Heath Th.L. — Diophantus of Alexandria. A Study in the History of Greek Algebra :: Электронная библиотека попечительского совета мехмата МГУ

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Heath Th.L. — Diophantus of Alexandria. A Study in the History of Greek Algebra

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Название: Diophantus of Alexandria. A Study in the History of Greek Algebra

Автор: Heath Th.L.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Год издания: 1910

Количество страниц: 387

Добавлена в каталог: 14.08.2008

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Предметный указатель

(for Numerus) by Xylander, Bachet, Fermat and others      38
for unknown quantity, originated with Descartes      50 n.
$\bar{A}$ ryabhata      281
Ab $\bar{u}$ ’l — Faraj      1
Ab $\bar{u}$ ’l — Waf $\bar{a}$ al — B $\bar{u}$ zj $\bar{a}$ n $\bar{\imath}}$       6 19
Achm $\bar{\imath}}$ m Papyrus      45
Addition, Bombelli’s sign for      22
Addition, expressed in Dioph. by juxtaposition      42
Addition, first appearance of       49 n.
Ahmes      112
al — Karkh $\bar{\imath}$       5 41
al — Karkh $\bar{\imath}}$       5 41
al — Khuw $\bar{a}$ razm $\bar{\imath}}$ , Muhammad b. M $\bar{u}$ s $\bar{a}$       34 50
Alfraganus      20
Algebra, three stages of development      49—51
Algebraical notation, Bachet and Fermat      38
Algebraical notation, beginnings of modern signs      49—50 n.
Algebraical notation, Bombelli      22 38
Algebraical notation, Diophantus      34—39 41—44
Algebraical notation, earlier Italian algebraists      38
Algebraical notation, Vieta      38 39 50
Algebraical notation, Xylander      38 48
Aljabr      64
Almuk $\bar{a}$ bala      64
Amthor      122
Anatolius      2 18
Andreas Dudicius Sbardellatus      17 25
Angelas Vergetius      16
Anthology, arithmetical epigrams in      113—114
Anthology, indeterminate equations in      114
Anthology, on Diophantus      3
Apollonius of Perga      5 6 12 18 122
Approximations, Archimedes      278—279
Approximations, Diophantus      95—98
Approximations, Pythagoreans      117—118 278
Arabian scale of powers of unknown compared with that of Diophantus      40 41
Arabic versions and commentaries      19
Archimedes      11 12 35 278 279 290
Archimedes, Arenarius      35 122
Archimedes, Cattle — Problem      121—124 279
Archimedes, Codex Paris, of      48
Arenarius of Archimedes      35 122
Arithmetica of Diophantus, conspectus of problems in      260—266
Arithmetica of Diophantus, different titles by which known      4—5
Arithmetica of Diophantus, division into Books      5 17—18
Arithmetica of Diophantus, lost Books      5—12
Arithmetica of Diophantus, notation in      32—53
Arithmetical progression, summation of      248—249
Ars rei et census      20
Auria, Joseph      15 18
Bachet      12 16 17 21 22 25 26—29 35 45 48 80—82 87 101 107 109 110 140 173 196—197 213 220 230 232 234—235 246 271 273 287 293
Back-reckoning      56 89 93
Baillet      45 n.
Bessarion, Cardinal      17 20
Bh $\bar{a}$ skara      281
Bianchini      20
Billy, Jacques de      28 165 166 184 221 267 304 308 320 321 326
Bodleian MS. of Euclid      35
Bodleian MSS. of Dioph      15 34 35
Bombelli, Algebra of      21 22
Bombelli, Rafael      11 27
Bombelli, symbols used by      22 38
Brahmagupta      281
Brancker, Thomas      286 n.
Brouncker, William, Viscount      286 288
Camerarius, Joachim      21
Cantor, Moritz      3 n. 6 63 112 118 120 125 281
Cardano      21 23 40
Cattle — Problem of Archimedes      11 12 121—124 279
Cauchy      188 274
Censo, or Zensus, = square      40 41
Charmides, scholiast to, in      113 121—122
Chasles, n Cleonides      16 n.
Coefficient, expressed by $\pi\lambda\hat{\eta}\theta o \varsigma$ , multitude      64 n.
Colebrooke      6 281
Cosa, =the unknown      22 40
Coss      23
Cossali      1 21 40 41 140
Cracow MS. of Dioph      514 18
Cube, Euler’s solution of problem of finding all sets of three cubes having a cube for their sum      329—334
