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

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Год издания: 1908

Количество страниц: 424

Добавлена в каталог: 02.04.2008

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Предметный указатель

Given, $\delta\epsilon\delta o\mu\epsilon\nu os$ , different senses      132—133
Gnomon, (2) carpenter's square for drawing right angles      371
Gnomon, (3) figure placed round square to make larger square      351 371
Gnomon, (4) use extended by Euclid to parallelograms      371
Gnomon, (5) by Heron and Theon to any figures      371—372
Gnomon, arithmetical use of      358—360 371
Gnomon, Euclid's method of denoting in figure      383
Gnomon, Indian use of gnomon in this sense      362
Gnomon, introduced into Greece by Anaximander      370
Gnomon, literally "that enabling (something)      to be known" 64 370
Gnomon, successive senses of, (1) upright marker of sundial      181 185 271—272
Gorland, A.      233 234
Gow, James      135n.
Gracilis, Stephanus      101—102
Grandi, Guido      107
Gregory of St Vincent      401 404
Gregory, David      102—103
Gromatici      91n. 95
Grynaeus      100—101
Halifax, William      108 110
Halliwell      95n.
Hankel, H.      139 144 232 234 344 354
Harmonica of Ptolemy, Comm. on      17
Harmony, Introduction to, not by Euclid      17
Harun ar-Rashid      75
Hauff, J.K.F.      108
Helix, cylindrical      161 162 329 330
Helmholtz      226 227
Henrici and Treutlein      313 404
Henrion, Denis      108
Herigone, Pierre      108
Herlin, Christian      100
Hermotimus of Colophon      1
Herodotus      37n. 370
Heron of Alexandria      137n. 159 163 168 170 171—172 176 183 184 185 188 189 222 223 243 253 285 287 299 351 369 371 405 407 408
Heron of Alexandria, addition to I.      47 366—368
Heron of Alexandria, apparently originated semi-algebraical method of proving theorems of Book II.      373 378
Heron of Alexandria, commentary on Euclid's Elements      20—24
Heron of Alexandria, comparison of areas of triangles in I.      24 334—335
Heron of Alexandria, direct proof of I.      25 301
Heron of Alexandria, Heron and Vitruvius      20—21
Heron of Alexandria, mechanicus, date of      20—21
Heron, Proclus' instructor      29
Hieronymus of Rhodes      305
hilbert      157 193 201 228—231 249 313 328
Hipparchus      4n. 30n.
Hippias of Elis      42 265—266
Hippocrates of Chios      8n. 29 35 38 116 135 136 386—387
Hippopede $(i\pi\pi ov\;\pi\epsilon\delta\nu)$ , a certain curve used by Eudoxus      162—163 176
Hoffmann, Heinrich      107
Hoffmann, John Jos. Ign.      108 365
Holiel, J.      219
Holtzmann, Wilhelm (Xylander)      107
Homoeomeric (uniform) lines      40 161 162
Hoppe, E.      21
Hornlike (angle), $\kappa\epsilon\rho\alpha\tau o\epsilon i\delta\nu s$       177 178 182 265
Horsley, Samuel      106
Hudson, John      102
Hultsch, F.      20 329 400
Hunain b. Ishaq al-'Ibadi      75
Hypotheses, confused by Proclus with definitions      121—122
Hypotheses, geometer's hypotheses not false (Aristotle)      119
Hypotheses, in Aristotle      118—120
Hypotheses, in Plato      122
Hypothetical construction      199
Hypsicles      5
Iamblichus      63 83
Ibn al-'Amld      86
Ibn al-Haitham      88 89
Ibn al-Lubudi      90
Ibn Rahawaihi al-Arjani      86
Ibn Sina (Avicenna)      77 89
Incomposite (of lines)      160—161 (ofsurfaces)i7o
Indivisible lines $(\alpha\tau o\mu oi\;\gamma\rho\alpha\mu\mu\alpha i)$ , theory of, rebutted      268
Infinite, Aristotle on the      232—234
Infinite, infinite division not assumed, but proved, by geometers      268
Infinity, parallels meeting at      192—193
Ingrami, G.      175 193 195 201 227—228
Interior and exterior (of angles)      263 280
Interior and opposite angle      280
