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530 COMMENTATORS AND BYZANTINES number of books which he wrote, including a large number of commentaries, mostly on the dialogues of PJato (e.g. the Timaeus, the Republic, the Parmenides, the Cratylus). He was an acute dialectician and pre-eminent among his contemporaries in the range of his learning; he was a competent mathematician ; he was even a poet. At the same time he was a believer in all sorts of myths and mysteries, and a devout worshipper of divinities both Greek and Oriental. He was much more a philosopher than a mathematician. In his commentary on the Timaeus, when referring to the question whether the sun occupies a middle place among the planets, he speaks as no real mathematician could have spoken, rejecting the view of Hipparchus and Ptolemy because 6 Qzovpyos (sc. the Chaldean, says Zeller) thinks otherwise, whom it is not lawful to disbelieve '. Martin observes too, ' rather neatly, that for ' Proclus the Elements of Euclid had the good fortune not to be contradicted either by the Chaldean Oracles or by the speculations of Pythagoreans old and new '. Commentary on Euclid, Book I. For us the most important work of Proclus is his commentary on Euclid, Book I, because it is one of the main sources of our information as to the history of elementary geometry. Its great value arises mainly from the fact * that Proclus had access to a number of historical and critical works which are now lost except for fragments preserved by Proclus and others. (a) Sources of the Commentary. The historical work the loss of which is most deeply to be deplored is the History of Geometry by Eudemus. There appears to be no reason to doubt that the work of Eudemus was accessible to Proclus at first hand. For the later writers Simplicius and Eutocius refer to it in terms such as leave no doubt that they had it before them. Simplicius, quoting Eudemus as the best authority on Hippocrates's quadratures of lunes, says he will set out what Eudemus says * word for word ', adding only a little explanation in the shape of references to Euclid's Elements 'owing to the memorandum-like style of Eudemus, who sets out his explanations in the abbre-
— PROCLUS 531 viated form usual with ancient writers. Now in the second book of the history of geometry he writes as follows '} In like manner Eutocius speaks of the paralogisms handed down in connexion with the attempts of Hippocrates and Antiphon to square the circle, 'with which I imagine that all persons are accurately acquainted who have examined {kTrz
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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
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292 TRIGONOMETRY seeing that Diodor
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; 294 TRIGONOMETRY on the mirror wh
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296 TRIGONOMETRY I. To prove I. 28,
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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
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306 HERON OF ALEXANDRIA the surface
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: 308 HERON OF ALEXANDRIA education
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310 HERON OF ALEXANDRIA Besthorn an
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312 HERON OF ALEXANDRIA triangle wh
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: ; 314 HERON OF ALEXANDRIA Now the
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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
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322 HERON OF ALEXANDRIA chap. 30 of
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. , ^ the square) is . ' 26J-| inst
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326 HERON OF ALEXANDRIA is given as
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; 328 HERON OF ALEXANDRIA Heron. As
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, 330 HERON OF ALEXANDRIA (£) Segm
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332 HERON OF ALEXANDRIA view of the
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334 HERON OF ALEXANDRIA The method
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336 HERON OF ALEXANDRIA Book III. D
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338 HERON OF ALEXANDRIA area'. Thes
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340 HERON OF ALEXANDRIA lines ', an
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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
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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
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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
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 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
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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
Page 604:
PRINTED IN ENGLAND AT THE OXFORD UN
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