Heath T.L. (ed.) — Thirteen Books of Euclid's Elements, Vol. 1 :: Электронная библиотека попечительского совета мехмата МГУ

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Heath T.L. (ed.) — Thirteen Books of Euclid's Elements, Vol. 1

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Название: Thirteen Books of Euclid's Elements, Vol. 1

Автор: Heath T.L. (ed.)

Аннотация:

Volume 1 of three-volume set containing complete English text of all 13 books of the Elements plus critical apparatus analyzing each definition, postulate and proposition in great detail. Covers textual and linguistic matters; mathematical analyses of Euclid's ideas; classical, medieval, Renaissance and modern commentators; refutations, supports, extrapolations, reinterpretations and historical notes. Total in set: 995 figures.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1908

Количество страниц: 424

Добавлена в каталог: 02.04.2008

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Предметный указатель

Caiani, Angelo      101
Camerarius, Joachim      101
Camerer, J. G.      103 293
Camorano, Rodrigo      112
Campanus, Johannes      3 78 94—96 104 106 110 407
Candalla, Franciscus Flussates (Francois de Foix, Comte de Candale)      3 104 110
Cantor, Moritz      7n. 20 272 304 318 320 333 352 355 357—358 360 401
Carduchi, L.      112
Carpus, on Astronomy      34 43 45 127 128 177
Case, technical term      134
Cases interpolated      58 59
Casiri      4n. 9n.
Cassiodorius, Magnus Aurelius      92
Cataldi, Pietro Antonio      106
Catoptrica, "Cause" consideration of, omitted by commentators      19 45
Catoptrica, attributed to Euclid, probably Theon's      17
Catoptrica, Catoptrica of Heron      21 253
Catoptrica, cause = middle term (Aristotle)      149
Catoptrica, definition should state cause (Aristotle)      149
Catoptrica, question whether geometry should investigate cause (Geminus)      45 150n.
Censorinus      91
Centre, $\kapa\epsilon\nu\tau\rho o \nu$       184—185
Ceria Aristotelica      35
Chasles on Porisms of Euclid      10 11 14 15
Chinese, "Tcheou pei"      355
Chinese, knowledge of triangle      3 4 5 352
Chrysippus      330
Cicero      91 351
Circle = $\pi\epsilon\pho i \phi\epsilon\pho o \gamma\pho\alpha\mu\mu o\nu$ (Aristotle)      184
Circle = round, $\sigma\tau\rho o \gamma\gamma v \lambda o\nu$ (Plato)      184
Circle, a plane figure      183—184
Circle, bisected by diameter (Thales)      185 184—185
Circle, centre of      184—185
Circle, definition of      183—185
Circle, intersections with another circle      238—240 242—243 293—294
Circle, intersections with straight linei      237—238 272—274
Circle, pole of      185
Circumference, $\pi\epsilon\pho i \phi\epsilon\pho\epsilon i\alpha$       184
Cissoid      161 164 176 330
Clairaut      328
Clavius (Christoph Schliissel)      103 105 194 232 381 $91 407
Claymundus, Joan.      101
Cleonides, Introduction to Harmony      17
Cochlias or cochlion (cylindrical helix)      162
Codex Leidensis      399
Codex Leidensis, I      22 27n. 79n.
Coets, Hendrik      109
Commandinus      4 102 103 104—105 106 110 111 407
Commandinus, edited (with Dee) De divisionibus      8 9 110
Commandinus, scholia included in translation of Elements      73
Commentators on Eucl. criticised by Proclus      19 26 45
Common Notions, = axioms      62 120—121 221—222
Common Notions, called "axioms" by Proclus      221
Common Notions, meaning and appropriation of term      221
Common Notions, which are genuine?      22—23 sq.
Complement, $\pi\alpha\rho\alpha\pi\lambda\nu\pho\omega\mu\alpha,$ "about diameter"      341
Complement, $\pi\alpha\rho\alpha\pi\lambda\nu\pho\omega\mu\alpha,$ meaning of      341
Complement, $\pi\alpha\rho\alpha\pi\lambda\nu\pho\omega\mu\alpha,$ not necessarily parallelograms      341
Complement, $\pi\alpha\rho\alpha\pi\lambda\nu\pho\omega\mu\alpha,$ use for application of areas      342—343
Composite, ativderos, (of lines)      160
Composite, ativderos, (of surfaces)      170
Conchoids      160—161 265—266 330
Conclusion, $\sigma v \mu\pi\epsilon\pho\alpha\sigma\mu\alpha,$ definition merely stating conclusion      149
Conclusion, $\sigma v \mu\pi\epsilon\pho\alpha\sigma\mu\alpha,$ necessary part of a proposition      129—130
Conclusion, $\sigma v \mu\pi\epsilon\pho\alpha\sigma\mu\alpha,$ particular conclusion immediately made general      131
Congruence theorems for triangles, recapitulation of      305—306
Congruence-Axioms or Postulates, Common Notion      4 in 129—130
Congruence-Axioms or Postulates, modern systems of (Pasch, Veronese, Hilbert)      228—231
Conics, focus-directrix property proved by Pappus      15
Conics, fundamental property as proved by Apollonius equivalent to Cartesian equation      344—345