Interpolations by Theon      46 55—56
Interpolations I.      40
Interpolations in the Elements before Theon's time      58—63
Interpolations interpolated      338
Irrational, "irrational diameter of 5", (Pythagoreans, and, Plato)      399—400
Irrational, approximation to $\sqrt{2}$ by means of "side-" and " diagonal-" numbers      399—401
Irrational, claim of India to priority of discovery      363—364
Irrational, discovered with reference to $\sqrt{2}$       351
Irrational, Indian approximation to $\sqrt{2}$       361 363—364
Irrational, irrational ratio $(\alpha\rho\rho\nu\tau os\;\lambda o\gamma os)$       137
Irrational, unordered irrationals (Apollonius)      42 115
Isaacus Monachus (or Argyrus)      73—74 407
Ishaq b. Hunain b. Ishaq al- Ibadi, Abu Yaqub, translation of Elements by      75—80 83—84
Ismail b. Bulbul      88
Isoperimetric (or isometric), figures, Pappus and Zenodorus on      26 27 333
Isosceles $(i \sigma o\sigma\kappa\epsilon\lambda\nu s)$       187
Isosceles $(i \sigma o\sigma\kappa\epsilon\lambda\nu s)$ of numbers (=even)      188
Isosceles $(i \sigma o\sigma\kappa\epsilon\lambda\nu s),$ isosceles right-angled triangle      352
Jakob b. Machir      76
Joannes Pediasimus      72—73
Junge, G., and discovery of irrationals to Pythagoras      351
Junge, G., on attribution of theorem of I.      47
Kaestner, A.G.      78 97 101
Katyayana Sulba — Sutra      360
Keill, John      105 110—121
Kepler      193
Killing, W.      194 219 225—226 235 242 272
Klamroth, M.      75—84
Kliigel, G.S.      212
Knesa, Jakob      112
Knoche      32n. 33n. 73
Kroll, W.      399—400
Lambert, J.H.      212—213
Lardner, Dionysius      112 246 250 298 404
Lascaris, Constantinus      3
Leading theorems (as distinct from converse)      257
Leading theorems (as distinct from converse) leading variety of conversion      256—257
Leeke, John      110
Lefevre, Jacques      100
Legendre, Adrien Marie      112 169 215—219
Leibniz      145 169 176 194
Leiden MS.      399
Leiden MS. I of al-Hajjaj and an-Nairizi      22
Lemma      114
Lemma, especially from Pappus      67
Lemma, lemmas interpolated      59—60
Lemma, meaning      133—134
Leodamas of Thasos      36 134
Leon      116
Limdgren, F.A.A.      113
Linderup, H.C.      113
Line, "asymptotic" or non-secant $(\alpha\sigma v\mu\pi\tau\omega\tau os),$ secant $(\sigma v\mu\pi\tau\omega\tau os)$       161
Line, "divisible or continuous one way" (Aristotle)      158—159
Line, "flux of point"      159
Line, "magnitude extended one way" (Aristotle, "Heromides")      158
Line, Apollonius on      159
Line, classification of lines, Heron      159—160
Line, classification of lines, Plato and Aristotle      159—160
Line, composite $(\sigma v\nu\theta\epsilon\tau os)$ , incomposite $(\alpha\sigma v\nu\theta\epsilon\tau os),$ "forming a figure" $(\sigma\chi\eta\mu\alpha\tau o\pi oiov\sigma\alpha)$ , determinate $(\omega\pho i\sigma\mu\epsilon\nu\eta)$ , indeterminate $(\alpha o\rho i\sigma\tau os)$       160
Line, Geminus, first classification      160—161
Line, Geminus, second classification      161
Line, homoeomeric (uniform)      161—162
Line, loci on lines      329 330
Line, objection of Aristotle      158
Line, Platonic definition      158
Line, Proclus on lines without extremities      165
Line, simple, "mixed"      161—162
Line, straight $(\epsilon v\theta\epsilon i\alpha)$ , curved $(\kappa\alpha\mu\pi v\lambda\nu)$ , circular $(\pi\epsilon\rho i\phi\epsilon\rho\nu s)$ , spiral-shaped $(\epsilon\lambda i\kappa o\epsilon i\delta\nu s),$ bent $(\kappa\epsilon\kappa\alpha\mu\mu\epsilLine, on\nu\eta)$ , broken $(\kappa\epsilon\kappa\lambda\alpha\sigma\mu\emsilon\mu)$ , round $(\sigma\tau\rho o\gamma\gamma v\lambda os)$       159
Linear, loci      330
Linear, problems      330