Cube, Fermat’s extensions, ibid., a cube cannot be the sum of two cubes      144
Cube, sign for cube of unknown or $x^{3}$       38 129
Cube, Vieta’s formulae for transforming the sum of two cubes into a difference of two cubes and vice versa      101—103
Cubic equation, simple case of      66—67 242
Cuttaca (“pulveriser”), Indian method of      283
Definitions of Diophantus      32 38 39 129—131
Denominator      137
Descartes      271 273
Descartes notation      50 n.
Determinate equations, a particular cubic      66—67
Determinate equations, mixed quadratics      59—65
Determinate equations, of first and second degrees      58
Determinate equations, pure      58—59
Determinate equations, simultaneous equations leading to quadratics      66
Dionysius      2 n. 9 129
Diophantus, commentators and editors      18—31
Diophantus, date      1—2
Diophantus, Dioph. not inventor of algebra      111—116
Diophantus, epigram on      3
Diophantus, his extensions of theory of polygonal numbers      127
Diophantus, his work a collection in best sense      124
Diophantus, in Arabia      5—6 19
Diophantus, methods of solution      54—98
Diophantus, MSS. of      14—18
Diophantus, nor of indeterminate analysis      115—124
Diophantus, notation of      32—53
Diophantus, numbers as sums of four squares      110
Diophantus, numbers not sum of three squares      108—109
Diophantus, numbers which are not the sum of two squares      107—108
Diophantus, on numbers which are the sum of two squares      105—106
Diophantus, other assumptions      103 sqq.
Diophantus, porisms of      3 8—10 99—101
Diophantus, spelling of name      1
Diophantus, theorems in theory of numbers      110
Diophantus, works      3—13
Diophantus, “Pseudepigraphus”      31
Division, how represented by Dioph.      44—47
Doppelmayer      20 n.
Double-equations (for making two expressions in simultaneously squares)      11 73—87 91—92
Double-equations (for making two expressions in simultaneously squares), double equations for making one expression a square and another a cube      91—92
Double-equations (for making two expressions in simultaneously squares), general rule for solving      73 146
Double-equations (for making two expressions in simultaneously squares), two expressions of Double-equations (for making two expressions in simultaneously squares), first degree      73—80 80—82
Double-equations (for making two expressions in simultaneously squares), two expressions of second degree or one of first and one of second      81—87
Dudicius Sbardellatus, Andreas      17 25
Egyptians, beginnings of algebra, haw-calculations      111—112
Egyptians, hau, sign for      37
Egyptians, method of writing fractions      112
Egyptians, names for successive powers      41
Eisenlohr      112 n.
Enestr $\ddot{o}$ m      63 n. 286
Epanthema of Thymaridas      114—116
Epigrams, arithmetical, in Anthology      113—114
Epigrams, arithmetical, in Anthology, on Diophantus      3
Epigrams, arithmetical, in Anthology, one in Diophantus (V. 30)      124
Equality, abbreviation for      47—48
Equality, sign in Xylander      48
Equality, the sign = due to Recorde      50 n.
Equations      see Determinate Indeterminate Double Triple etc.
Eratosthenes      121
Euclid      8 11 12 19 63 117 124 132 144 191
Eudoxus      124
Euler      56 71—72 83—85 86 90 10n. 102 107 110 145 151 160 162 178 181—182 188 224 236 241 242 268 272 274 275 286 288—292 294 297 299
Euler, J. A.      360
Euler, Supplement      329—379 passim
Eutocius      5 6
Exponents, modem way of writing due to Descartes      50 n.
Fakhr $\bar{\imath}$       5 41
Fermat      28 29 30 38 78 90 101 102 103 106 107 108 109 110 144—145 163 173 179—180 182 183 184 188 190—191 197 202 204 205 213—214 218 220 223 229 230 231 232 233 235 236 239 240 241 242 246 254
Fermat, $x^{4}-y^{4}=z^{2}$ cannot be solved in integers      224 293—297
Fermat, Fermat on numbers which are, or are not, the sums of two, three, or four squares respectively      110 267—275

