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' VI XIV. CONTENTS CONTINUED. B. Apollonius of Perga PAGES 126-196 The text of the Conies 126-128 Apollonius's own account of the Conks 128-133 Extent of claim to originality 132-133 Great generality of treatment 133 Analysis of the Conies 133-175 Book I 133-148 Conies obtained in the most general way from oblique cone 134-138 New names, parabola ' ........ ' ', ellipse ', ' hyperbola 138-139 Fundamental properties equivalent to Cartesian equations 139-141 Transition to new diameter and tangent at its 141-147 147-148 148-150 150-157 157-158 158-167 159-163 163-164 ........ extremity First appearance of principal axes Book II Book III Book IV BookV of evolute of conic ...... Normals as maxima and minima .... Number of normals from a point Propositions leading immediately to determination Construction of normals ..... BookVL Book VII Other works by Apollonius . (a) On the Cutting -off of a Ratio (\6yov dnoTOjxr]), two Books (3) On the Cutting-off of an Area {\(opiov «7toto/lii/), two Books ....... (y) On Determinate Section {dia>pi(riJL€vr} rofxr]), two Books (8) On Contacts or Tangencies {encKpal), two Books . (e) Plane Loci, two Books (£) Neuo-fty {Vergings or Inclinations), two Books . • {r}) Comparison of dodecahedron wi'h icosahedron {&) General Treatise ...... (i) On the Cochlias ....... (k) On Unordered Irrationals . . . . . Astronomy......... (X) On the Burning-mirror . {(i) 'Qkvtokiov 164-166 166-167 167-168 168-174 175-194 175-179 179-180 180-181 181-185 185-189 189-192 192 192-193 193 193 194 194 195-196 XV. THE SUCCESSORS OF THE GREAT GEOMETERS 197-234 Nicomedes Diocles Perseus Isoperimetric figures. Hypsicles . Dionysodorus . Posidonius Zenodorus 199 200-203 203-206 206-213 213-218 218-219 219-222
CONTENTS vii Geminus pages 222-234 Attempt to prove the Parallel-Postulate . . . 227-230 On Meteorologica of Posidonius 231-232 Introduction to the Phaenomena attributed to Geminus 232-234 XVJ. SOME HANDBOOKS 235-244 Cleomedes, De motu circulars 235-238 Nicomachus 238 Theon of Smyrna, Expositio rerum mathematicarum ad legendum Platonem utilium 238-244 XVII. TRIGONOMETRY: HIPPARCHUS, MENELAUS, PTO- LEMY 245-297 Theodosius 245-246 Works by Theodosius 246 Contents of the Spha erica 246-252 No actual trigonometry in Theodosius . . . 250-252 The beginnings of trigonometry 252-253 Hipparchus . 253-260 The work of Hipparchus . . ' . . . . 254-256 First systematic use of trigonometry .... 257-259 Table of chords 259-260 Menelaus 260-273 The Spkaerka of Menelaus 261-273 (a) Menelaus's theorem ' ' for the sphere . . 266-268 (ft) Deductions from Menelaus's theorem . . 268-269 (y) Anharmonic property of four great circles through one point ..... 269-270 (d) Propositions analogous to Eucl. VI. 3 . . 270 Claudius Ptolemy 273-297 The MaOtinaTiKr) T
Page 5 and 6: A HISTORY OF GREEK MATHEMATICS VOLU
Page 7 and 8: A HISTORY OF GREEK MATHEMATICS BY S
Page 9: CONTENTS OF VOL II XII. ARISTARCHUS
Page 13 and 14: CONTENTS ix The Synagoge or Collect
Page 15: CONTENTS XI XXI. COMMENTATORS AND B
Page 18 and 19: ' 2 ARISTARCHUS OF SAMOS stamping t
Page 20 and 21: : 4 ARISTARCHUS OF SAMOS Archimedes
Page 22 and 23: 6 ARISTARCHUS OF SAMOS (3) that the
Page 24 and 25: 8 ARISTARCHUS OF SAMOS The first pa
Page 26 and 27: ; 10 ARISTARCHUS OF SAMOS Therefore
Page 28 and 29: 12 ARISTARCHUS OF SAMOS (2) ON: (di
Page 30 and 31: . 14 ARISTARCHUS OF SAMOS Prop. 14
Page 32 and 33: ; XIII ARCHIMEDES The siege and cap
Page 34 and 35: 18 ARCHIMEDES the making of spheres
Page 36 and 37: 20 ARCHIMEDES birth to the calculus
Page 38 and 39: : 22 ARCHIMEDES on the Quadrature o
Page 40 and 41: 24 • ARCHIMEDES " works on the le
Page 42 and 43: 26 ARCHIMEDES private hands. In 149
Page 44 and 45: 28 ARCHIMEDES Mechanical Theorems,
Page 46 and 47: 30 ARCHIMEDES the whole segment of
Page 48 and 49: V 32 ARCHIMEDES circles are section
Page 50 and 51: 34 ARCHIMEDES Therefore AX: AG = (A
Page 52 and 53: 3 36 ARCHIMEDES that, if we continu
Page 54 and 55: ,' 38 ARCHIMEDES Therefore B is not
Page 56 and 57: 40 ARCHIMEDES less than a hemispher
