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| Heath T.L. (ed.) — Thirteen Books of Euclid's Elements, Vol. 1 |
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| Предметный указатель |
"Abthiniathus" (or "Anthisathus") 203
"Anthisathus" (or "Abthiniathus") 203
"Aqaton" 88
"Diagonal" numbers see “"Side-" and "diagonal-" numbers”
"Gnomon-wise"  , old name for perpendicular  36 181 272
"Golden section" = section in extreme and mean ratio 137
"Golden section", connexion with theory of irrationals 137
"Goose's foot" (pes anseris), name for Eucl. III. 7 99
"Heavy and Light," tract on 18
"Heromides" 158
"Herundes" 156
"Iflaton" 88
"Mixed" (lines) 161—162
"Mixed" (surfaces) 162 170
"Mixed" different meanings of "mixed" 162
"Peacock's tail," name for III. 8 99
"Platonic" figures 2
"Side-" and "diagonal-" numbers, connexion with Eucl. II. 9 10 398—400
"Side-" and "diagonal-" numbers, described 398—400
"Side-" and "diagonal-" numbers, due to Pythagoreans 400
"Side-" and "diagonal-" numbers, use for approximation to  399
"Similar" ( = equal) angles 182 252
"Similar" ( = equal) angles, "similar" numbers 357
"Solid loci" 329 330
"Solid loci", Solid Loci of Aristaeus 16 329
"Solid problems" 329 330
'All b. Ahmad Abu 'l Qasim al-Antaki 86
Abu 'All al-Hasan b. al-Hasan b. al-Haitham 88 89
Abu 'l 'Abbas al-Fadl b. Hatim see “an-Nairizi”
Abu 'l Wafa al-Bozjani 77 85 86
Abu 'Uthman ad-Dimashql 25 77
Abu Da'ud Sulaiman b. 'Uqba 85 90
Abu Ja'far al-Khazin 77 85
Abu Ja'far Muh. b. Muh. b. al-Hasan Nasiraddin at-Tusi see “Naslraddm”
Abu Muh. al-Hasan b. 'Ubaidallah b. Sulaiman b. Wahb 87
Abu Muh. b. AbdalbaqI al-Bagdadi al-Faradi 8n. 90
Abu Nasr Gars al-Na'ma 90
Abu Nasr Mansur b. 'All b. 'Iraq 90
Abu Nasr Muh. b. Muh. b. Tarkhan b. Uzlag al-Farabl 88
Abu Sahl Wijan b. Rustam al-Kuhl 88
Abu Said Sinan b. Thabit b. Qurra 88
Abu Yusuf Ya'qub b. Ishaq b. as-Sabbah al-Kindi 86
Abu Yusuf Ya'qub b. Muh. ar-Razi 86
Abu' Abdallah Muh. b. Mu'adh al-Jayyani 90
Abu'All al-Basri 88
Adjacent  , meaning 181
Aenaeas (or Aigeias) of Hierapolis 28 311
Aganis 27—28 191
Ahmad b. 'Umar al-Karabisi 85
Ahmad b. al-Husain al-Ahwazi al-Katib 89
Aigeias (? Aenaeas) of Hierapolis 28 311
al-'Abbas b. Said al-Jauhari 85
al-Ahwazi 89
al-Antaki 86
al-Arjanl, Ibn Rahawaihi 86
al-Blruni 90
al-Faradl 8n. 90
al-Haitham 88 89
al-Hajjaj b. Yusuf b. Matar, translator of the Elements 22 75 76 79 80 83 84
al-Hasan b. 'Ubaidallah b. Sulaiman b. Wahb 87
al-Jauhari, al-'Abbas b. Sa'id 85
al-Jayyani 90
al-KarabisI 85
al-Khazin, Abu Jafar 77 85
al-Kindi 5n. 86
al-Kuhi 88
al-Ma'mun, Caliph 75
Al-Mahani 85
al-Mansur, Caliph 75
al-Mustasim, Caliph 90
al-Mutawakkil, Caliph 75
al-Qifti 4n. 94
Alexander Aphrodisiensis 7n. 29
Algebra, geometrical 372—374
Algebra, geometrical, algebraical equivalents of propositions in Book II 372—373
Algebra, geometrical, and favoured by Pappus 373
Algebra, geometrical, classical method was that of Eucl. II. (cf. Apollonius) 373
Algebra, geometrical, geometrical equivalents of algebraical operations 374
Algebra, geometrical, preferable to semi-algebraical method 377—378
Algebra, geometrical, semi-algebraical method due to Heron 373
Allman, G.J. 135n. 318 352
Alternate (angles) 308
Alternative proofs, interpolated 58 59
Amaldi 175 179—180 193 201 313 328
Ambiguous case 306—307
Amphinomus 125 128 150n.
