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| Heath T.L. (ed.) — Thirteen Books of Euclid's Elements, Vol. 3 |
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| Ïðåäìåòíûé óêàçàòåëü |
Data of Euclid, Prop. 93 II. 227
Data of Euclid, Props. 56 and 68 II. 249
Data of Euclid, Props. 59 and 84 II. 266—267
de Errard, Jean, Bar-le-Duc I. 108
De levi et ponderoso, tract I. 18
De Morgan, A. I. 246 260 269 284 291 298 300 309 313 314 315 369 376 II. 7 9—10 11 15 20 22 29 56 76—77 83 101 104 116—119 120 130 139 145 197 202 217—218 232 233 234 272 275
De Morgan, A. on compound ratio II. 132—133 234
De Morgan, A. on definition of ratio II. 116—117
De Morgan, A. on extension of meaning of ratio to cover incommensurabies II. 118
De Morgan, A. on necessity of proof that tests for greater and less, or greater and equal, ratios cannot coexist II. 130—131 157
De Morgan, A., defence and explanation of V. Def. 5 II. 121—124
De Morgan, A., means of expressing ratios between incommensurables by approximation to any extent II. 118—119
De Morgan, A., sketch of proof of existence of fourth proportional (assumed in V. 18) II. 171
De Morgan, A., sketch of proof of existence of fourth proportional (assumed in V. 18), proposed lemma about duplicate ratios as alternative means of proving VI. 22 II. 246—247
De Morgan, A., sketch of proof of existence of fourth proportional (assumed in V. 18), proposed lemma about duplicate ratios as alternative means of proving VI. 22 on Book X. III. 8
de Vaux, Carra I. 20
De Zolt I. 328
Deahna I. 174
Dechales, Claude Francois Milliet I. 106 107 108 110 II.
Dedekind's theory of irrational numbers corresponds exactly to Eucl. V. Def. 5 II. 124—126
Dedekind's theory of irrational numbers, Dedekind's Postulate and applications of I. 235—240 III.
Dee, John I. 109 110
Dee, John, discovered De divisionibus I. 8 9
Definition, in sense of "closer statement", one of formal divisions of a proposition I. 129
Definition, in sense of "closer statement", one of formal divisions of a proposition, may be unnecessary I. 130
Definitions, a class of thesis (Aristotle) I. 120
Definitions, Aristotle on I. 117 119 120 143
Definitions, Aristotle on unscientific definitions I. 148—149
Definitions, Aristotle's requirements in I. 146—150
Definitions, Aristotle's requirements in, exceptions I. 148
Definitions, definitions of technical terms in Aristotle and Heron, not in Euclid I. 150
Definitions, distinguished from hypotheses I. 119
Definitions, distinguished from hypotheses, but confused therewith by Proclus I. 121—122
Definitions, Euclid's definitions agree generally with Aristotle's doctrine I. 146
Definitions, interpolated definitions I. 61 62
Definitions, must be assumed I. 117—119
Definitions, must be assumed, but say nothing about existence (except in the case of a few primary things) I. 119 143
Definitions, real and nominal definitions (real = nominal plus postulate or proof), Mill anticipated by Aristotle, Saccheri and Leibniz I. 143—145
Definitions, should state cause or middle term and be genetic I. 149—150
Definitions, terms for I. 143
Demetrius Cydonius I. 72
Democritus I. 38
Democritus on parallel and infinitely near sections of cone II. 40 III.
Democritus, On difference of gnomon etc. (? on "angle of contact") II. 40
Democritus, stated, without proving, propositions about volumes of cone and pyramid II. 40 III.
Democritus, treatise on irrational III. 4
Democritus, was evidently on the track of the infinitesimal calculus III. 368
Dercyllides II. 111
Desargues I. 193
Describe on contrasted with construct I. 348
Diagonal I. 185
Diameter of circle or parallelogram I. 185
Diameter of sphere III. 261 269 270
Diameter, as applied to figures generally I. 325
Diameter, as applied to figures generally, "rational" and "irrational" diameter of 5 (Plato) I. 399
Diameter, as applied to figures generally, "rational" and "irrational" diameter of 5 (Plato), Aristotle's requirements in, taken from Pythagoreans I. 399—400 III. 525
Dihedral angle = inclination of plane to plane, measured by a plane angle III. 264—265
dimensions I. 157 158
Dimensions, Aristotle's view of I. 158—159 III.
Dimensions, Aristotle's view of, speaks of six III. 263
Dinostratus I. 117 266
Diocles I. 164
Diodorus I. 203
Diogenes Laertius I. 37 305 317 351 III.