Page 58 and 59: 42 ARCHIMEDES ttt 2 .2 sin -^- ~2n
Page 60 and 61:
, 44 ARCHIMEDES values for each of
Page 62 and 63:
46 ARCHIMEDES the curves touch at t
Page 64 and 65:
48 ARCHIMEDES Draw QMN through M pa
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50 ARCHIMEDES To return to Archimed
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52 ARCHIMEDES and Zeuthen) is that
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, 54 ARCHIMEDES Now the triangles A
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56 ARCHIMEDES case of all, where we
Page 74 and 75:
58 ARCHIMEDES first of the three pr
Page 76 and 77:
60 ARCHIMEDES by planes obliquely i
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, 62 ARCHIMEDES II. In the case of
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} 64 ARCHIMEDES The conclusion, con
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66 ARCHIMEDES points of intersectio
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: 68 ARCHIMEDES Let QGO meet the or
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70 ARCHIMEDES touches it at one poi
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72 ARCHIMEDES Let OF'G meet the spi
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74, ARCHIMEDES And OB, OP, OQ, . .
Page 92 and 93:
76 ARCHIMEDES proofs. We do not fin
Page 94 and 95:
. 78 ARCHIMEDES Hence the centre of
Page 96 and 97:
. 80 ARCHIMEDES area. Lastly (Prop.
Page 98 and 99:
82 ARCHIMEDES of the universe, has
Page 100 and 101:
; 84 ARCHIMEDES the sun when it has
Page 102 and 103:
86 ARCHIMEDES generally), then howe
Page 104 and 105:
88 ARCHIMEDES that is, it takes the
Page 106 and 107:
90 ARCHIMEDES Taking the limit, wc
Page 108 and 109:
: ; 92 ARCHIMEDES deduced from Post
Page 110 and 111:
; ; 94 ARCHIMEDES method attributed
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; 96 ARCHIMEDES where k is the axis
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98 ARCHIMEDES Secondly, it is requi
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; 100 ARCHIMEDES symmetrically, fro
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102 ARCHIMEDES of the two smaller s
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104 ERATOSTHENES Long as the presen
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106 ERATOSTHENES geometric mean bet
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; 108 ERATOSTHENES out of 83 contai
Page 126 and 127:
XIV CONIC SECTIONS. APOLLONIUS OF P
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112 CONIC SECTIONS a section throug
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114 CONIC SECTIONS But, by similar
Page 132 and 133:
116 CONIC SECTIONS at right angles)
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: ' 118 CONIC SECTIONS areas, manip
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120 CONIC SECTIONS Proof from Pappu
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; ; 122 CONIC SECTIONS chords drawn
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124 CONIC SECTIONS only : p is simp
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126 APOLLONIUS OF PERGA for the oth
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128 APOLLONIUS OF PERGA Gregory, ho
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130 APOLLONIUS OF PERGA minima and
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132 APOLLONIUS OF PERGA Preface to
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134 APOLLONIUS OF PERGA straight li
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136 APOLLONIUS OF PERGA as particul
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138 APOLLONIUS OF PERGA Therefore Q
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; 140 APOLLONIUS OF PERGA ' If in a
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142 APOLLONIUS OF PERGA /
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; 144 APOLLONIUS OF PERGA Therefore
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146 APOLLONIUS OF PERGA (2) In the
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148 APOLLONIUS OF PERGA It has been