Lionardo da Vinci, proof of I.      47 365—366
Lippert      88n.
Lobachewsky, N.I.      174—175 213 219
Locus-theorems $(\tau o\pi i\kappa\alpha\;\theta\epsilon)$ and loci $(\tau o\pi oi)$ as an area which is locus of area (parallelogram or triangle)      330
Locus-theorems $(\tau o\pi i\kappa\alpha\;\theta\epsilon)$ and loci $(\tau o\pi oi)$ corresponding distinction between plane and solid problems, to which Pappus adds linear problems      330
Locus-theorems $(\tau o\pi i\kappa\alpha\;\theta\epsilon)$ and loci $(\tau o\pi oi)$ further distinction in Pappus between (1), $\epsilon\phi\epsilon\kappa\tau i\kappa oi$ (2), $\delta i\epsilon\xi o\delta i\kappa oi$ (3), $\alpha\nu\alpha\sigma\tau\rho o\phi i\kappa oi\;\tau o\pi oi$       330
Locus-theorems $(\tau o\pi i\kappa\alpha\;\theta\epsilon)$ and loci $(\tau o\pi oi)$ loci likened by Chrysippus to Platonic ideas      330—331
Locus-theorems $(\tau o\pi i\kappa\alpha\;\theta\epsilon)$ and loci $(\tau o\pi oi)$ locus defined by Proclus      329
Locus-theorems $(\tau o\pi i\kappa\alpha\;\theta\epsilon)$ and loci $(\tau o\pi oi)$ locus-theorems and loci (1) on lines (a) plane loci (straight lines and circles) (b) solid loci (conies), (2) on surfaces      329
Locus-theorems $(\tau o\pi i\kappa\alpha\;\theta\epsilon)$ and loci $(\tau o\pi oi)$ Proclus regards locus in I.      35
Locus-theorems $(\tau o\pi i\kappa\alpha\;\theta\epsilon)$ and loci $(\tau o\pi oi)$ Proclus regards locus in III.      21 31
Logical conversion, distinct from geometrical      256
Logical deductions      256 284—285 300
Logical deductions, logical equivalents      309 314—315
Lore      163
Lorenz, J.F.      107—108
Loria, Gino      7n. 10n. 11n. 12n.
Luca Paciuolo      98—99 100
Machir, Jakob b.      76
Magni, Domenico      106
Magnitude, common definition vicious      148
Mansion, P.      219
Manuscripts of Elements      46—51
Martianus Capella      91 155
Martin, T.H.      20 29n. 30n.
Mas'ud b. al-Qass al-Bagdadi      90
Maximus Planudes, scholia and lectures on Elements      72
meguar = axis      93
Mehler, F.G.      404
Meier, Rudolf      21n.
Menaechmus story of M. and Alexander I on elements      114 117 125 133n.
Menelaus      21 23
Menelaus, direct proof of I.      25 300
Middle term, or cause, in geometry, illustrated by III.      31 149
Miisa b. Muh. b. Mahmud Qadizade ar-Rumi      5n. 90
Mill, J.S.      144
Mocenigo, Prince      97—98
Mollweide, C.B.      108
Mondore (Montaureus), Pierre      102
Moses b. Tibbon      76
Motion, in mathematics      226
Motion, in mathematics, but shown by Veronese to be petitio principii      226—227
Motion, in mathematics, motion without deformation considered by Helmholtz necessary to geometry      226—227
Mueller, J.W.      365
Muh. b. 'Isa Abu 'Abdallah al-Mahani      85
Muh. b. Ahmad Abu 'r-Raihan al-Biruni      90
Muh. b. Ashraf Shamsaddin as-Samarqandi      89
Muhammad (b. 'Abdalbaqi) al-Bagdadi, translator of De divisionibus      8n. 90 110
Muller, J.H.T.      189
Munich MS. of enunciations (R)      94—95
Musici Elements of (Sectio Canonis)y by Euclid      17
Napoleon      103
Nasiraddin at-Tusi      4 5n. 77 84 89 208—210
Nazif b. Yumn (Yaman) al-Qass      76 77 87
Neide, J.G.C.      103
Nicomachus      92
Nicomedes      42 160—161 265—266
Nipsus, Marcus Junius      305
Nominal and real definitions      see “Definitions”
Objection $(\epsilon\nu\sigma\tau\alpha\sigma is)$ , in logic (Aristotle)      135
Objection $(\epsilon\nu\sigma\tau\alpha\sigma is)$ , technical term, in geometry      135 257 260 265
Oblong      151 188
Oenopides of Chios      34 36 126 271 295 371
Ofterdinger, L.F.      9n. 10
Olympiodorus      29
Oppermann      151
Optics of Euclid      17
Oresme, N.      97