Diophantus I. 86
Diorismus = (a) "definition" or "specification" a formal division of a proposition I. 129
Diorismus = (b) condition of possibility I. 128
Diorismus = (b) condition of possibility, determines how far solution possible and in how many ways I. 130—131 243
Diorismus, diorismi said to have been discovered by Leon I. 116
Diorismus, first instances in Elements I. 234 293
Diorismus, for solution of quadratic II. 259
Diorismus, introduced I. 293
Diorismus, revealed by analysis I. 142
Dippe I. 108
Direction, as primary notion, discussed I. 179
Direction, direction-theory of parallels I. 191—192
Discrete proportion, in four terms II. 131 293
Distance = radius I. 199
Distance, in Aristotle has usual general sense and = dimension I. 199
Dividendo (of ratios) see "Separation separando"
Division (method of), Plato's I. 134
Divisions (of figures), found by Woepcke in Arabic I. 9
Divisions (of figures), found by Woepcke in Arabic and by Dee in Latin translation I. 8 9 110
Divisions (of figures), proposition from II. 5
Divisions (of figures), translated by Muhammad al-Bagdadi I. 8
Divisions (of figures), treatise by Euclid I. 8 9
Dodecahedron, decomposition of faces into elementary triangles II. 98
Dodecahedron, definition of III. 262
Dodecahedron, dodecahedra found, apparently dating from centuries before Pythagoras III. 438
Dodecahedron, dodecahedra found, apparently dating from centuries before Pythagoras, though said to have been discovered by Pythagoreans III. 438
Dodecahedron, problem of inscribing in sphere, Euclid's solution III. 493
Dodecahedron, problem of inscribing in sphere, Pappus' solution III. 501—503
Dodgson, C.L. I. 194 254 261 313 II. 275
Dou, Jan Pieterszoon I. 108
Duhamel, J.M.C. I. 139 328
Duplicate ratio II. 133
Duplicate ratio, "duplicate" of given ratio found by VI. 11 II. 214
Duplicate ratio, duplicate, distinct, double (= ratio 2 : 1), though use of terms not uniform II. 133
Duplicate ratio, lemma on duplicate ratio as alternative to method of VI. 22 (De Morgan and others) II. 242—247
Duplication of cube, reduction of, by Hippocrates, to problem of finding two mean proportionals I. 135 II.
Duplication of cube, wrongly supposed to be alluded to in Timaeus 32 A, B II. 294—295n.
Egyptians II. 112
Egyptians, knowledge of right-angled triangles I. 352
Egyptians, view of number II. 280
Elements, Arabian versions compared with Greek text I. 79—83
Elements, Arabian versions compared with one another I. 83 84
Elements, Arabic translations (1) by al-Hajjaj I. 75 76 79 80 83—84
Elements, Arabic translations (2) by Ishaq and Thabit b. Qurra I. 75—80 83—84
Elements, Arabic translations (3) Nasiraddin at-Tusi I. 77—80 84
Elements, commentators on I. 19—45
Elements, commentators on, Aenaeas (Aigeias) I. 28
Elements, commentators on, an-Nairizi I. 21—24
Elements, commentators on, Heron I. 20—24
Elements, commentators on, Pappus I. 24—27
Elements, commentators on, Porphyry I. 24
Elements, commentators on, Proclus I. 19 29—45
Elements, commentators on, Simplicius I. 28
Elements, contributions to, by Eudoxus I. 1 37 11 112 III. 365—366 374 441
Elements, contributions to, by Hermotimus of Colophon I. 117
Elements, contributions to, by Theaetetus I. 1 37 III. 438
Elements, Euclid's Elements, ultimate aims of I. 2 115—116
Elements, external sources throwing light on text, Heron, Taurus, Sextus Empiricus, Proclus, Iamblichus I. 62—63
Elements, first principles of, definitions, postulates, common notions (axioms) I. 117—124
Elements, Greek texts, August's I. 103
Elements, Greek texts, editio princeps I. 100—101
Elements, Greek texts, Gregory's I. 102—103
Elements, Greek texts, Peyrard's I. 103
Elements, Hebrew translation by Moses b. Tibbon or Jakob b. Machir I. 76
Elements, immediate recognition of I. 116
Elements, interpolations before Theon's time I. 58—63
Elements, introduction into England 10th c. I. 95
Elements, means of comparing Theonine with ante-Theonine text I. 51—53
Elements, MSS. of I. 46—51
Elements, no definitions of such technical terms I. 150
Elements, old translation of 10th c. I. 92
Elements, on the nature of elements (Aristotle) I. 116
Elements, on the nature of elements (Menaechmus) I. 114
Elements, on the nature of elements (Proclus) I. 114—116
Elements, pre-Euclidean Elements, by Hippocrates of Chios, Leon I. 116
Elements, pre-Euclidean Elements, by Theudius I. 117
Elements, Proclus on advantages of Euclid's Elements I. 115
Elements, scholia I. 64—74 III.
