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8 342 HERON OF ALEXANDRIA and, solving for x — a, we obtain " (a+l)(d l -8l )-\-a(d — 8 2 2y (a+l)^-^) or #A =a + (a + 1) (d x - X ) + a(d 2 -8 2 ) Since 8 V 8 2 neglect them for a first approximation, and we have are in any case the cubes of fractions, we may (a + l)d 1 + ad 2 C i \ D Xl \ i \ / /, - - h 1 * "^^***** "'" , a H K z a B III. 22, which shows how to cut a frustum of a cone in a given ratio by a section parallel to the bases, shall end our account of the Metrica. I shall give the general formulae on the left and Heron's case on the right. Let ABED be the frustum, let the diameters of the bases be a, a, and the height h. Complete the cone, and let the height of GDE be x. Suppose that the frustum has to be cut by a plane FG in such a way that (frustum DG) : (frustum In the case taken by Heron FB) — m : n. a = 28, a'= 21, h = 12, m =^4, n = 1. Draw DH perpendicular to A B.
, Since (DG) : (FB) = m : Now DIVISIONS OF n, (DB):(DG) = (m + n):m. (2)5) = '^irh (a 2 + a
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A HISTORY OF GREEK MATHEMATICS VOLU
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A HISTORY OF GREEK MATHEMATICS BY S
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CONTENTS OF VOL II XII. ARISTARCHUS
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CONTENTS vii Geminus pages 222-234
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CONTENTS ix The Synagoge or Collect
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CONTENTS XI XXI. COMMENTATORS AND B
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' 2 ARISTARCHUS OF SAMOS stamping t
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: 4 ARISTARCHUS OF SAMOS Archimedes
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6 ARISTARCHUS OF SAMOS (3) that the
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8 ARISTARCHUS OF SAMOS The first pa
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; 10 ARISTARCHUS OF SAMOS Therefore
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12 ARISTARCHUS OF SAMOS (2) ON: (di
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. 14 ARISTARCHUS OF SAMOS Prop. 14
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; XIII ARCHIMEDES The siege and cap
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18 ARCHIMEDES the making of spheres
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20 ARCHIMEDES birth to the calculus
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: 22 ARCHIMEDES on the Quadrature o
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24 • ARCHIMEDES " works on the le
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26 ARCHIMEDES private hands. In 149
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28 ARCHIMEDES Mechanical Theorems,
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30 ARCHIMEDES the whole segment of
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V 32 ARCHIMEDES circles are section
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34 ARCHIMEDES Therefore AX: AG = (A
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3 36 ARCHIMEDES that, if we continu
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,' 38 ARCHIMEDES Therefore B is not
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40 ARCHIMEDES less than a hemispher
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42 ARCHIMEDES ttt 2 .2 sin -^- ~2n
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, 44 ARCHIMEDES values for each of
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46 ARCHIMEDES the curves touch at t
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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
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58 ARCHIMEDES first of the three pr
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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, . .
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76 ARCHIMEDES proofs. We do not fin
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. 78 ARCHIMEDES Hence the centre of
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. 80 ARCHIMEDES area. Lastly (Prop.
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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
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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
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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
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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
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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:
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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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' 224 SUCCESSORS OF THE GREAT GEOME
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; 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
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250 TRIGONOMETRY the required numer
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252 TRIGONOMETRY We may contrast wi
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254 TRIGONOMETRY The work of Hippar
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\ 256 TRIGONOMETRY Improved Instrum
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258 TRIGONOMETRY in relation to one
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' 260 TRIGONOMETRY by ¥Jo from §
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262 TRIGONOMETRY translation by Mau
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264 TRIGONOMETRY Eucl. I. 16, 32 ar
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266 TRIGONOMETRY (a) ' Menelaus s t
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268 TRIGONOMETRY But, by the propos
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270 TRIGONOMETRY It follows that th
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272 TRIGONOMETRY (1) If * 1 >P 1 >2
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274 TRIGONOMETRY the superlative /x
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: : 276 TRIGONOMETRY bo given here.
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. ; 278 TRIGONOMETRY The constructi
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280 TRIGONOMETRY The equation in fa
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; 282 TRIGONOMETRY greater, then sh
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284 TRIGONOMETRY the sines obtained
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286 TRIGONOMETRY , Thus AC is found
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288 TRIGONOMETRY the diagram is one
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, ; 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 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
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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
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406 PAPPUS OF ALEXANDRIA Props. 32,
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408 PAPPUS OF ALEXANDRIA VI. Props.
