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| Heath T.L. (ed.) — Thirteen Books of Euclid's Elements, Vol. 3 |
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| Предметный указатель |
Aristotle on definitions of odd and even by one another II. 281
Aristotle on definitions of surface I. 170
Aristotle on distinction between hypotheses and axioms I. 120
Aristotle on distinction between hypotheses and definitions I. 119 120
Aristotle on distinction between hypotheses and postulates I. 118 119
Aristotle on figure and definition of I. 182—183
Aristotle on first principles I. 177sqq.
Aristotle on gnomon I. 351 355 359
Aristotle on inverse ratio II. 134 149
Aristotle on lines, classification of I. 159—160
Aristotle on lines, definitions of I. 158—159
Aristotle on nature of elements I. 116
Aristotle on non-applicability of arithmetical proofs to magnitudes if these are not numbers II. 113
Aristotle on number II. 280
Aristotle on parallels I. 190—192 308—309
Aristotle on points I. 155—156 165
Aristotle on prime numbers II. 284—285
Aristotle on priority as between right and acute angles I. 181—182
Aristotle on proportion as "equality of ratios" II. 119
Aristotle on proportion in three terms (continuous), and in four terms (discrete) II. 131 293
Aristotle on reductio ad absurdum I. 136
Aristotle on reduction I. 135
Aristotle on representation of numbers by pebbles forming figures II. 288
Aristotle on similar rectilineal figures II. 188
Aristotle on sum of angles of triangle I. 319—321
Aristotle on sum of exterior angles of polygon I. 322
Aristotle on the angle I. 176—178
Aristotle on the infinite I. 232—234
Aristotle on the objection I. 135
Aristotle on theorem in proportion (alternando) not proved generally till his time II. 113
Aristotle on theorem of angle in a semicircle I. 149
Aristotle on unit II. 279
Aristotle, axioms indemonstrable I. 121
Aristotle, body "bounded by surfaces" III. 263
Aristotle, definition of "body" as that which has three dimensions or as "depth" III. 262
Aristotle, definition of sphere III. 269
Aristotle, definitions of "squaring" I. 149—150 410
Aristotle, gives pre-Euclidean proof of Eucl. I. 5 I. 252—253
Aristotle, gives proof (no doubt Pythagorean) of incommensurability of  III. 2
Aristotle, has locus-theorem (arising out of Eucl. VI. 3) also given in Apollonius' Plane Loci II. 198—200
Aristotle, has proof (pre-Euclidean) that angle in semicircle is right II. 63
Aristotle, quotes Plato's definition of straight line I. 166
Aristotle, speaks of six "dimensions" III. 263
Aristotle, supposed postulate or axiom about divergent lines taken by Proclus from I. 45 207
Arithmetic, Elements of, anterior to Euclid II. 295
Ashkal at-ta'sis I. 5n.
Ashraf Shamsaddin as-Samarqandi, Muh. b. I. 5n. 89
Astaroff, Ivan I. 113
Asymptotic (non-secant) of lines I. 40 161 203
Asymptotic (non-secant) of parallel planes III. 265
at-Tusi see "Nasiraddin"
Athelhard of Bath I. 78 93—96
Athenaeus of Cyzicus I. 117
August, E.F. I. 103 II. 25 149 238 256 412 III. 48
Austin, W. I. 103 111 II. 188 211 259
Autolycus, on the moving sphere I. 17
Avicenna I. 77 89
Axioms = "common (things)" or "common opinions" in Aristotle I. 120 221
Axioms, "axiom" with Stoics = every simple declaratory statement I. 41 221
Axioms, attempt by Apollonius to prove I. 222—223
Axioms, axioms of congruence, (1) Euclid's Common Notion 4 I. 224—227
Axioms, axioms of congruence, (2) modern systems (Pasch, Veronese and Hilbert) I. 228—231
Axioms, axioms tacitly assumed, in Book V. II. 137
Axioms, axioms tacitly assumed, in Book VI. II. 294
Axioms, called "common notions" in Euclid I. 121 221
Axioms, common to all sciences I. 119 120
Axioms, distinguished from hypotheses, by Aristotle I. 120—121
Axioms, distinguished from hypotheses, by Proclus I. 121—122
Axioms, distinguished from postulates by Aristotle I. 118—119
Axioms, distinguished from postulates by Proclus (Geminus and "others") I. 40 121—123
Axioms, indemonstrable I. 121
Axioms, interpolated axioms I. 224 232
Axioms, Pappus' additions to axioms I. 25 223 224 232
Axioms, Proclus on difficulties in distinctions I. 123—124
Axioms, Proclus recognises five I. 222
Axioms, Proclus recognises five, Heron three I. 222
Axioms, which are genuine? I. 221sqq.