Conics, of Apollonius      3 16
Conics, of Aristaeus      3 16
Conies, of Euclid      3 16
Constantinus Lascaris      3
Construct $(\sigma v\nu i\sigma\tau\alpha\sigma\theta\alpha i)$ contrasted with apply to      343
Construct $(\sigma v\nu i\sigma\tau\alpha\sigma\theta\alpha i)$ contrasted with describe on      348
Construct $(\sigma v\nu i\sigma\tau\alpha\sigma\theta\alpha i)$ special connotation      259 289
Construction, $\kappa\alpha\tau\alpha\sigma\kappa\epsilon v\eta$ , one of formal divisions of a proposition      129
Construction, mechanical      151 387
Construction, sometimes unnecessary      130
Construction, turns nominal into real definition      146
Continuity, principle of      234 sq. 242 272 294
Conversion, geometrical, "leading" and partial varieties      256—257 337
Conversion, geometrical, distinct from logical      256
Copernicus      101
Cordonis, Mattheus      97
Cratistus      133
Crelle, on the plane      172—174
Ctesibius      20 21 39n.
Cunn, Samuel      111
Curtze, Maximilian, editor of an-NairizI      22 78 92 94 96 97n.
Curves, classification of      see “Line”
Cylindrical helix      161 162 329 330
Czecha, Jo.      113
Dasypodius (Rauchfuss), Conrad      73 102
Data of Euclid      8 132 141 385 391
De levi et ponderoso, tract      18
De Morgan      246 260 269 284 291 298 300 309 313 314 315 369 376
De Zolt      328
Deahna      174
Dechales, Claude Francois Milliet      106 107 108 110
Dedekind's Postulate, and applications      235—240
Dee, discovered De divisionibus      8 9
Dee, John      109 110
Definition, in sense of "closer statement" $\delta io\pho i\sigma\mu os$ , one of formal divisions of a proposition      129
Definition, may be unnecessary      130
Definitions, a class of thesis (Aristotle)      120
Definitions, Aristotle on      117 119 120 143
Definitions, Aristotle on unscientific definitions $(\epsilon\kappa\;\mu\nu\;\pi\rho o\tau\epsilon\rho\omega\nu)$       148—149
Definitions, Aristotle's requirements in      146—150
Definitions, but confused therewith by Proclus      121—122
Definitions, but say nothing about existence (except in the case of a few primary things)      119 143
Definitions, definitions of technical terms in Aristotle and Heron, not in Euclid      150
Definitions, distinguished from hypotheses      119
Definitions, Euclid's definitions agree generally with Aristotle's doctrine      146
Definitions, exceptions      148
Definitions, interpolated definitions      61 62
Definitions, must be assumed      117—119
Definitions, real and nominal definitions (real = nominal plus postulate or proof), Mill anticipated by Aristotle, Saccheri and Leibniz      143—145
Definitions, should state cause or middle term and be genetic      149—150
Definitions, terms for, $\delta\pho os$ and $\delta\pho i\sigma\mu os$       143
Demetrius Cydonius      72
Democritus      38
Desargues      193
Describe on $(\alpha\nu\alpha\gamma\pho\alpha\phi\epsilon i\nu\;\alpha\pi o)$ contrasted with construct      348
Diagonal $(\delta i \alpha\gamma\omega\nu ios)$       185
Diameter $(\delta i\alpha\mu\epsilon\tau\rho os)$ , "rational" and "irrational" diameter of      5
Diameter $(\delta i\alpha\mu\epsilon\tau\rho os)$ , (Plato)      399
Diameter $(\delta i\alpha\mu\epsilon\tau\rho os)$ , as applied to figures generally      325
Diameter $(\delta i\alpha\mu\epsilon\tau\rho os)$ , of circle or parallelogram      185
Diameter $(\delta i\alpha\mu\epsilon\tau\rho os)$ , taken from Pythagoreans      399—400
Dimensions $(cf. \;\delta i\alpha\sigma\tau\alpha\sigma\epsilon is)$       157 158
Dimensions $(cf. \;\delta i\alpha\sigma\tau\alpha\sigma\epsilon is)$ , Aristotle's view of      158—159
Dinostratus      117 266
Diodes      164
Diodorus      203
Diogenes Laertius      37 305 317 351
Diophantus      86
Diorismus $(\delta io\pho i\sigma\mu os)$ (b) condition of possibility      128
Diorismus $(\delta io\pho i\sigma\mu os)$ = (a) "definition" or "specification, " a formal division of a proposition      129
Diorismus $(\delta io\pho i\sigma\mu os)$ determines how far solution possible and in how many ways      130—131 243
Diorismus $(\delta io\pho i\sigma\mu os)$ diorismi said to have been discovered by Leon      116
Diorismus $(\delta io\pho i\sigma\mu os)$ first instances in elements      234 293
Diorismus $(\delta io\pho i\sigma\mu os)$ introduced by $\delta\epsilon i\;\delta\eta$       293
Diorismus $(\delta io\pho i\sigma\mu os)$ revealed by analysis      142
Dippe      108
Direction, as primary notion, discussed      179
Direction, direction-theory of parallels      191—192
Distance, $\delta i\alpha\sigma\tau\eta\mu\alpha$ = radius      199
Distance, $\delta i\alpha\sigma\tau\eta\mu\alpha$ in Aristotle has usual general sense and = dimension      199