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150 APOLLONIUS OF PERGA the last pr
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152 APOLLONIUS OF PERGA Adding the
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154 APOLLONIUS OF PERGA The general
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156 APOLLONIUS Ot PERGA L, 1/ and M
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; 158 APOLLONIUS OF PERGA tively. T
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) 160 APOLLONIUS OF PERGA Next Apol
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162 APOLLONIUS OF PERGA Similarly,
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: 164 APOLLONIUS OF PERGA (2) if A
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166 APOLLONIUS OF PERGA The proposi
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168 APOLLONIUS OF PERGA each make e
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: 170 APOLLONIUS OF PERGA Secondly,
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172 APOLLONIUS OF PERGA A number of
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: A 174 APOLLONIUS OF PERGA 2AGPT:
Page 192 and 193:
176 APOLLONIUS OF PERGA a given poi
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178 APOLLONIUS OF PERGA the value o
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180 APOLLONIUS OF PERGA treatment o
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182 APOLLONIUS OF PERGA a circle, (
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184 APOLLONIUS OF PERGA HG meeting
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186 AP0LL0N1US OF PERGA of a line.
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.; 188 APOLLONIUS OF PERGA cut off
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190 APOLLONIUS OF PERGA III. Given
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192 APOLLONIUS OF PERGA But, by sim
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194 APOLLONIUS OF PERGA (A) On the
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196 APOLLONIUS OF PERGA another hyp
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198 SUCCESSORS OF THE GREAT GEOMETE
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; 200 SUCCESSORS OF THE GREAT GEOME
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; 202 SUCCESSORS OF -THE GREAT GEOM
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Page 222 and 223:
Page 224 and 225:
Page 226 and 227:
Page 228 and 229:
Page 230 and 231:
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
Page 240 and 241:
' 224 SUCCESSORS OF THE GREAT GEOME
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Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
Page 252 and 253:
; 236 SOME HANDBOOKS the first cent
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238 SOME HANDBOOKS larger than the
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; 240 SOME HANDBOOKS numbers, plane
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242 SOME HANDBOOKS the earth, repre
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: 244 SOME HANDBOOKS We next have (
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246 TRIGONOMETRY dosius was of Bith
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; 248 TRIGONOMETRY circle from its
Page 266 and 267:
250 TRIGONOMETRY the required numer
Page 268 and 269:
252 TRIGONOMETRY We may contrast wi
Page 270 and 271:
254 TRIGONOMETRY The work of Hippar
Page 272 and 273:
\ 256 TRIGONOMETRY Improved Instrum
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258 TRIGONOMETRY in relation to one
Page 276 and 277:
' 260 TRIGONOMETRY by ¥Jo from §
Page 278 and 279:
262 TRIGONOMETRY translation by Mau
Page 280 and 281:
264 TRIGONOMETRY Eucl. I. 16, 32 ar
Page 282 and 283:
266 TRIGONOMETRY (a) ' Menelaus s t
Page 284 and 285:
268 TRIGONOMETRY But, by the propos
Page 286 and 287:
270 TRIGONOMETRY It follows that th
Page 288 and 289:
272 TRIGONOMETRY (1) If * 1 >P 1 >2
Page 290 and 291:
274 TRIGONOMETRY the superlative /x
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: : 276 TRIGONOMETRY bo given here.