Elements, sections of Book I. I. 308
Elements, technical terms in connexion with I. 125—142
Elements, Theon's changes in text I. 54—58
Elements, translation by Billingsley I. 109—110
Elements, translation by Boethius I. 92
Elements, translations and editions generally I. 97—113
Elements, translations by Athelhard I. 93—96
Elements, translations by Campanus I. 94—96 97—100
| Elements, translations by Commandinus I. 104—105
Elements, translations by Gherard of Cremona I. 93—94
Elements, translations by Zamberti I. 98—100
Elements, writers on Book X. III. 8—9
Elinuam I. 95
Enestroem, G. III. 521
Engel and Staeckel I. 219 321
Enriques, F. I. 157 175 193 195 201 313 II. 126
Enunciation, one of formal divisions of a proposition I. 129—130
Epicureans, objection to Eucl. I. 20 I. 41 287
Epicureans, Savile on I. 287
Equality, in sense different from that of congruence (= "equivalent" Legendre) I. 327—328
Equality, modern definition of I. 228
Equality, two senses of equal (1) "divisibly-equal" (Hilbert) or "equivalent by-sum" (Amaldi), (2) "equal in content" (Hilbert) or "equivalent by difference" (Amaldi) I. 328
Equimultiples, "any equimultiples whatever" II. 120
Equimultiples, should include once each magnitude II. 145
Equimultiples, stereotyped phrase "other, chance, equimultiples" II. 143—144
Eratosthenes I. 1 162
Eratosthenes, Archimedes' "Method" addressed to III. 366
Eratosthenes, contemporary with Archimedes I. 1 2
Eratosthenes, measurement of obliquity of ecliptic (23° 51' 20'') II. 111
Erycinus I. 27 290 329
Escribed circles of triangle II. 85 86—87
Euclid, "of Tus" I. 4 5n.
Euclid, "of Tyre" I. 4—6
Euclid, (according to Proclus) a Platonist I. 2
Euclid, account of, in Proclus’ summary I. 1
Euclid, allusions to, in Archimedes I. 1
Euclid, Arabian derivation of name ("key of geometry") I. 6
Euclid, Arabian list of works I. 17 18
Euclid, Arabian traditions about I. 4 5
Euclid, bibliography I. 91—113
Euclid, date I. 1—2
Euclid, Elements, ultimate aim of I. 2 115—116
Euclid, not "of Megara" I. 3 4
Euclid, on "three- and four-line locus" I. 3
Euclid, other works, Conics I. 16
Euclid, other works, Data I. 8 132 141 385 391
Euclid, other works, Elements of Music or Sectio Canonis I. 17 II.
Euclid, other works, On divisions (of figures) I. 8 9
Euclid, other works, Optics I. 17
Euclid, other works, Phaenomena I. 16 17
Euclid, other works, Porisms I. 10—15
Euclid, other works, Pseudaria I. 7
Euclid, other works, Surface-loci I. 15 16
Euclid, Pappus on personality of I. 3
Euclid, story of (in Stobaeus) I. 3
Euclid, supposed to have been bom at Gela I. 4
Euclid, taught at Alexandria I. 2
Eudemus I. 29
Eudemus, History of Geometry I. 34 35—38 278 295 304 317 320 387 II. 111 III. 366 524
Eudemus, On the Angle I. 34 38 177—178
Eudoxus I. 1 37 116 II. 99 280 295 III. 522 523 526
Eudoxus on the golden section I. 137
Eudoxus, discoverer of method of exhaustion I. 234 III. 374
Eudoxus, discoverer of theory of proportion covering incommensurables as expounded generally in Bks. V., VI. I. 137 351 II.
Eudoxus, first to prove theorems about volume of pyramid (Eucl. XII. 7 Por.) and cone (Eucl. XII. 10), also theorem of Eucl. XII. 2 III. 15
Eudoxus, inventor of a certain curve, the hippopede, horse-fetter I. 163
Eudoxus, possibly wrote Sphaerica I. 17
Eudoxus, theorems of Eucl. XIII. 1-5 probably due to III. 441
Eudoxus, used "Axiom of Archimedes" III. 15
Euler, Leonhard I. 401
Eutocius I. 25 35 39 142 161 164 259 317 329 330 373
Eutocius on "VI. Def. 5" II. 116 132 189—190
Eutocius, gives locus-theorem from Apollonius’ Plane Loci II. 198—200
Even (number), definitions by Pythagoreans and in Nicomachus II. 281
Even (number), definitions of odd and even by one another unscientific (Aristotle) I. 148—149 II.