Fermat, Fermat’s “triple-equations”      321—328
Fermat, on equation $x^{2} - Ay^{2}= 1$       285—287
Fermat, on numbers of form $x^{2}+3 y^{2}$       275
Fermat, on numbers of form $x^{2}-2 y^{2}$ or $2 x^{2}-y^{2}$       276—277
Fermat, on numbers of of form $x^{2}+ 5 y^{2}$       276 277
Fermat, problems on right-angled triangles      204—205 n. 218—219 220 229 230 231—233 235 236 239—240 297—318
Fermat, Supplement      267—328 passim 364
Fermat, “great theorem of Fermat”      144—145 n.
Fr $\acute{e}$ nicle      102 n. 276 277 285 287 295—297 309 310 313 314
Fractions, representation of, in Diophantus      44—47
Fractions, sign for $\frac{1}{2}$       45
Fractions, sign for $\frac{2}{3}$       45
Fractions, sign for submultiple      45—47
G $\ddot{u}$ nther      6 278 279
Gardthausen      35 36
Geminus      4
Georg v. Peurbach      20
Georgius Pachymeres      18 19 31 37
Girard, Albert      30 106
Gnomons      125
Gollob      14 18
Grammateus (Schreiber), Henricus      49 n. 50
Greater and less, signs for      50 n.
H $\acute{e}$ rigone      50 n.
hankel      6 54—55 108 281 283 284 286
Harriot      50 n.
Hau ( = “heap”), the Egyptian unknown quantity      37 112
Heiberg      35 48 118 205
Henry, C.      13 28
Heron      12 13 35 36 43 44 45 63 129
Hippocrates of Chios      63 124
Holzmann, Wilhelm      see Xylander
Hultsch      2 n. 3 4 9 10 11 12 19 35 36 37 47 63 118 122 253
Hydruntinus, Ioannes      16
Hypatia      5 6 14 18
Hypsicles      2
Hypsicles, on polygonal numbers      125—126 252 253
Iamblichus      2 3 37 49 50 115—116 126
Ibn ab $\bar{\imath}$ Usaibi’a      19
Ibn al — Haitham      19
Identical formulae in Diophantus      104 105
Indeterminate equations, $2 x^{2}-y^{2}= \pm 1$ solved by Pythagoreans      117—118 278 310
Indeterminate equations, double-equations for making one expression a square and another a cube      91—92
Indeterminate equations, double-equations for making two expressions simultaneously squares      11
Indeterminate equations, double-equations for making two expressions simultaneously squares, two expressions of first degree      73—80 80—82
Indeterminate equations, double-equations for making two expressions simultaneously squares, two of second degree, or one of second and one of first      81—87
Indeterminate equations, how to find fresh solutions when one is known      68—70
Indeterminate equations, indeterminate equations in Anthology      114
Indeterminate equations, other Greek examples      118—121
Indeterminate equations, rule for solving double-equations in which two expressions are to be made squares      73 146
Indeterminate equations, single, of higher degrees      87—91
Indeterminate equations, single, of second degree      67—73
Indian method      12—13 21
Indian solution of $x^{2} - Ay^{2}= 1$       281—285 290 292
Inventum Novum of J. de Billy      28 165 184 198 204 205 n. 230 231 239
Inventum Novum of J. de Billy, Supplement      267—328 passim
Ioannes Hydruntinus      16
Ish $\bar{a}$ q b. Y $\bar{u}$ nis      19
Italian scale of powers      40 41
jacobi      108 n. 288
Kausler      31
Kaye, G. R.      381
Ka’b, Arabic term for cube of unknown      41 n.
Kenyon      45
Konen      378 379 281 385 386 388 391
kronecker      388
Krumbiegel      113
Kummer      145 n.
Lagrange      73 110 188 373 373 274 275 276 277 285 387 388 290 293 299 300
Lato, “side”      40 n.
legendre      107 n. 109 188 273
Lehmann      35
Lejeune — Dirichlet      145 288
Leon      124
Leonardo of Pisa      11 41 120
Less and greater, signs for      50 n.
Limits, approximation to      95—98