Page 294 and 295:
. ; 278 TRIGONOMETRY The constructi
Page 296 and 297:
280 TRIGONOMETRY The equation in fa
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; 282 TRIGONOMETRY greater, then sh
Page 300 and 301:
284 TRIGONOMETRY the sines obtained
Page 302 and 303:
286 TRIGONOMETRY , Thus AC is found
Page 304 and 305:
288 TRIGONOMETRY the diagram is one
Page 306 and 307:
, ; 290 TRIGONOMETRY both in the pl
Page 308 and 309:
292 TRIGONOMETRY seeing that Diodor
Page 310 and 311:
; 294 TRIGONOMETRY on the mirror wh
Page 312 and 313:
296 TRIGONOMETRY I. To prove I. 28,
Page 314 and 315:
XVIII MENSURATION: HERON OF ALEXAND
Page 316 and 317:
300 HERON OF ALEXANDRIA Pappus goes
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' 302 HERON OF ALEXANDRIA with Hero
Page 320 and 321:
304 HERON OF ALEXANDRIA And first w
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306 HERON OF ALEXANDRIA the surface
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: 308 HERON OF ALEXANDRIA education
Page 326 and 327:
310 HERON OF ALEXANDRIA Besthorn an
Page 328 and 329:
312 HERON OF ALEXANDRIA triangle wh
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: ; 314 HERON OF ALEXANDRIA Now the
Page 332 and 333:
316 HERON OF ALEXANDRIA or any angl
Page 334 and 335:
318 HERON OF ALEXANDRIA formed by t
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320 HERON OF ALEXANDRIA in an Archi
Page 338 and 339:
322 HERON OF ALEXANDRIA chap. 30 of
Page 340 and 341:
. , ^ the square) is . ' 26J-| inst
Page 342 and 343:
326 HERON OF ALEXANDRIA is given as
Page 344 and 345:
; 328 HERON OF ALEXANDRIA Heron. As
Page 346 and 347:
, 330 HERON OF ALEXANDRIA (£) Segm
Page 348 and 349:
332 HERON OF ALEXANDRIA view of the
Page 350 and 351:
334 HERON OF ALEXANDRIA The method
Page 352 and 353:
336 HERON OF ALEXANDRIA Book III. D
Page 354 and 355:
338 HERON OF ALEXANDRIA area'. Thes
Page 356 and 357:
340 HERON OF ALEXANDRIA lines ', an
Page 358 and 359:
8 342 HERON OF ALEXANDRIA and, solv
Page 360 and 361:
344 HERON OF ALEXANDRIA Quadratic e
Page 362 and 363:
346 HERON OF ALEXANDRIA that to mee
Page 364 and 365:
348 HERON OF ALEXANDRIA case suppos
Page 366 and 367:
' 350 HERON OF ALEXANDRIA between t
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1 ' 352 HERON OF ALEXANDRIA do grea
Page 370 and 371:
354 HERON OF ALEXANDRIA reversing t
Page 372 and 373:
356 PAPPUS OF ALEXANDRIA Date of Pa
Page 374 and 375:
358 PAPPUS OF ALEXANDRIA however, a
Page 376 and 377:
360 PAPPUS OF ALEXANDRIA who is men
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362 PAPPUS OF ALEXANDRIA a problem
Page 380 and 381:
364 PAPPUS OF ALEXANDRIA the proble
Page 382 and 383:
366 PAPPUS OF ALEXANDRIA triangle w
Page 384 and 385:
368 PAPPUS OF ALEXANDRIA the other,
Page 386 and 387:
370 PAPPUS OF ALEXANDRIA contained
Page 388 and 389:
372 PAPPUS OF ALEXANDRIA There is,
Page 390 and 391:
374 PAPPUS OF ALEXANDRIA But theref
Page 392 and 393:
376 PAPPUS OF ALEXANDRIA IV. We now
Page 394 and 395:
378 PAPPUS OF ALEXANDRIA With as ce
Page 396 and 397:
380 PAPPUS OF ALEXANDRIA principii.
Page 398 and 399:
382 PAPPUS OF ALEXANDRIA curve, des
Page 400 and 401:
384 PAPPUS OF ALEXANDRIA » Now (se
Page 402 and 403:
386 PAPPUS OF ALEXANDRIA means of a
Page 404 and 405:
388 PAPPUS OF ALEXANDRIA Measure DA
Page 406 and 407:
390 PAPPUS OF ALEXANDRIA ambrosia i
Page 408 and 409:
39.2 PAPPUS OF ALEXANDRIA Draw AE a
Page 410 and 411:
394 PAPPUS OF ALEXANDRIA which have
Page 412 and 413:
396 PAPPUS OF ALEXANDRIA synthetica
Page 414 and 415:
398 PAPPUS OF ALEXANDRIA in length
Page 416 and 417:
400 PAPPUS OF ALEXANDRIA book, prac
Page 418 and 419:
402 PAPPUS OF ALEXANDRIA Eratosthen
Page 420 and 421:
404 PAPPUS OF ALEXANDRIA If the pas
Page 422 and 423:
406 PAPPUS OF ALEXANDRIA Props. 32,
Page 424 and 425:
408 PAPPUS OF ALEXANDRIA VI. Props.
Page 426 and 427:
410 PAPPUS OF ALEXANDRIA but also w
Page 428 and 429:
412 PAPPUS OF ALEXANDRIA Therefore
Page 430 and 431:
414 PAPPUS OF ALEXANDRIA I need onl
Page 432 and 433:
416 PAPPUS OF ALEXANDRIA solution *
Page 434 and 435:
: 418 PAPPUS OF ALEXANDRIA This is
Page 436 and 437:
' 420 PAPPUS OF ALEXANDRIA opposite
Page 438 and 439:
i 4?2 PAPPUS OF ALEXANDRIA Props. 1
Page 440 and 441:
424 PAPPUS OF ALEXANDRIA And, since
Page 442 and 443:
; 426 PAPPUS OF ALEXANDRIA is fond
Page 444 and 445:
428 PAPPUS OF ALEXANDRIA Historical
Page 446 and 447:
' 430 PAPPUS OF ALEXANDRIA in bette
Page 448 and 449:
432 PAPPUS OF ALEXANDRIA We have ne
Page 450 and 451:
! ; 434 PAPPUS OF ALEXANDRIA about
Page 452 and 453:
436 PAPPUS OF ALEXANDRIA to this di
Page 454 and 455:
438 PAPPUS OF ALEXANDRIA Take point
Page 456 and 457:
XX ALGEBRA: DIOPHANTUS OF ALEXANDRI
Page 458 and 459:
442 ALGEBRA: DIOPHANTUS OF ALEXANDR
Page 460 and 461:
} 444 ALGEBRA: DIOPHANTUS OF ALEXAN
Page 462 and 463:
446 ALGEBRA: DIOPHANTUS OF ALEXANDR
Page 464 and 465:
;: 448 ALGEBRA: DIOPHANTUS OF ALEXA
Page 466 and 467:
450 DIOPHANTUS OF ALEXANDRIA betwee
Page 468 and 469:
* 452 DIOPHANTUS OF ALEXANDRIA catt
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454 DIOPHANTUS OF ALEXANDRIA Greek.
Page 472 and 473:
456 DIOPHANTUS OF ALEXANDRIA litera
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: x a 458 DIOPHANTUS OF ALEXANDRIA
Page 476 and 477:
460 DIOPHANTUS OF ALEXANDRIA Attach
Page 478 and 479:
;' ' 462 DIOPHANTUS OF ALEXANDRIA T
Page 480 and 481:
1 464 DIOPHANTUS OF ALEXANDRIA equa
Page 482 and 483:
: :; 466 DIOPHANTUS OF ALEXANDRIA (
Page 484 and 485:
# 468 DIOPHANTUS OF ALEXANDRIA subs
Page 486 and 487:
i £> ', n 470 DIOPHANTUS OF ALEXAN
Page 488 and 489:
: 472 DIOPHANTUS OF ALEXANDRIA or,
Page 490 and 491:
. 474 DIOPHANTUS OF ALEXANDRIA The
Page 492 and 493:
: 476 DIOPHANTUS OF ALEXANDRIA More
Page 494 and 495:
; — 478 DIOPHANTUS OF ALEXANDRIA
Page 496 and 497:
480 DIOPHANTUS OF ALEXANDRIA 2. If
Page 498 and 499:
1 482 DIOPHANTUS OF ALEXANDRIA hypo
Page 500 and 501:
484 DIOPHANTUS OF ALEXANDRIA or fra
Page 502 and 503:
486 DIOPHANTUS OF ALEXANDRIA I. 12.
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' . 488 DIOPHANTUS OF ALEXANDRIA IV
Page 506 and 507:
i 490 DIOPHANTUS OF ALEXANDRIA (v)
Page 508 and 509:
492 DIOPHANTUS OF ALEXANDRIA II. 1
Page 510 and 511:
I III. 494 DIOPHANTUS OF ALEXANDRIA
Page 512 and 513:
; 496 DIOPHANTUS OF ALEXANDRIA afte
Page 514 and 515:
498 DIOPHANTUS OF ALEXANDRIA Simila
Page 516 and 517:
500 DIOPHANTUS OF ALEXANDRIA V. 6.
Page 518 and 519:
502 DIOPHANTUS OF ALEXANDRIA (V. 24
Page 520 and 521:
^ ~ } 504 DIOPHANTUS OF ALEXANDRIA
Page 522 and 523:
506 DIOPHANTUS OF ALEXANDRIA 9 A; 2
Page 524 and 525:
— - 508 DIOPHANTUS OF ALEXANDRIA
Page 526 and 527:
) 510 DIOPHANTUS OF ALEXANDRIA Lemm
Page 528 and 529:
- £ 512 DIOPHANTUS OF ALEXANDRIA s
Page 530 and 531:
514 DIOPHANTUS OF ALEXANDRIA term i
Page 532 and 533:
2 516 DIOPHANTUS OF ALEXANDRIA 4. T
Page 534 and 535:
XXI COMMENTATORS AND BYZANTINES We
Page 536 and 537:
520 COMMENTATORS AND BYZANTINES pro
Page 538 and 539:
522 COMMENTATORS AND BYZANTINES (Pr
Page 540 and 541:
. 524 COMMENTATORS AND BYZANTINES u
Page 542 and 543:
; 526 COMMENTATORS AND BYZANTINES A
Page 544 and 545:
; 528 COMMENTATORS AND BYZANTINES a
Page 546 and 547:
530 COMMENTATORS AND BYZANTINES num
Page 548 and 549:
: 532 COMMENTATORS AND BYZANTINES U
Page 550 and 551:
534 COMMENTATORS AND BYZANTINES cas
Page 552 and 553:
536 COMMENTATORS AND BYZANTINES reg
Page 554 and 555:
538 COMMENTATORS AND BYZANTINES com
Page 556 and 557:
540 COMMENTATORS AND BYZANTINES mad
Page 558 and 559:
542 COMMENTATORS AND BYZANTINES By
Page 560 and 561:
• 544 COMMENTATORS AND BYZANTINES
Page 562 and 563:
; 546 COMMENTATORS AND BYZANTINES a
Page 564 and 565:
548 COMMENTATORS AND BYZANTINES The
Page 566 and 567:
550 COMMENTATORS AND BYZANTINES ins
Page 568 and 569:
; ; ; ; 552 COMMENTATORS AND BYZANT
Page 570 and 571:
— 554 COMMENTATORS AND BYZANTINES
Page 572 and 573:
' APPENDIX On Archimedes's 'proof o
Page 574 and 575:
558 APPENDIX the small increases of
Page 576 and 577:
560 APPENDIX Next, for the point Q'
Page 579 and 580:
, vddcov INDEX OF GREEK WORDS [The
Page 581 and 582:
: INDEX OF GREEK WORDS 565 of unkno
Page 583 and 584:
1 : : INDEX OF GREEK WORDS 567 vuaa
Page 585 and 586:
INDEX OF GREEK WORDS 569 jutp?;?, v
Page 587 and 588:
: ENGLISH INDEX 571 Anthemius of Tr
Page 589 and 590:
ENGLISH INDEX 573 Babylonians : civ
Page 591 and 592:
: ENGLISH INDEX 575 448 : works and
Page 593 and 594:
:: Ghetaldi, Marino, ii. 190. Girar
Page 595 and 596:
: Jan, C. 444. Joachim Catnerarius
Page 597 and 598:
: ENGLISH INDEX 581 of Euclid and A
Page 599 and 600:
: ENGLISH INDEX 583 Gizeh, and Medu
Page 601 and 602:
: ENGLISH INDEX 58; numbers) 77 : a
Page 604:
PRINTED IN ENGLAND AT THE OXFORD UN
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