Axis of cone III. 261 271
Axis of cylinder III. 262 271
Axis of sphere III. 261 269
Babylonians, knowledge of triangle 3, 4, 5 I. 352
Babylonians, supposed discoverers of "harmonic proportion" II. 112
Bacon, Roger I. 94
Baermann, G.F. II. 213
Balbus, de mensuris I. 91
Baltzer, R. II. 30
Barbarin I. 219
Barlaam, arithmetical commentary on Eucl. II. I. 74
Barrow I. 103 105 110 111 II. 117 121 186 238
Base of cone III. 262
Base of cylinder III. 262
Base, meaning I. 248—249
Basel editio princeps of Eucl. I. 100—101
Basilides of Tyre I. 5 6 III.
Baudhayana Sulba-Sutra I. 360
Bayfius (Baif, Lazare) I. 100
Becker, J.K. I. 174
Beez I. 176
Beltrami, E. I. 219
Benjamin of Lesbos I. 113
Bergh, P. 400—401
Bernard, Edward I. 102
Besthorn and Heiberg, edition of al-Hajjaj's translation and an-Nairizi's commentary I. 22 27n. 79n.
Bhaskara I. 355
Billingsley, Sir Henry I. 109—110 II. 238 III.
Bimedial (straight line), first and second, and biquadratic equations of which they are roots III. 7
Bimedial (straight line), first bimedial defined III. 84—85
Bimedial (straight line), first bimedial defined, equivalent to square root of second binomial III. 84 120—123
Bimedial (straight line), first bimedial defined, uniquely divided III. 94—95
Bimedial (straight line), second bimedial defined III. 85—87
Bimedial (straight line), second bimedial defined, equivalent to square root of third binomial III. 84 124—125
Bimedial (straight line), second bimedial defined, uniquely divided III. 95—97
Binomial (straight line), binomial equivalent to square root of first binomial III. 116—120
Binomial (straight line), binomial uniquely divided, and algebraical equivalent of this fact III. 92—94
Binomial (straight line), biquadratic of which binomial is a positive root III. 7
Binomial (straight line), cannot be apotome also III. 240—242
Binomial (straight line), compound irrational straight line (sum of two "terms") III. 7
Binomial (straight line), connected by Theaetetus with arithmetic mean III. 3 4
Binomial (straight line), defined III. 83 84
Binomial (straight line), different from medial (straight line) and from other irrationals (first bimedial etc.) of same series with itself III. 242
Binomial (straight line), first, second, third, fourth, fifth and sixth binomials, quadratics from which arising III. 5—6 III.
Binomial (straight line), first, second, third, fourth, fifth and sixth binomials, quadratics from which arising, and found respectively (X. 48-53) III. 102—115
Binomial (straight line), first, second, third, fourth, fifth and sixth binomials, quadratics from which arising, are equivalent to squares of binomial, first bimedial etc. III. 132—145
Binomial (straight line), used to rationalise apotome with proportional terms III. 248—252 252—254
Bjornbo, Axel Anthon I. 17n. 93
Boccaccio I. 96
Bodleian MS. (B) I. 47 48 III.
Boeckh I. 351 371
Boethius I. 92 95 184 II.
Bologna ms. (b) I. 49
Bolyai, J. I. 219
Bolyai, W. I. 174—175 219 328
Bolzano I. 167
Boncompagni I. 93n. 104n.
Bonola, R. I. 202 219 237
Borelli, Giacomo Alfonso I. 106 194 II. 84
Boundary I. 182 183
Brakenhjelm, P.R. I. 113
Breadth (of numbers) = second dimension or factor II. 288
Breitkopf, Joh. Gottlieb Immanuel I. 97
Bretschneider I. 136n. 137 295 304 344 354 358 III. 442
Briconnet, Francois I. 100
Briggs, Henry I. 102 II.
Brit. Mus. palimpsest, 7th-8th c. I. 50
Bryson I. 8n.