Even (number), Nicom. divides even into three classes (1) even-times even and (2) even-times odd as extremes, and (3) odd-times even as intermediate II. 282—283
Even-times even, Euclid’s use differs from use by Nicomachus, Theon of Smyrna and Iamblichus II. 281—282
Even-times odd in Euclid different from even-odd of Nicomachus and the rest II. 282—284
Ex aequali, ex aequali propositions (V. 20, 22), and ex aequali "in perturbed proportion" (V. 21, 23) II. 176—178
Ex aequali, of ratios II. 136
Exhaustion, method of III. 374—377
Exhaustion, method of, discovered by Eudoxus I. 234 III.
Exhaustion, method of, evidence of Archimedes III. 365—366
Exterior and interior (of angles) I. 263 280
Extreme and mean ratio (line cut in), defined II. 188
Extreme and mean ratio (line cut in), irrationality of segments of (apotomes) III. 19 449—451
Extreme and mean ratio (line cut in), known to Pythagoreans I. 403 II. III. 525
Extremity I. 182 183
Faifofer II. 126
Falk, H. I. 113
Fermat III. 526—527
Figure, according to Posidonius is confining boundary only I. 41 183
Figure, angle-less figure I. 187
Figure, as viewed by Aristotle I. 182—183
Figure, as viewed by Euclid I. 183
Figure, as viewed by Plato I. 182
Figure, figures bounded by two lines classified I. 187
Figures, printing of I. 97
Fihrist I. 4n. 5n. 17 21 24 25 27
Fihrist, list of Euclid’s works in I. 17 18
Finaeus, Orontius (Oronce Fine) I. 101 104
Flauti, Vincenzo I. 107
Florence MS. Laurent. XXVIII. 3 (F) I. 47
Flussates see "Candalla"
Forcadel, Pierre I. 108
Fourier, definition of plane based on Eucl. XI. 4 I. 173—174 III.
Fourth proportional, assumption of existence of, in V. 18, and alternative methods for avoiding (Saccheri, De Morgan, Simson, Smith and Bryant) II. 170—174
Fourth proportional, Clavius made the assumption an axiom II. 170
Fourth proportional, condition for existence of number which is a fourth proportional to three numbers II. 409—411
Fourth proportional, sketch of proof of assumption by De Morgan II. 171
Frankland, W.B. I. 173 199
Frischauf, J. I. 174
Galileo Galilei, on angle of contact II. 42
Gartz I. 9n.
Gauss I. 172 193 194 202 219 321
Geminus I. 21 27—28 37 44 45 133n. 203 265 330
Geminus, classification of angles I. 178—179
Geminus, classification of surfaces I. 170
Geminus, comm. on Posidonius I. 39
Geminus, elements of astronomy I. 38
Geminus, name not Latin I. 38—39
Geminus, on "mixed" lines (curves) and surfaces I. 162
Geminus, on homoeomeric (uniform) lines I. 162
Geminus, on parallels I. 191
Geminus, on Postulate 4 I. 200
Geminus, on postulates and axioms I. 122—123 III.
Geminus, on stages of proof of theorem of I. 32 I. 317—320
Geminus, on theorems and problems I. 128
Geminus, Proclus’ obligations to I. 39—42
Geminus, title of work quoted from by Proclus I. 39
Geminus, title of work quoted from by Proclus, and by Schol. III. 522
Geminus, two classifications of lines (or curves) I. 160—162
Geometric means II. 357sqq.
Geometric means, one mean between square numbers II. 294 363
Geometric means, one mean between square numbers, or between similar plane numbers II. 371—372
Geometric means, two means between cube numbers II. 294 364—365
Geometric means, two means between cube numbers, or between similar solid numbers II. 373—375
Geometrical algebra I. 372—374
Geometrical algebra, Euclid’s method in Book II. evidently the classical method I. 373
Geometrical algebra, preferable to semi-algebraical method I. 377—378
Geometrical progression II. 346sqq.
Geometrical progression, summation of n terms of (IX. 35) II. 420—421
Gherard of Cremona, translator of an-Nairizi’s commentary I. 22 94 II.
Gherard of Cremona, translator of Elements I. 93—94
Gherard of Cremona, translator of tract De divisionibus I. 9
Giordano, Vitale I. 106 176
Given, different senses I. 132—133
Gnomon, arithmetical use of I. 358—360 371 II.
Gnomon, Euclid’s method of denoting in figure I. 383
Gnomon, literally "that enabling (something) to be known" I. 64 370
Gnomon, successive senses of, (1) upright marker of sundial I. 181 185 271—272
Gnomon, successive senses of, (2) carpenter’s square for drawing right angles I. 371
Gnomon, successive senses of, (3) figure placed round square to make larger square I. 351 371
Gnomon, successive senses of, (4) use extended by Euclid to parallelograms I. 371
Gnomon, successive senses of, (5) by Heron and Theon to any figures I. 371—372
Gnomon, successive senses of, Indian use of gnomon in this sense I. 362
Gnomon, successive senses of, introduced into Greece by Anaximander I. 370
Goerland, A. I. 233 234
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