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A HISTORY OF GREEK MATHEMATICS BY SIR THOMAS HEATH K.C.B., K.C.V.O., F.R.S. SC.D. CAMB. ; HON. D.SC. OXFORD HONORARY FELLOW (FORMERLY FELLOW) OF TRINITY COLLEGE, CAMBRIDGE ' . . . An independent world, Created out of pure intelligence.' Wordsworth. VOLUME II FROM ARISTARCHUS TO DIOPHANTUS OXFORD AT THE CLARENDON PRESS 1921
Page 5: A HISTORY OF GREEK MATHEMATICS VOLU
Page 9 and 10: CONTENTS OF VOL II XII. ARISTARCHUS
Page 11 and 12: CONTENTS vii Geminus pages 222-234
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
Page 66 and 67:
50 ARCHIMEDES To return to Archimed
Page 68 and 69:
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
Page 80 and 81:
} 64 ARCHIMEDES The conclusion, con
Page 82 and 83:
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
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. 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
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; 84 ARCHIMEDES the sun when it has
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86 ARCHIMEDES generally), then howe
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88 ARCHIMEDES that is, it takes the
Page 106 and 107:
90 ARCHIMEDES Taking the limit, wc
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: ; 92 ARCHIMEDES deduced from Post
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; ; 94 ARCHIMEDES method attributed
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; 96 ARCHIMEDES where k is the axis
Page 114 and 115:
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
Page 120 and 121:
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
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XIV CONIC SECTIONS. APOLLONIUS OF P
Page 128 and 129:
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)
Page 134 and 135:
: ' 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
Page 142 and 143:
126 APOLLONIUS OF PERGA for the oth
Page 144 and 145:
128 APOLLONIUS OF PERGA Gregory, ho
Page 146 and 147:
130 APOLLONIUS OF PERGA minima and
Page 148 and 149:
132 APOLLONIUS OF PERGA Preface to
Page 150 and 151:
134 APOLLONIUS OF PERGA straight li
Page 152 and 153:
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
Page 162 and 163:
146 APOLLONIUS OF PERGA (2) In the
Page 164 and 165:
148 APOLLONIUS OF PERGA It has been
Page 166 and 167:
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
Page 196 and 197:
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
Page 208 and 209:
192 APOLLONIUS OF PERGA But, by sim
Page 210 and 211:
194 APOLLONIUS OF PERGA (A) On the
Page 212 and 213:
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
Page 242 and 243:
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 (
Page 262 and 263:
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
Page 274 and 275:
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
Page 298 and 299:
; 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
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300 HERON OF ALEXANDRIA Pappus goes
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' 302 HERON OF ALEXANDRIA with Hero
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304 HERON OF ALEXANDRIA And first w
Page 322 and 323:
306 HERON OF ALEXANDRIA the surface
Page 324 and 325:
: 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
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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
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. , ^ 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
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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
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344 HERON OF ALEXANDRIA Quadratic e
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346 HERON OF ALEXANDRIA that to mee
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348 HERON OF ALEXANDRIA case suppos
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' 350 HERON OF ALEXANDRIA between t
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1 ' 352 HERON OF ALEXANDRIA do grea
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354 HERON OF ALEXANDRIA reversing t
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356 PAPPUS OF ALEXANDRIA Date of Pa
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358 PAPPUS OF ALEXANDRIA however, a
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360 PAPPUS OF ALEXANDRIA who is men
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362 PAPPUS OF ALEXANDRIA a problem
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364 PAPPUS OF ALEXANDRIA the proble
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366 PAPPUS OF ALEXANDRIA triangle w
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368 PAPPUS OF ALEXANDRIA the other,
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370 PAPPUS OF ALEXANDRIA contained
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372 PAPPUS OF ALEXANDRIA There is,
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374 PAPPUS OF ALEXANDRIA But theref
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376 PAPPUS OF ALEXANDRIA IV. We now
Page 394 and 395:
378 PAPPUS OF ALEXANDRIA With as ce
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380 PAPPUS OF ALEXANDRIA principii.
Page 398 and 399:
382 PAPPUS OF ALEXANDRIA curve, des
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384 PAPPUS OF ALEXANDRIA » Now (se
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386 PAPPUS OF ALEXANDRIA means of a
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388 PAPPUS OF ALEXANDRIA Measure DA
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390 PAPPUS OF ALEXANDRIA ambrosia i
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39.2 PAPPUS OF ALEXANDRIA Draw AE a
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394 PAPPUS OF ALEXANDRIA which have
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396 PAPPUS OF ALEXANDRIA synthetica
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398 PAPPUS OF ALEXANDRIA in length
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400 PAPPUS OF ALEXANDRIA book, prac
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402 PAPPUS OF ALEXANDRIA Eratosthen
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404 PAPPUS OF ALEXANDRIA If the pas
Page 422 and 423:
406 PAPPUS OF ALEXANDRIA Props. 32,
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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
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416 PAPPUS OF ALEXANDRIA solution *
Page 434 and 435:
: 418 PAPPUS OF ALEXANDRIA This is
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' 420 PAPPUS OF ALEXANDRIA opposite
Page 438 and 439:
i 4?2 PAPPUS OF ALEXANDRIA Props. 1
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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
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' 430 PAPPUS OF ALEXANDRIA in bette
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432 PAPPUS OF ALEXANDRIA We have ne
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! ; 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
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XX ALGEBRA: DIOPHANTUS OF ALEXANDRI
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442 ALGEBRA: DIOPHANTUS OF ALEXANDR
Page 460 and 461:
} 444 ALGEBRA: DIOPHANTUS OF ALEXAN
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446 ALGEBRA: DIOPHANTUS OF ALEXANDR
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;: 448 ALGEBRA: DIOPHANTUS OF ALEXA
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450 DIOPHANTUS OF ALEXANDRIA betwee
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* 452 DIOPHANTUS OF ALEXANDRIA catt
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454 DIOPHANTUS OF ALEXANDRIA Greek.
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456 DIOPHANTUS OF ALEXANDRIA litera
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: x a 458 DIOPHANTUS OF ALEXANDRIA
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460 DIOPHANTUS OF ALEXANDRIA Attach
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;' ' 462 DIOPHANTUS OF ALEXANDRIA T
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1 464 DIOPHANTUS OF ALEXANDRIA equa
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: :; 466 DIOPHANTUS OF ALEXANDRIA (
Page 484 and 485:
# 468 DIOPHANTUS OF ALEXANDRIA subs
Page 486 and 487:
i £> ', n 470 DIOPHANTUS OF ALEXAN
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: 472 DIOPHANTUS OF ALEXANDRIA or,
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. 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
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1 482 DIOPHANTUS OF ALEXANDRIA hypo
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484 DIOPHANTUS OF ALEXANDRIA or fra
Page 502 and 503:
486 DIOPHANTUS OF ALEXANDRIA I. 12.
Page 504 and 505:
' . 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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