Burk, A. I. 352 360—364
Burklen I. 179
Buteo (Borrel), Johannes I. 104
Cabasilas, Nicolaus and Theodorus I. 72
Caiani, Angelo I. 101
| Camerarius, Joachim I. 101 III.
Camerer, J.G. I. 103 293 II. 25 28 33 34 40 67 121 121 189 213 244
Camorano, Rodrigo I. 112
Campanus, Johannes I. 3 78 94—96 104 106 110 407 II. 41 56 90 116 119 121 146 189 211 234 235 253 275 320 322 328
Candalla, Franciscus Flussates (Francois de Foix, Comte de Candale) I. 3 104 110 II.
Cantor, Moritz I. 7n. 20 272 304 318 320 333 352 355 357—358 360 401 II. 40 97 III. 15 438
Cardano, Hieronimo II. 41 III.
Carduchi, L. I. 112
Carpus, on Astronomy I. 34 43 45 127 128 177
Case, cases interpolated I. 58 59
Case, Greeks did not infer limiting cases but proved them separately II. 75
Case, technical term I. 134
Casey, J. II. 227
Casiri I. 4n. 9n.
Cassiodorius, Magnus Aurelius I. 92
Catalan III. 527
Cataldi, Pietro Antonio I. 106
Catoptrica, attributed to Euclid, probably Theon's I. 17
Catoptrica, Catoptrica of Heron I. 21 253
Cauchy III. 267
Cauchy, proof of Eucl. XI. 4 III. 280
Censorinus I. 91
Centre I. 184—185
Ceria Aristotelica I. 35
Cesaro, E. III. 527
Chasles on Porisms of Euclid I. 10 11 14 15
Chinese, "Tcheou pei" I. 355
Chinese, knowledge of triangle 3, 4, 5 I. 352
Christensen III. 8
Chrysippus I. 330
Chrystal, G. III. 19
Cicero I. 91 351
Circle = round, (Plato) I. 184
Circle, (Aristotle) I. 184
Circle, a plane figure I. 183—184
Circle, bisected by diameter (Thales) I. 185
Circle, bisected by diameter (Thales), (Saccheri) I. 185—186
Circle, centre of I. 184—185
Circle, circles intersecting and touching, difficulties in Euclid's treatment of II. 25—27 28—29
Circle, circles intersecting and touching, modern treatment of II. 30—32
Circle, circles touching, meaning of definition II. 3
Circle, definition of I. 183—185
Circle, definition of "equal circles" II. 2
Circle, exceptionally in sense of "circumference" II. 23
Circle, intersections with straight line I. 237—238 272—274
Circle, intersections with straight line, with another circle I. 238—240 242—243 293—294
Circle, pole of I. 185
Circumference I. 184
Cissoid I. 161 164 176 330
Clairaut I. 328
Clavius (Christoph Schluessel) I. 103 105 194 232 381 391 407 II. 41 42 47 49 53 56 67 70 73 130 170 190 231 238 244 271 III. 331 341 350 359 433
Claymundus, Joan. I. 101
Cleonides, Introduction to Harmony I. 17
Cochlias or cochlion (cylindrical helix) I. 162
Codex Leidensis 399, 1 I. 22 27n. 79n.
Coets, Hendrik I. 109
Commandinus I. 4 102 103 104—105 106 110 111 407 II. 130 190
Commandinus, edited (with Dee) De divisionibus I. 8 9 110
Commandinus, scholia included in translation of Elements I. 73
Commensurable, commensurable in length, commensurable in square, and commensurable in square only defined III. 10 11
Commensurable, defined III. 10
Commensurable, symbols used in notes for these terms III. 34
Commentators on Eucl. criticised by Proclus I. 19 26 45
Common Notions = axioms I. 62 120—121 221—222
Common Notions, called "axioms" by Proclus I. 221
Common Notions, meaning and appropriation of term I. 221
Common Notions, which are genuine? I. 221sq.
Complement, "about diameter" I. 341
Complement, meaning of I. 341
Complement, not necessarily parallelograms I. 341
Complement, use for application of areas I. 342—343
Componendo see ""Composition" of ratios"
Componendo, componendo and separando used relatively to each other II. 168 170
Composite, (of lines) I. 160
Composite, (of numbers) II. 286
Composite, (of surfaces) I. 170
Composite, with Eucl. and Theon of Smyrna composite numbers may be even, but with Nicom. and Iamblichus are a subdivision of odd II. 286
Composite, with Eucl. and Theon of Smyrna composite numbers may be even, but with Nicom. and Iamblichus are a subdivision of odd, plane and solid numbers are species of II. 286
Composition of ratio, denoted by componendo, distinct from compounding ratios II. 134—135
Compound ratio, (interpolated?) definition of II. 189—190 III.