Limits, method of      57 94 95
Logistica speciosa and Logistica numerosa distinguished by Vieta      49
Loria      63 n. 157 168 175 176 195 197 207 340 241
Lousada, Abigail      31
Luca Paciuolo      31 40
M $\bar{a}$ l, Arabic term for square      41 n.
Madrid MS.      14 15 16
Manuscripts of Diophantus      14—18
Maximus Planudes      13 14 19 21 31 43 44 45 46 48
Measurement of a Circle (Archimedes)      122
Mendoza      17
Metrica of Heron      43 44 45 63 129
Metrica of Heron, MS. of      118
Metrodorus      5 113
Minus, Diophantus’ sign for      41—44 130
Minus, Diophantus’ sign for, Bombelli’s abbreviation      22
Minus, Diophantus’ sign for, modern sign for      49
Minus, Diophantus’ sign for, same sign in Heron’s Metrica      43 44
Minus, Diophantus’ sign for, Vieta’s sign for difference between (= for $\sim$ )      50 n.
Montchall, Carl      v 18
Montucla      28
Moriastica of Diophantus      3—4
Muhammad b. M $\bar{u}$ s $\bar{a}$ al —Khuw $\bar{a}$ razm $\bar{\imath}$       34 50
Multiplication, signs for      50 n.
Murr, Ch. Th.      v 10
Negative quantities not recognised by Diophantus as real      53—53
Nesselmann      6—10 21 35 26 39 34 49—51 55—58 67 87 89 93 108 140 173 304 207 252 329
Nicomachus      3 136 127
Notation, algebraic, Diophantus’ notation      33—49 51—53
Notation, algebraic, three stages      49—51
Nu $\tilde{n}$ ez      23
Numbers which are the sum of two squares      105—107 368—371
Numbers which are the sum of two squares, corresponding theorem for triangles, pentagons, etc      188 373
Numbers which are the sum of two squares, numbers not square are the sum of two, three or four squares      110 373 374
Numbers which are the sum of two squares, numbers which are not      107—108 371—373
Numbers which are the sum of two squares, numbers which are the sum of three squares      373—373
Numbers which are the sum of two squares, numbers which are the sum of three squares, numbers which are not      108—109 373
Numerus, numero, term for unknown quantity      38 40
Oughtred      50 n.
Ozanam      288
Pachymeres, Georgius      18 19 31 37
Paciuolo, Luca      21 40
Pappus      11 13
Papyrus Rhind      113
Papyrus Rhind, Berlin papyrus 6619      113
Paris MSS. of Diophantus      15 16 18
Pazzi, A. M.      31
Pell, John      31 386 288
Peurbach, G. von      20
Philippus of Opus on polygonal numbers      125
Planudes, Maximus      13 14 19 21 31 43 44 45 46 48
Plato      4 38 111 113 116 125
Plus, signs for      23 49
Plus, signs for, expressed in Diophantus by juxtaposition      39
Plutarch      137
Polygonal Numbers, began with Pythagoreans      124—125
Polygonal Numbers, Diophantus’ extensions      137
Polygonal Numbers, figured by arrangement of dots      125
Polygonal Numbers, Hypsicles on      125—136 353 353
Polygonal Numbers, sketch of history of subject      124—127
Polygonal Numbers, treatise on      3 11—12 247—259
Porisms of Diophantus      3 8—10 99—101 301 303 314
Poselger      30 98
Powers of unknown quantity and signs for      37—39 139
Powers of unknown quantity and signs for, Egyptian scale      41
Powers of unknown quantity and signs for, Italian and Arabian scale (multiplicative) contrasted with Diophantine (additive)      40—41
Proclus      4 113 116 117 118 242
Psellus      2 14 18 41 111
Ptolemy      18 44
Pythagoreans      3
Pythagoreans on rational right-angled triangles      116 24 2
Pythagoreans, on indeterminate equation $2 x^{2} - y^{2}= \pm 1$       117—118 378 310
Pythagoreans, on polygonal numbers      134—135

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