Amyclas of Heraclea 117
An-Nairizi, Abu 'l 'Abbas al-Fadl b. Hatim 21—24 85 184 190 191 195 223 232 258 270 285 299 303 326 364 367 369 373 405 408
Analysis (and synthesis) 18
Analysis (and synthesis), alternative proofs of XIII. 1—5 by 137
Analysis (and synthesis), analysis and synthesis of problems 140—142
Analysis (and synthesis), analysis should also reveal dcopia-fids (conditions of possibility) 142
Analysis (and synthesis), definitions of, interpolated 138
Analysis (and synthesis), described by Pappus 138—139
Analysis (and synthesis), example from Pappus 141—142
Analysis (and synthesis), method of analysis and precautions necessary to 139—140
Analysis (and synthesis), modern studies of Greek analysis 139
Analysis (and synthesis), theoretical and problematical analysis 138
Analysis (and synthesis), Treasury of analysis  8 10 11 138
Analysis (and synthesis), two parts of analysis (a) transformation, (b) resolution, and two parts of synthesis, (a) construction, (b) demonstration 141
Analytical method 36
Analytical method, supposed discovery of, by Plato 134 137
Anaximander 370
Anchor-ring 163
Andron 126
Angle, adjacent angles 181
Angle, alternate 308
Angle, angle as duster of straight lines or rays 180—181
Angle, angle in a semicircle, theorem of 317—329
Angle, angle of a segment 253
Angle, angle of a semicircle 182 253
Angle, Apolloius' view of, as contraction 176 177
Angle, Aristotle's notion of angle as icXdacs 176
Angle, as part of a plane ("angular sector") 179—180
Angle, classification of angles (Geminus) 178—179
Angle, constmction by Apollonius of angle equal to angle 296
Angle, curvilineal and "mixed" angles 26 178—179
Angle, Curvilineal and rectilineal, Euclid's definition of 176sq.
