Euclidis opera omnia

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154 AEAOMENA. BAF ycovCa iGiq i] vnh t&v H&A^ nul i7tEâv%%^c36av KL ZA, AH, xal 'i]xd-G} xd&srog r] AM. ircal tdt] i0rlv 7] 'hnh r&v BAA rf] vnh r&v A@H, E6rt de xal y] vtco rStv &AH rf] 'bnh ABF l'0r]^ xal 5 koniY] aQa i] yjro r&v BFA Xoiiif] rfj 'vnh rav @HA £6nv t6y]' ofiOLOV aQa s6r\ rh BAF rQiycovov ra &HA rQiyd)v
DATA. 155 struatur ad rectam @H et punctum in ea positum ® angulo BAF aequalis angulus H@A [I, 23], et ducantur ZA, AH, et perpendicularis ducatur AM. quoniam est /. BAA = A@H, est autem etiam L@AH = ABF [III, 21; X. svv. 1], etiam reliquus angulus BFA reliquo angulo @HA aequalis erit [1,32]. quare ^ BAF ^ @HA [VI, 4; VI def. 1]. et per- pendiculares ductae sunt BA, AM. quare AF.BA =@H: AM [VI, 4; V, 22]. erat ^Viieva AF-.BA = @'H: ZK', nam ita supposuimus. itaque @H : AM = @H : ZK [V, 11]. quare ZK rectae AM aequalis est [V, 9]. uerum etiam parallelae sunt [I, 28]. itaque etiam ZA rectae ®H parallela est [I, 33]. quare est LZA@ = A@H [I, 29]. sed L A@H= BAT et LZA@ = ZH® [UI, 21]. itaque etiam LBAr=ZH@. uerum etiam L-^Br=@ZH. reliquus igitur angulus BFA reliquo angulo Z®H aequalis est [I, 32]. ergo triangulus ABF triangulo *Z@H aequiangulus est. LXXX. Si triangulus unum angulum datum habet, et rectangulum comprehensum rectis datum angulum comprehendentibus ad quadratum reliqui lateris rationem habet datam, triangulus datus est specie. sit triangulus ABF datum habens angulum ad A BAh. 8. BJ] ABd h. 9. AM — 10. rrjV] om. b. 10. vitov.Hxui ydq\ om. b. 11. AM — ZK] ZK, ovtwg 17 @E TtQog rriv AM h. 13. ieriv] om. b. 14. r^] rijg h. &ixdh. 16. rcbv ZA& Vat.v. larf] om. b. 18. @ZH] corr. ex Z@H m. 2 Vat. 19. BTA] BAF v. Z@H] Z@ b, item lin. 20. 24. svQ-siaov] om. ^ (non b). 25. nXavQ&g rsrQa,- ycavov] om. b.
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.^ '4*-- . ; ^ ^ "^- :,* ..-:. ii-.
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EUCLIDIS C^) LGr E8feH OPERA OMNIA.
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litPBIAE: TTPIS B. O. THITBKEBT.
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YI PRAEFATIO. atque ex illa libroru
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Vm PRAEFATIO. nimis caute uel relig
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X PRAEFATIO. c = scliolia cod. Laur
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De codicibus fatisque Datorum et eo
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PROLEGOMENA. XV 23) cod. Paris. Gr.
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PROLEGOMENA. XVII ex P cod. 7 totus
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PEOLEGOMENA. XIX insi -p. 8%, 2 Azt
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PROLEGOMENA. XXI ijtiL 18 So9Eiacc
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PROLEGOMENA. XXIII quo codice usa m
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PEOLEGOMENA. XXV an Thuano debeatur
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PEOLEGOMENA. XXVH rriv EA Xoyog 21
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PROLEGOMENA. XXIX rJB 10 BJ 12 tov'
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PKOLEGOMENA. XXXI ubi codd. Pv ab V
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PROLEGOMENA. XXXEI satis difficile
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PKOLEGOMENA. XXXV p. 200, 12 rjfiiG
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PROLEGOMENA. XXXVII Plures Theonis
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PROLEGOMENA. XXXIX Restant ii loci,
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PEOLEGOMENA. XLI lam ad idem illud
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PEOLEGOMENA. XLIII legisse atque ca
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PEOLEGOMENA. XLV addenda uel omitte
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PROLEGOMENA. XLVII totidemque omitt
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PEOLEGOMENA. XLIX periatur, quo The
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PROLEGOMENA. LI SiayQdfifiaci.v tco
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PEOLEGOMENA. LDI ad Datorum libruin
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PROLEGOMENA. LV Datorum partem Lati
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ioyco] om. Monac, Zamb. ; p. 58, PE
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PROLEGOMENA. LEK Tisus esse uidetur
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PROLEGOMENA. LXI (238, 11) TtSQicpi
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AEAOMENA. Suclides, edd. Heiberg et
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Definitiones. 1. Data magnitudine d
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DATA. 5 magnitudine et bases segmen
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DATA. 7 nam quoniam data est magnit
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DATA. III. Si quotlibet magnitudine
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DATA. 1 magnitudo FB [def. 1]. aeqi
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DATA. 13 AB ad utramque magiiitudii
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DATA. 15 ergo etiam utraque magnitu
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DATA. 17 se rationem habeant datam
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' maior ! nam i j ratio ! data I ma
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DATA. 21 cum maguitudine BA data es
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DATA.- 23 tudiue AF, data maior sit
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DATA. 25 magnitudmem j4B maguitudin
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; DATA. 27 ! tudo JTZ. i [def. 11].