Division (method of), Plato's      134
Divisions (of figures) by Euclid      8 9
Divisions (of figures) by Euclid and (by Dee) in Latin translation      8 9 110
Divisions (of figures) by Euclid found (by Woepcke) in Arabic      9
Divisions (of figures) by Euclid translated by Muhammad al-Bagdadi      8
Dodgson, C.L.      194 254 261 313
Dou, Jan Pieterszoon      108
Duhamel.      139 328
Egyptians, knowledge of right-angled triangles      352
Elements, Arabian versions compared with Greek text      79—83
Elements, Arabian versions compared with one another      83 84
Elements, Arabic translations (1) by al-Hajjaj      75 76 79 80 83—84
Elements, Arabic translations (2) by Ishaq and Thabit b. Qurra      75—80 83—84
Elements, Arabic translations (3) Naslraddin at-Tusi      77—80 84
Elements, August's      103
Elements, Campanus      94—96 97—100
Elements, Campanus etc., Zamberti      98—100
Elements, Commandinus      104—105
Elements, contributions to, by Eudoxus      1 37
Elements, contributions to, Theaetetus      1 37
Elements, Euclid's Elements, commentators on      19—45
Elements, Euclid's Elements, ultimate aims of      2 115—116
Elements, external sources throwing light on text, Heron, Taurus, Sextus Empiricus, Proclus, Iamblichus      62—63
Elements, first principles of, definitions, postulates, common notions (axioms)      117—124
Elements, Gherard of Cremona      93—94
Elements, Greek texts, editio princeps      100—101
Elements, Gregory's      102—103
Elements, Hebrew translation by Moses b. Tibbon or Jakob b. Machir      76
Elements, Heiberg's passim translations and editions generally      97—113
Elements, Hermotimus of Colophon      117
Elements, immediate recognition of      116
Elements, interpolations before Theon's time      58—63
Elements, introduction into England 10th c      95
Elements, means of comparing Tfreonine with ante-Theonine text      51—53
Elements, no definitions of such technical terms      150
Elements, old translation of      10th c. 92
Elements, on the nature of elements (Aristotle)      116
Elements, on the nature of elements (Menaechmus)      114
Elements, on the nature of elements (Proclus)      114—116
Elements, Peyrard's      103
Elements, pre-Euclidean Elements, by Hippocrates of Chios, Leon      116
Elements, pre-Euclidean Elements, Theudius      117
Elements, Proclus      19 29—45
Elements, Proclus and passim, Aenaeas (Aigeias)      28
Elements, Proclus and passim, Aenaeas (Aigeias) mss. of      46—51
Elements, Proclus and passim, an-Nairlzi      21—24
Elements, Proclus and passim, Heron      20—24
Elements, Proclus and passim, Pappus      24—27
Elements, Proclus and passim, Porphyry      24
Elements, Proclus and passim, Simplicius      28
Elements, Proclus on advantages of Euclid's Elements      115
Elements, scholia      64—74
Elements, sections of Book I.      308
Elements, technical terms in connexion with      125—142
Elements, Theon's changes in text      54—58
Elements, translation by Athelhard      93—96
Elements, translation by Billingsley      109—110
Elements, translation by Boethius      92
Elinuam      95
Engel and Staeckel      219 321
Enriques, F.      157 175 193 195 201 313
Enunciation $(\pi\rho o \tau\alpha\sigma is)$ , one of formal divisions of a proposition      129—130
Epicureans, objection to I.      20 41 287
Epicureans, Savile on      287
Equality, in sense different from that of congruence (= "equivalent," Legendre)      327—328
Equality, modern definition of      228
Equality, two senses of equal (1), "divisiblyequal" (Hilbert), or "equivalent by sum" (Amaldi), (2), "equal in content" (Hilbert), or "equivalent by difference" (Amaldi)      328