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410 PAPPUS OF ALEXANDRIA but also w
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412 PAPPUS OF ALEXANDRIA Therefore
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414 PAPPUS OF ALEXANDRIA I need onl
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416 PAPPUS OF ALEXANDRIA solution *
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: 418 PAPPUS OF ALEXANDRIA This is
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' 420 PAPPUS OF ALEXANDRIA opposite
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i 4?2 PAPPUS OF ALEXANDRIA Props. 1
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424 PAPPUS OF ALEXANDRIA And, since
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; 426 PAPPUS OF ALEXANDRIA is fond
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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
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436 PAPPUS OF ALEXANDRIA to this di
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438 PAPPUS OF ALEXANDRIA Take point
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XX ALGEBRA: DIOPHANTUS OF ALEXANDRI
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442 ALGEBRA: DIOPHANTUS OF ALEXANDR
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} 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 (
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# 468 DIOPHANTUS OF ALEXANDRIA subs
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i £> ', n 470 DIOPHANTUS OF ALEXAN
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: 472 DIOPHANTUS OF ALEXANDRIA or,
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. 474 DIOPHANTUS OF ALEXANDRIA The
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: 476 DIOPHANTUS OF ALEXANDRIA More
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; — 478 DIOPHANTUS OF ALEXANDRIA
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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
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486 DIOPHANTUS OF ALEXANDRIA I. 12.
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' . 488 DIOPHANTUS OF ALEXANDRIA IV
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i 490 DIOPHANTUS OF ALEXANDRIA (v)
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492 DIOPHANTUS OF ALEXANDRIA II. 1
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I III. 494 DIOPHANTUS OF ALEXANDRIA
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; 496 DIOPHANTUS OF ALEXANDRIA afte
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498 DIOPHANTUS OF ALEXANDRIA Simila
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500 DIOPHANTUS OF ALEXANDRIA V. 6.
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502 DIOPHANTUS OF ALEXANDRIA (V. 24
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^ ~ } 504 DIOPHANTUS OF ALEXANDRIA
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506 DIOPHANTUS OF ALEXANDRIA 9 A; 2
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— - 508 DIOPHANTUS OF ALEXANDRIA
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) 510 DIOPHANTUS OF ALEXANDRIA Lemm
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- £ 512 DIOPHANTUS OF ALEXANDRIA s
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514 DIOPHANTUS OF ALEXANDRIA term i
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2 516 DIOPHANTUS OF ALEXANDRIA 4. T
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XXI COMMENTATORS AND BYZANTINES We
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520 COMMENTATORS AND BYZANTINES pro
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522 COMMENTATORS AND BYZANTINES (Pr
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. 524 COMMENTATORS AND BYZANTINES u
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; 526 COMMENTATORS AND BYZANTINES A
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; 528 COMMENTATORS AND BYZANTINES a
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530 COMMENTATORS AND BYZANTINES num
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: 532 COMMENTATORS AND BYZANTINES U
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534 COMMENTATORS AND BYZANTINES cas
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536 COMMENTATORS AND BYZANTINES reg
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538 COMMENTATORS AND BYZANTINES com
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540 COMMENTATORS AND BYZANTINES mad
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542 COMMENTATORS AND BYZANTINES By
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• 544 COMMENTATORS AND BYZANTINES
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; 546 COMMENTATORS AND BYZANTINES a
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548 COMMENTATORS AND BYZANTINES The
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550 COMMENTATORS AND BYZANTINES ins
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; ; ; ; 552 COMMENTATORS AND BYZANT
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— 554 COMMENTATORS AND BYZANTINES
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' APPENDIX On Archimedes's 'proof o
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558 APPENDIX the small increases of
Page 576 and 577:
560 APPENDIX Next, for the point Q'
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, vddcov INDEX OF GREEK WORDS [The
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: INDEX OF GREEK WORDS 565 of unkno
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1 : : INDEX OF GREEK WORDS 567 vuaa
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INDEX OF GREEK WORDS 569 jutp?;?, v
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: ENGLISH INDEX 571 Anthemius of Tr
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ENGLISH INDEX 573 Babylonians : civ
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: ENGLISH INDEX 575 448 : works and
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:: Ghetaldi, Marino, ii. 190. Girar
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: Jan, C. 444. Joachim Catnerarius
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: ENGLISH INDEX 581 of Euclid and A
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: ENGLISH INDEX 583 Gizeh, and Medu
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: ENGLISH INDEX 58; numbers) 77 : a
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PRINTED IN ENGLAND AT THE OXFORD UN
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