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DATA. 29 iam ne sit eadem et fiat A
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DATA. . 31 {AH.rZ data est. data es
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DATA. 33 €rgo magnitudo ZB, compa
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36 AEAOMENA. 'Eav i] tQia fiEysd^r]
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38 AEAOMENA. Êccv fi dvo ^sysd-rj
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40 AEAOMENA. xa'. Êav fi 8vo y.sya
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42 AEAOMENA. dvo yccQ Êyid^ri xa A
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44 AEAOMENA. ^B TCQog ixdtSQOv t&v
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46 AEAOMENA. yCQog t6 VTcb r&v A^ F
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48 AEAOMENA. i'(?rco Trj dîêi. lE
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50 AEAOMENA. tris ÂE rj d-e6Lg. dc
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52 AEAOMENA. l'. 'Eccv anb dedofisv
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54 AEAOMENA. svd^sia. iav de dvo yQ
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56 AEAOMENA. A/. 'Eav etg naQaXXyjX
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58 AEAOMENA. £ig yocQ TtaQaXliqlov
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60 AEAOMENA. fjxOâ yccQ ajtb rov A
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DATA. 63 rectae BF parallela clucat
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DATA. 65 sumatur enim iii recta AB
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A E N M DATA. 67 EH rationem Sid EZ
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DATA. 69 ponatur enim recta positio
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DATA. 71 XL. Si trianguli singali a
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DATA. 73 XLI. Si triangulus unum an
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DATA. 70 latera angulos Bî F, zlZE
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DATA. 77 rectarum H®, &K, KH magni
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DATA. 79 EJ>Z [V,16-, V, 14]. aptet
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DATA. 81 sit triangulus ABT unum ha
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est [def. 3]. sed ratio AB : etiam
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DATA. 85 data est [def. 2]. et datu
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DATA. 87 XLVII. Rectilineae figurae
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DATA. 89 describantui* ABF, AAB. di
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DATA. 91 nam in eadem recta AB duae
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\ et f E E A B r J H DATA. 93 sumat
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AB : DATA. 95 Jz/ data et in rectis
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Bzi : Z& DATA. 97 sint duae figurae
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DATA. 99 et simiKs est A figurae B.
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DATA. 101 spatium A datum est. quar
Page 169 and 170: DATA. 103 latera aequales angulos F
Page 171 and 172: DATA. 105 datus est, qui relinquitu
Page 173 and 174: DATA. 107 ^r data est magnitudine (
Page 175 and 176: DATA. 109 [I, 36; I, 43]. itaque KA
Page 177 and 178: DATA. 111 nam quomam datum est AH,
Page 179 and 180: DATA. 113 [I, 34; def. 3]. sed figu
Page 181 and 182: f I grammum ; nam ' beant ' angulo
Page 183 and 184: DATA. 117 LXIII. Si triangulus spec
Page 185 and 186: DATA. 119 pendicularis AA. dico, sp
Page 187 and 188: DATA. 121 minus est quadratis later
Page 189 and 190: DATA. 123 sit triangulus ABF datum
Page 191 and 192: DATA. 125 AA = AT, erit etiam z/5 =
Page 193 and 194: DATA. 127 uerum ratio AzJ^ : ^F^ da
Page 195 and 196: — DATA. 129 ratio j4B : EH data e
Page 197 and 198: DATA. 131 tt expleatur parallelogra
Page 199 and 200: DATA. 133 sit enim jTz/ aequiangulu
Page 201 and 202: DATA. 135 reliquus L^KF datus est [
Page 203 and 204: DATA. 137 rationem habebunt datam [
Page 205 and 206: DATA, 139 data est^ et anguli ad pu
Page 207 and 208: DATA. 141 AF ai KF in eadem recta s
Page 209 and 210: FB : ZH= FM : DATA. 143 ZE : FA. et
Page 211 and 212: DATA. 145 quoniam JT© parallelogra
Page 213 and 214: DATA. 147 sint duo trianguli ABF, A
Page 215 and 216: DATA. 149 datus est. quare etiam re
Page 217 and 218: DATA. 151 Lxxvni. Si data figura ad
Page 219: DATA. 153 datam esse. quare etiam r
Page 223 and 224: DATA. 157 positum, et BAx AF ad BF^
Page 225 and 226: DATA. 159 perpendicularis HK. quare
Page 227 and 228: DATA. 161 quus extremus* ad reliquu
Page 229 and 230: DATA. 163 Lxxxn. Si quattuor rectae
Page 231 and 232: DATA. 165 positarum rationeni habet
Page 233 and 234: DATA. 167 sit data quam BJ[. dico,
Page 235 and 236: DATA. 169 J E, et expleatur A^. et
Page 237 and 238: DATA. 171 et quoniam AB X BF datum
Page 239 and 240: DATA. et data est BzJ). et datum es
Page 241 and 242: DATA. 175 Lxxxvni. Si m circulum ma
Page 243 and 244: DATA. 177 jr. quoniam datum est utr
Page 245 and 246: DATA. 179 positione datus est. datu
Page 247 and 248: UATA. 181 nam intra circulum positi
Page 249 and 250: DATA. 183 ducatur B F abscindens se
Page 251 and 252: DATA. .185 permutando [V/ 16] BA-{-
Page 253: DATA. 187 tur EZ. dico, datum esse
Page 256 and 257: DEMONSTRATIONES ALTERAE. 1. Ad prop
Page 258 and 259: .5 ->; A 1 92 • APPENDIX. 2. Ad p
Page 260 and 261: 194 APPENDIX. naQU %î6Bi dsdo^svrj
Page 262 and 263: 196 APPENDIX. rrjv ZE svd^sta yQa^^
Page 264 and 265: 198 APPENDIX. xal rj rzl' dodêtâ
Page 266 and 267: 200 APPENDIX. Twv ©, K 0r]^si(ov.