Angle, definition criticised by Syrianus 176
Angle, definitions of angle classified 179
Angle, defiried by Veronese 180
Angle, Euclid 178
Angle, exterior and interior (to a figure) 263 280
Angle, exterior when reentrant 263
Angle, flat angle (Veronese etc.) 180—181 269
Angle, horn-like  177 178 182 265
Angle, interior and opposite 280
Angle, lune-like  26 178—179
Angle, Plutarch and Carpus on 177
Angle, quale, Aristotle and Eudemus 177—178
Angle, recent Italian views 179—181
Angle, relation, Euclid 178
Angle, scraper-like  178
Angle, similar ( = equal) 178 182 252
Angle, Syrianus' compromise 178
Angle, three kinds of angles, which is prior (Aristotle)? 181—182
Angle, to which category does it belong? quantum, Plutarch, Carpus, "Aganis" 177
Angle, treatise on the Angle by Eudemus 34 38 177—178
Angle, trisection of angle, by conchoid of Nicomedes 265—266
Angle, trisection of angle, by quadratrix of Hippias 266
Angle, trisection of angle, by spiral of Archimedes 267
Angle, vertical 278
Antiphon 7n. 35
Apastamba — Sulba — Sutra 352
Apastamba — Sulba — Sutra, and use of gnomon 360—364
Apastamba — Sulba — Sutra, approximation to and Thibaut's explanation 361 363—364
Apastamba — Sulba — Sutra, Biirk's claim that Indians had discovered the irrational 363—364
Apastamba — Sulba — Sutra, evidence in, as to early discovery of Eucl. I. 47
Apastamba — Sulba — Sutra, inaccurate values of  in 364
Apollodorus "Logisticus" 37 319 351
| Apollonius, a "carpenter" 5
Apollonius, adaptation to conies "of theory of application of areas 344—345
Apollonius, comparison of dodecahedron and icosahedron 6
Apollonius, constructions by, for a perpendicular 270
Apollonius, constructions by, for an angle equal to an angle 296
Apollonius, constructions by, for bisection of straight line 268
Apollonius, disparaged by Pappus in comparison with Euclid 3
Apollonius, general definition of diameter 325
Apollonius, geometrical algebra in 373
Apollonius, his "general treatise" 42
Apollonius, on elementary geometry 42
Apollonius, on parallel-axiom (?) 42—43
Apollonius, on the angle 176
Apollonius, on the cochlias 34 42 162
Apollonius, on the line 159
Apollonius, on unordered irrationals 42 115 138 188 221 222 246 259 370 373
Apollonius, Plane Loci 14 259 330
Apollonius, Plane veOaeis 151
Apollonius, supposed by some Arabians to be author of the Elements 5
Apollonius, tried to prove axioms 42 62 222—223
Application of areas 36 343—345
Application of areas, adaptation to conies (Apollonius) 344—345
Application of areas, application contrasted with construction (Proclus) 343
Application of areas, complete method equivalent to geometric solution of mixed quadratic equation 344—345 383—385 386—388
Application of areas, contrasted with exceeding and falling-short 343
ar-Razi, Abu Yiisuf Ya'qub b. Muh. 86
Arabian editors and commentators 75—90
Arabic numerals in scholia to Book X., 12th c 71
Archimedes 116 142
Archimedes, "Porisms" in, IIn 13
Archimedes, "postulates" in 120 123
Archimedes, famous "lemma" (assumption) known as Postulate of Archimedes 234
Archimedes, on plane 171—172 225 370
Archimedes, on straight line 166
Archimedes, spiral of 26 267
Archytas 20
Areskong, M.E. 113
Arethas, Bishop of Caesarea 48
Arethas, had famous Plato MS. of Patmos (Cod. Ciarkianus) written 48
Arethas, owned Bodleian MS. (B) 47—48
Argyrus, Isaak 74
Aristaeus 138
Aristaeus, comparison of five (regular solid) figures 6
Aristaeus, on conies 3
Aristaeus, Solid Loci 16 329
Aristotelian Problems 166 182 187
Aristotle, axioms indemonstrable 121
Aristotle, definitions of "squaring" 149—150 410
Aristotle, gives pre-Euclidean proof of I. 5 252—253
Aristotle, on attributes  and  319 320 325
Aristotle, on axioms 119—121
Aristotle, on definition by negation 156—157
Aristotle, on definitions 117 119—120 143—144 146—150
Aristotle, on definitions of surface 170
Aristotle, on distinction between hypotheses and axioms 120
Aristotle, on distinction between hypotheses and definitions 119 120
Aristotle, on distinction between hypotheses and postulates 118 119
Aristotle, on figure and definition of 182—183
Aristotle, on first principles 117 sqq.
