, astronomy, Pythagorean system, on hypothesis of concentric spheres      329 335 ii.
Aristotle, astronomy, Pythagorean system, on Plato's view about the earth      314Ч315
Aristotle, geometry, curves and solids in A.      341
Aristotle, geometry, illustrations from      335 336 338Ч340
Aristotle, geometry, illustrations from, on parallels      339
Aristotle, geometry, illustrations from, on quadrature by lunes (Hippocrates)      184Ч185 198Ч199
Aristotle, geometry, illustrations from, on quadratures      184Ч185 221 223 224n. 271
Aristotle, geometry, illustrations from, proofs differing from Euclid's      338Ч339
Aristotle, geometry, illustrations from, propositions not in Euclid      340
Aristotle, geometry, on Plato and regular solids      159
Aristotle, mechanics      344Ч346 445Ч446
Aristotle, mechanics, 'Aristotle's wheel'      ii. 347Ч348
Aristotle, mechanics, parallelogram of velocities      346
Aristotle, on first principles, definitions, postulates, axioms      336Ч338
Aristotle, on mathematical subjects      16Ч17
Aristotle, on origin of science      8
Aristotle, on the continuous and infinite      342Ч343
Aristotle, on the continuous and infinite, encomium on Democritus      176
Aristotle, on the continuous and infinite, on Hippocrates      22
Aristotle, on the continuous and infinite, on principle of exhaustion      340
Aristotle, on the continuous and infinite, on Zeno's paradoxes      272 275Ч277 278Ч279 282
Aristotle, on the continuous and infinite, proof of incommensurability of diagonal      91
Aristoxenus      24n. 66
Arithmetic (1) = theory of numbers      13Ч16
Arithmetic (1) = theory of numbers, early 'Elements of Arithmetic'      90 216
Arithmetic (1) = theory of numbers, systematic treatises, Nicomachus Introd. Ar.      97Ч112
Arithmetic (1) = theory of numbers, systematic treatises, Nicomachus Introd. Ar., Domninus      ii. 538
Arithmetic (1) = theory of numbers, systematic treatises, Nicomachus Introd. Ar., Iamblichus, Comm. on Nicomachus      113Ч115
Arithmetic (1) = theory of numbers, systematic treatises, Nicomachus Introd. Ar., Theon of Smyrna      112Ч113
Arithmetic (2) practical arithmetic, originated with Phoenicians      120Ч121
Arithmetic (2) practical arithmetic, originated with Phoenicians, in primary education      19Ч20
Arithmetic mean, defined      85
Arithmetica of Diophantus      15Ч16 ii.
Arithmetical operations      see "Addition" "Subtraction"
Arrow of Zeno      276 280Ч281
Aryabhatta      234
Asclepius of Tralles      99
Astronomy in elementary education      19
Astronomy in elementary education, as secondary subject      20Ч21
Athelhard of Bath, first translator of Euclid      362Ч364
Athenaeus      144 145
Athenaeus of Cyzicus      320Ч321
August, E.F.      299 302 361
Autolycus of Pitane      348
Autolycus of Pitane, relation to Euclid      351Ч352
Autolycus of Pitane, works on risings and settings      352Ч353
Autolycus of Pitane, works on the moving sphere      348Ч352
Auverus, C.      ii. 26
Axioms = common notions in Euclid      376
Axioms, Aristotle on      336
Axioms, axiom of Archimedes      326Ч328 ii.
Babylonians, 'perfect proportion'      86
Babylonians, civilization of      8 9
Babylonians, sexagesimal fractions      29
Babylonians, system of numerals      28Ч29
Bachet, editor of Diophantus      ii. 454Ч455 ii.
Bacon, Roger, on Euclid      367Ч368
Baillet, J.      ii. 543
Baldi, B.      ii. 308
Barlaam      ii. 324n. ii.
Barocius      ii. 545
Barrow, I., edition of Euclid      369Ч370
Barrow, I., edition of Euclid, on Book V      384
Bathycles      142
Baudhayana, S.S.      146
Baynard, D.      ii. 128
Benecke, A.      298 302Ч303
Benedetti, G.B.      344 446
Bertrand, J.      ii. 324n.
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