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: 308 HERON OF ALEXANDRIA education for centuries. The geometrical or mensurational books in particular gave scope for expansion by multiplication of examples, so that it is difficult to disentangle the genuine Heron from the rest of the collections which have come down to us under his name. Hultsch's considered criterion is as follows : The Heron texts which have come down to our ' time are authentic in so far as they bear the author's name and have kept the original design and form of Heron's works, but are unauthentic in so far as, being constantly in use for practical purposes, they were repeatedly re-edited and, in the course of re-editing, were rewritten with a view to the particular needs of the time.' List of Treatises. Such of the works of Heron as have survived have reached us in very different ways. Those which have come down in the Greek are I. The Metrica, first discovered in 1896 in a manuscript of the eleventh (or twelfth) century at Constantinople by R. Schone and edited by his son, H. Scheme (Heronis Opera, iii, Teubner, 1903). II. On the Dioptra, edited in an Italian version by Venturi in 1814 ; the Greek text was first brought out by A. J. H. Vincent 1 in 1858, and the critical edition of it byH. Schone is included in the Teubner vol. iii just mentioned. III. The Pneumatica, in two Books, which appeared first in a Latin translation by Commandinus, published after his death in 1575; the Greek text was first edited by TheVenot in Vetevum mathematicovum opera Graece et Latine edita (Paris, 1693), and is now available in Heronis Opera, i (Teubner, 1899), by W. Schmidt. IV. On the art of constructing automata (irepl avTo/jiaToiroLrjTLKrjs), or The automaton-theatre, first edited in an Italian translation by B. Baldi in 1589 ; the Greek text was included in TheVenot's Vet, math., and now forms part of Heronis Opera, vol. i, by W. Schmidt. V. Belopoe'ica (on the construction of engines of war), edited 1 Notices et extraits des manuscrits de la Biblioiheque impe'riale, xix, pt. 2, pp. 157-337.
LIST OF TREATISES 309 by B. Baldi (Augsburg, 1616), Thevenot (Vet. math.), Kochly and Riistow (1853) and by Wescher (Pollorcetique des Grecs, 1867, the first critical edition). VI. The Cheirobalistra ('Hpcovos ^ipofiaWicrTpas KaracrKevrj Kal
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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
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 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
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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
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378 PAPPUS OF ALEXANDRIA With as ce
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380 PAPPUS OF ALEXANDRIA principii.
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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
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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
Page 478 and 479:
;' ' 462 DIOPHANTUS OF ALEXANDRIA T
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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
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; — 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
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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
Page 530 and 531:
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
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
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:: 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
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: 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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