Aristotle, on gnomon 351 355 359
Aristotle, on lines, classification of 159—160
Aristotle, on lines, definitions of 158—159
Aristotle, on nature of elements 116
Aristotle, on parallels 190—192 308—309
Aristotle, on points 155—156 165
Aristotle, on priority as between right and acute angles 181—182
Aristotle, on reductio ad absurdum 136
Aristotle, on reduction 135
Aristotle, on sum of angles of triangle 319—321
Aristotle, on sum of exterior angles of polygon 322—338 322—345 117 150n. 181 184 185 187 188 195 202 203 221 222 223 226 259 262—263 283
Aristotle, on the angle 176—178
Aristotle, on the infinite 232—234
Aristotle, on the objection 135
Aristotle, on theorem of angle in a semicircle 149
Aristotle, quotes Plato's definition of straight line 166
Aristotle, supposed postulate or axiom about divergent lines taken by Proclus from 45 207
Ashkal *at-ta'sls 5n.
Ashraf Shamsaddin as-Samarqandi, Muh. b. 5n 89
Astaroff, Ivan 113
Asymptotic (non-secant) lines 40 161 203
at-Tusi see “Nasiraddin”
Athelhard of Bath 78 93—96
Athenaeus of Cyzicus 117
August, E.F. 103
Austin, W. 103 111
Author of Book XIV. 5 6
Autolycus, on the moving sphere 17
Avicenna 77 89
Axioms, "axiom" with Stoics = every simple declaratory statement 41 221
Axioms, = "common (things)" or "common opinions" in Aristotle 120 221
Axioms, at-tempt by Apollonius to prove 222—223
Axioms, axioms of congruence, (1) Euclid's Common Notion 4 224—227
Axioms, axioms of congruence, (2) modern systems (Pasch Veronese and 224—227
Axioms, called "common notions" in Euclid 121 221
Axioms, common to all sciences 119 120
Axioms, distinguished from hypotheses, by Aristotle 120—121
Axioms, distinguished from hypotheses, by Proclus 121—122
Axioms, distinguished from postulates by Aristotle 118—119
Axioms, distinguished from postulates by Proclus (Geminus and "others") 40 121—123
Axioms, Heron three 222
Axioms, indemonstrable 121
Axioms, interpolated axioms 224 232
Axioms, Pappus' additions to axioms 25 223 224 232
Axioms, Proclus on difficulties in distinctions 123—124
Axioms, Proclus recognises five 222
Axioms, which are genuine? 221sqq.
Babylonians, knowledge of triangle 3 4 5 352
Bacon, Roger 94
Balbus, de mensuris 91
Barbarin 219
Barlaam, arithmetical commentary on Eucl. II. 74
Barrow 103 105 110 111
Base, meaning 248—249
Basel, editio princeps of Eucl. 100—101
Basilides of Tyre 5 6
Baudhayana Sulba — Sutra 360
Bayfius (Bai'f, Lazare) 100
Becker, J.K. 174
Beez 176
Beltrami, E. 219
Benjamin of Lesbos 113
Bergh, P. 400—401
Bernard, Edward 102
Besthorn and Heiberg, edition of al-Hajjaj's translation and an-Nairizi's commentary 22 27n. 79n.
Bhaskara 355
Billingsley, Sir Henry 109—110
Bjoernbo, Axel Anthon 17n. 93
Boccaccio 96
Bodleian MS. (B) 47 48
Boeckh 351 371
Boethius 92 95 184
Bologna ms. (b) 49
Bolyai, J. 219
Bolyai, W. 174—175 219 328
Bolzano 167
Boncompagni 93n. 104n.
Bonola, R. 202 219 237
Borelli, Giacomo Alfonso 106 194
Boundary (6pos) 182 183
Brakenhjelm, P. R. 113
Breitkopf, Joh. Gottlieb Immanuel 97
Bretschneider 136n 137 295 304 344 354 358
Briconnet, Francois 100
Briggs, Henry 102
Brit. Mus. palimpsest 7—175
Bryson 8n.
Buerk, A. 352 360—364
Buerklen 179
Buteo (Borrel), Johannes 104
Cabasilas, Nicolaus and Theodorus 72
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