A history of Greek mathematics - Wilbourhall.org

More documents

Recommendations

Info

^ to > CD & •-3 H» CO H- O •1 PONTIFICAL INSTITUTE OF MEDIAEVAL STUDIES 59 QUEEN'S PARK CRESCENT TORONTO— 5, CANADA 15975
Page 5 and 6:
A HISTORY OF GREEK MATHEMATICS VOLU
Page 7 and 8:
A HISTORY OF GREEK MATHEMATICS BY S
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
Page 70 and 71:
, 54 ARCHIMEDES Now the triangles A
Page 72 and 73:
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
Page 78 and 79:
, 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
Page 84 and 85:
: 68 ARCHIMEDES Let QGO meet the or
Page 86 and 87:
70 ARCHIMEDES touches it at one poi
Page 88 and 89:
72 ARCHIMEDES Let OF'G meet the spi
Page 90 and 91:
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
Page 112 and 113:
; 96 ARCHIMEDES where k is the axis
Page 114 and 115:
98 ARCHIMEDES Secondly, it is requi
Page 116 and 117:
; 100 ARCHIMEDES symmetrically, fro
Page 118 and 119:
102 ARCHIMEDES of the two smaller s
Page 120 and 121:
104 ERATOSTHENES Long as the presen
Page 122 and 123:
106 ERATOSTHENES geometric mean bet
Page 124 and 125:
; 108 ERATOSTHENES out of 83 contai
Page 126 and 127:
XIV CONIC SECTIONS. APOLLONIUS OF P
Page 128 and 129:
112 CONIC SECTIONS a section throug
Page 130 and 131:
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
Page 136 and 137:
120 CONIC SECTIONS Proof from Pappu
Page 138 and 139:
; ; 122 CONIC SECTIONS chords drawn
Page 140 and 141:
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
Page 154 and 155:
138 APOLLONIUS OF PERGA Therefore Q
Page 156 and 157:
; 140 APOLLONIUS OF PERGA ' If in a
Page 158 and 159:
142 APOLLONIUS OF PERGA /
Page 160 and 161:
; 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
Page 168 and 169:
152 APOLLONIUS OF PERGA Adding the
Page 170 and 171:
154 APOLLONIUS OF PERGA The general
Page 172 and 173:
156 APOLLONIUS Ot PERGA L, 1/ and M
Page 174 and 175:
; 158 APOLLONIUS OF PERGA tively. T
Page 176 and 177:
) 160 APOLLONIUS OF PERGA Next Apol
Page 178 and 179:
162 APOLLONIUS OF PERGA Similarly,
Page 180 and 181:
: 164 APOLLONIUS OF PERGA (2) if A
Page 182 and 183:
166 APOLLONIUS OF PERGA The proposi
Page 184 and 185:
168 APOLLONIUS OF PERGA each make e
Page 186 and 187:
: 170 APOLLONIUS OF PERGA Secondly,
Page 188 and 189:
172 APOLLONIUS OF PERGA A number of
Page 190 and 191:
: A 174 APOLLONIUS OF PERGA 2AGPT:
Page 192 and 193:
176 APOLLONIUS OF PERGA a given poi
Page 194 and 195:
178 APOLLONIUS OF PERGA the value o
Page 196 and 197:
180 APOLLONIUS OF PERGA treatment o
Page 198 and 199:
182 APOLLONIUS OF PERGA a circle, (
Page 200 and 201:
184 APOLLONIUS OF PERGA HG meeting
Page 202 and 203:
186 AP0LL0N1US OF PERGA of a line.
Page 204 and 205:
.; 188 APOLLONIUS OF PERGA cut off
Page 206 and 207:
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
Page 214 and 215:
198 SUCCESSORS OF THE GREAT GEOMETE
Page 216 and 217:
; 200 SUCCESSORS OF THE GREAT GEOME
Page 218 and 219:
; 202 SUCCESSORS OF -THE GREAT GEOM
Page 220 and 221:
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
Page 254 and 255:
238 SOME HANDBOOKS larger than the
Page 256 and 257:
; 240 SOME HANDBOOKS numbers, plane
Page 258 and 259:
242 SOME HANDBOOKS the earth, repre
Page 260 and 261:
: 244 SOME HANDBOOKS We next have (
Page 262 and 263:
246 TRIGONOMETRY dosius was of Bith
Page 264 and 265:
; 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
Page 292 and 293:
: : 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
Page 316 and 317:
300 HERON OF ALEXANDRIA Pappus goes
Page 318 and 319:
' 302 HERON OF ALEXANDRIA with Hero
Page 320 and 321:
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
Page 330 and 331:
: ; 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
Page 336 and 337:
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
Page 368 and 369:
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
Page 378 and 379:
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
Page 470 and 471:
454 DIOPHANTUS OF ALEXANDRIA Greek.
Page 472 and 473:
456 DIOPHANTUS OF ALEXANDRIA litera
Page 474 and 475:
: 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.
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
show all

A history of Greek mathematics - Wilbourhall.org

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?