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


Язык: en

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
"Abthiniathus" (or "Anthisathus")      203
"Anthisathus" (or "Abthiniathus")      203
"Aqaton"      88
"Diagonal" numbers      see “"Side-" and "diagonal-" numbers”
"Gnomon-wise" $(\kapa\alpha\tau\alpha\;\gamma\nu\omega\mu o\nu\alpha)$, old name for perpendicular $(\kappa\alpha\theta\epsilon\tau os)$      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 $\sqrt{2}$      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 $\epsilon\phi\epsilon\xi\nu s$, 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 $(\tau o \pi os\;\alpha\nu\alpha\lambda v o\mu\epsilon\nu os)$      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 $(\kappa\epsilon\pho\alpha\tau o \epsilon i \delta\eta s)$      177 178 182 265
Angle, interior and opposite      280
Angle, lune-like $(\mu\eta\nu o \epsilon i \delta\nu s)$      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 $\xi v \omega\tau\rho o \epsilon i \delta\nu s$      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 $\sqrt{2}$ 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 $\pi$ 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 $\kappa\alpha\tau\alpha\;\pi\alpha\nu\tau os$ and $\pi\pho\omega\tau o \nu\;\kappa\alpha\theta o \lambda ov$      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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