Eratosthenes I      162
Eratosthenes I, contemporary with Archimedes      1 2
Errard, Jean, de Bar-le-Duc      108
Erycinus      27 290 329
Euclid, "of Tus"      4 5n.
Euclid, "of Tyre"      4—6
Euclid, account of, in Proclus' summary I date      1—2
Euclid, allusions to in Archimedes I (according to Proclus) a Platonist      2
Euclid, Arabian derivation of name (" key of geometry")      6
Euclid, Arabian list of works      17 18
Euclid, Arabian traditions about      4 5
Euclid, bibliography      91—113
Euclid, Data      8 132 141 385 391
Euclid, Elements of Music or Sectio Canonis      17
Euclid, Elements, ultimate aim of      2 115—116
Euclid, not "of Megara"      3 4
Euclid, on "three- and four-line locus"      3
Euclid, On divisions (of figures)      8 9
Euclid, Optics      17
Euclid, other works, Conies      16
Euclid, Pappus on personality of      3
Euclid, Phaenomena      16 17
Euclid, Porisms      10—15
Euclid, Pseudaria      7
Euclid, story of (in Stobaeus)      3
Euclid, supposed to have been born at Gela      4
Euclid, Surface-loci      15 16
Euclid, taught at Alexandria      2
Eudemus      29
Eudemus, History of Geometry      34 35—38 278 295 304 317 320 387
Eudemus, On the Angle      34 38 177—178
Eudoxus      1 37 116
Eudoxus, discoverer of theory of proportion as expounded generally in Bks. v., VI.      137 351
Eudoxus, founder of method of exhaustion      234
Eudoxus, inventor of a certain curve, the hippopede, horse-fetter      163
Eudoxus, on the golden section      137
Eudoxus, possibly wrote Sphaerica      17
Euler, Leonhard      401
Eutocius      25 35 39 142 161 164 259 317 329 330 373
Exterior and interior (of angles)      263 280
Extremity, $\pi\epsilon\rho\alpha s$       182 183
Falk, H.      113
Figure, according to Posidonius is confining boundary only      41 183
Figure, angle-less $(\alpha\gamma\omega\nu io\nu)$ figure      187
Figure, as viewed by Aristotle      182—183
Figure, as viewed by Euclid      183
Figure, as viewed by Plato      182
Figure, figures bounded by two lines classified      187
Figures, printing of      97
Fihrist      4n. 5n. 17 21 24 25 27
Fihrist, list of Euclid's works in      17 18
Finaeus, Orontius (Oronce Fine)      101 104
Flauti, Vincenzo      107
Florence MS. Laurent, XXVIII. 3, (F)      47
Flussates      see “Candalla”
Forcadel, Pierre      108
FOURIER      173—174
Frankland, W.B.      173 199
Frischauf      174
Gartz      9n.
Gauss      172 193 194 202 219 321
Geminus, classification of angles      178—179
Geminus, classification of surfaces      170
Geminus, comm. on Posidonius      39
Geminus, elements of astronomy      38
Geminus, name not Latin      38—39
Geminus, on "mixed" lines (curves) and surfaces      162
Geminus, on homoeomeric (uniform) lines      162
Geminus, on parallels      191
Geminus, on Postulate      4 200
Geminus, on postulates and axioms      122—123
Geminus, on stages of proof of theorem of I.      32 317—321 27—28 37 44 45 133n 203 265 330
Geminus, on theorems and problems      128
Geminus, Proclus' obligations to      39—42
Geminus, title of work $(\phi i\lanbda o\kappa\alpha\lambda i\alpha)$ quoted from by Proclus      39
Geminus, two classifications of lines (or curves)      160—162
Geometrical algebra      372—374
Geometrical algebra, Euclid's method in Book 11. evidently the classical method      373
Geometrical algebra, preferable to semi-algebraical method      377—378
Gherard of Cremona, translator of an-Nairizi's commentary      22 94
Gherard of Cremona, translator of Elements      93—94
Gherard of Cremona, translator of tract De divisionibus      9
Giordano, Vitale      106 176

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