Compound ratio, compounded ratios in V. 20-23 II. 176—178
Compound ratio, explanation of II. 132—133
Conchoids I. 160—161 265—266 330
Conclusion, definition merely stating conclusion I. 149
Conclusion, necessary part of a proposition I. 129—130
Conclusion, particular conclusion immediately made general I. 131
Cone, definitions of, by Apollonius III. 270
Cone, definitions of, by Euclid III. 262 270
Cone, distinction between right-angled, obtuse-angled and acute-angled cones a relic of old theory of conics III. 270
Cone, similar cones, definition of III. 262 271
Congruence theorems for triangles, recapitulation of I. 305—306
Congruence-Axioms or Postulates, Common Notion 4 in Euclid I. 224—225
Congruence-Axioms or Postulates, modern systems of (Pasch, Veronese, Hilbert) I. 228—231
Conics, focus-directrix property proved by Pappus I. 15
Conics, fundamental property as proved by Apollonius equivalent to Cartesian equation I. 344—345
Conics, of Apollonius I. 3 16
Conics, of Aristaeus I. 3 16
Conics, of Euclid I. 3 16
Consequents ("following" terms in a proportion) II. 134
Constantinus Lascaris I. 3
Construct contrasted with apply to I. 343
Construct contrasted with describe on I. 348
Construct, special connotation I. 259 289
Construction, mechanical constructions I. 151 387
Construction, one of formal divisions of a proposition I. 129
Construction, sometimes unnecessary I. 130
Construction, turns nominal into real definition I. 146
Continuity, principle of I. 234sq. 242 272 294
Continuous proportion in three terms II. 131
Conversion of ratio, denoted by convertendo II. 135
Conversion of ratio, denoted by convertendo, convertendo theorem not established by V. 19, Por. II. 174—175
Conversion of ratio, denoted by convertendo, convertendo theorem not established by V. 19, Por., but proved by Simson's Prop. E. II. 175 III.
Conversion of ratio, denoted by convertendo, Euclid's roundabout substitute III. 38
Conversion, geometrical, "leading" and partial varieties of I. 256—257 337
Conversion, geometrical, distinct from logical I. 256
Convertendo see "Conversion of ratios"
Copernicus I. 101
Cordonis, Mattheus I. 97
Corresponding magnitudes II. 134
Cossali III. 8
Cratistus I. 133
Crelle, on the plane I. 172—174 III.
Ctesibius I. 20 21 39n.
Cube, cube number, defined II. 291
Cube, defined III. 262
Cube, duplication of cube reduced by Hippocrates of Chios to problem of two mean proportionals I. 135 II.
Cube, problem of incribing in sphere, Euclid's solution III. 478—480
Cube, problem of incribing in sphere, Pappus' solution III. 480
Cube, two mean proportionals between two cube numbers II. 294 364—365
Cunn, Samuel I. 111
Curtze, Maximilian, editor of an-NairizI I. 22 78 92 94 96 97n.
Curves, classification of see "Line"
Cyclici of a particular kind of square number II. 291
Cyclomathia of Leotaud II. 42
Cylinder, definition of III. 262
Cylinder, similar cylinders defined III. 262
Cylindrical helix I. 161 162 329 330
Czecha, Jo. I. 113
da Vinci, Lionardo I. 365—366
Dasypodius (Rauchfuss) Conrad I. 73 102
Data of Euclid I. 8 132 141 385 391
Data of Euclid, Def. 2 II. 248
Data of Euclid, Prop. 24 II. 246—247
Data of Euclid, Prop. 55 II. 254
Data of Euclid, Prop. 58 II. 263—265
Data of Euclid, Prop. 67 assumes part of converse of Simson's Prop. B (Book VI.) II. 224
Data of Euclid, Prop. 70 II. 250
Data of Euclid, Prop. 8 II. 249—250
Data of Euclid, Prop. 85 II. 264
Data of Euclid, Prop. 87 II. 228
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