Orontius Finaeus (Oronce Fine)      101 104
Ozanam, Jaques      107 108
Paciuolo, Luca      98—99 100
Pamphile      317 319
Pappus      17 39 133n. 137 151 225 388 391 401
Pappus, additional axioms by      25 223 224 232
Pappus, commentary on Elements      24—27
Pappus, contrasts Euclid and Apollonius      3
Pappus, Data      8
Pappus, evidence of scholia as to Pappus' text      66—67
Pappus, extension of I.      47 366
Pappus, lemmas in Book X. interpolated from      67
Pappus, on Analysis and Synthesis      138—139 141—142
Pappus, on conchoids      161 266
Pappus, on converse of Post. 4      25 201
Pappus, on Euclid's Porisms      10—14
Pappus, on foci      329 330
Pappus, on isoperimetric figures      26 27 333
Pappus, on paradoxes of Erycinus      27 290
Pappus, on quadratrix      266
Pappus, on Treasury of Analysis      8 10 11 138
Pappus, partly preserved in scholia      66
Pappus, proof of I. 5 by      254
Pappus, semi-algebraical methods in      373 378
Pappus, Surface-loci      15 16
Papyrus, Fayum      51 337 338
Papyrus, Herculanensis No. 1061      50 184
Papyrus, Oxyrhynchus      50
Papyrus, Rhind      304
Paradoxes, an ancient "Budget of Paradoxes"      329
Paradoxes, in geometry      188
Paradoxes, of Erycinus      27 290 329
Parallelogram (= parallelogrammic area), first introduced      325
Parallelogram (= parallelogrammic area), rectangular parallelogram      370
Parallels, Aristotle on      190 191—192
Parallels, as equidistants      190—191 194
Parallels, definitions classified      192—194
Parallels, definitions, by "Aganis"      191
Parallels, definitions, by Geminus      191
Parallels, direction-theory of      191—192 194
Parallels, Legendre's attempt to establish theory of      213—219
Parallels, Parallel Postulate      see “Postulate 5”
Parallels, Posidonius      190
Parallels, Simplicius      190
Parallels, Veronese's definition and postulate      194
Paris MSS. of Elements, (p)      49
Paris MSS. of Elements, (q)      50
Pasch, M.      157 228 250
Pediasimus, Joannes      72—73
Peithon      203
Peletarius (Jacques Peletier)      103 104 249 407
Pena      104
Perpendicular $(\kappa\alpha\theta\epsilon\tau os),$ "plane" and "solid"      272
Perpendicular $(\kappa\alpha\theta\epsilon\tau os),$ definition      181
Perpendicular $(\kappa\alpha\theta\epsilon\tau os),$ perpendicular and obliques      291
Perseus      42 162—163
Pesch, J.G. van, De Prodi fontibus      23sqq. 29n.
Petrus Montaureus (Pierre Mondore)      102
Peyrard and Vatican MS.      190
Peyrard and Vatican MS. (P)      46 47 103 108
Pfleiderer, C.F.      168 298
Phaenomena of Euclid      16 17
Philippus of Mende I      116
Phillips, George      112
Philo of Byzantium      20 23
Philo, proof of I.      8 263—264
Philolaus      34 351 371 399
Philoponus      45 191—192
Pirckenstein, A.E. Burkh. von      107
Plane (or plane surface), "Plane loci"      329—330
Plane (or plane surface), "Plane problems"      329
Plane (or plane surface), "Simson's" definition and Gauss on      172—173
Plane (or plane surface), Archimedes' assumption      171 172
Plane (or plane surface), Beez      176
Plane (or plane surface), Crelle's tract on      172—174
Plane (or plane surface), Deahna      174
Plane (or plane surface), Enriques and Amaldi, Ingrami, Veronese and Hilbert on      175
Plane (or plane surface), evolution of, by Bolyai and Lobachewsky      174—175
Plane (or plane surface), J.K. Becker      174
Plane (or plane surface), Leibniz      176
Plane (or plane surface), other ancient definitions of, in Proclus, Heron, Theon of Smyrna, an-Nairizi      171—172
Plane (or plane surface), other definitions by Fourier      173

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