Page 268 and 269: 202 APPENDIX. XQog tijv BF dodsis.
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204 APPENDIX. • ccvaysyQu^p&co 6i
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206 APPENDIX. 13. Ad prop. LXVn. Ka
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208 APPENDIX. 14. Ad prop. LXVIL "A
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210 APPENDIX. KQa rijg AAT xal trig
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212 APPENDIX. AFE do&stdd a6TLV dad
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214 * APPENDIX. xal ijtsl i'6rj idT
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215 APPENDIX. 17 vjib AHZ dod^stâ,
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218 APPENDIX. do&Si6(x aQd, za\ rj
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220 APPENDIX. anb 6vvan,tporBQOv ri
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222 APPENDIX. eTfsl yccQ t6 ccTtb r
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224 APPENDIX. xal t6 anb rijg u4B'
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226 APPENDIX. 19. Ad prop. XCI. EiX
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228 APPENDIX. l'6rj' iGoyaviov ccQa
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230 APPENDIX. STtel l'6r) e6x\v r}
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MAEINI PHILOSOPHI COMMENTAKIUS m EU
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Primum statuendum est, datum quid s
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IN EUCLIDIS DATA. 237 id datum esse
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IN EUCLIDIS DATA. 239 definiunt igi
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1 qui I : esse. I unam m EUCLIDIS D
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IN EUCLIDIS DATA. 243 magnitudinein
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IN EUCLIDIS DATA. 245 inter se diff
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IN EUCLIDIS DATA. 247 ob rem proble
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IN EUCLIDIS DATA. 249 nale sit, ac
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IN EUCLIDIS DATA. 251 dam autem ad
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j qua 1 propositum ! dati IN EUCLID
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' demonstrationum : facultatem [ st
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; €0 IN EUCLIDIS DATA. 257 quam d
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Ad definitiones. 1. Tav dsdo^svav t
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SCHOLIA. 263 Ad deff. 9-10. 10. Ta
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SCHOLIA. 265 TiQog ccXXrjXcc Xoyog
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SCHOLIA. 267 29. 'O avrbg ccvra nsn
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SCHOLIA. 269 43. Kal t6 6vva^(p6tEQ
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SCHOLIA. 271 z/5 TCQOS rb BF loyov
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; To SCHOLIA. 273 rav AF^ AE^ Kal 6
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I^ SCHOLIA. 275 ^B [isysdôg 6vva^(
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avi6a. SCHOLIA. 277 Ad prop. XIV. 6
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SCHOLIA. 279 doQ^siSf ical TtdXiv t
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SCHOLIA. 281 Ad prop. XXVI. 82. Ta
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SCHOLIA. 283 Ad prop. XL. 91. îdot
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SCHOLIA. 285 97. Kccl cjg 6vvciii(p
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SCHOLIA. 287 106. Kal trjg Fzf ccqk
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\ (ICOV SCHOLIA. 289 Ad prop. LIX.
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SCHOLIA. 291 Ad prop. LXIII. 122. ^
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I tov SCHOLIA. 293 6iQva t6 oiKQaXX
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SCHOLIA. 295 A r TtQog t6 ABF tQLya
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SCHOLIA. 297 AE/i l'0ov fVrt Totg d
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SCHOLIA. 299 de TtQog xivL svd^sia
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)'/ ZE SCHOLIA. 301 JtQos PK' IdyG)
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SCHOLIA. 303 AB t(p FM i(5tLV i'0ov
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SCHOLIA. 305 Ad prop. LXXIX. 163. T
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SCHOLIA. 307 yQafiôv TQiyavG) ficc
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SCHOLIA. 309 TtQog tijv HK, xal ^x^
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SCHOLIA. 311 AB ri FE L'6rj ov6cc r
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SCHOLIA. 313 181. Kal ôiotfj ccQcc
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SCHOLIA. 315 Ad prop. XC. 191. KaL
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SCHOLIA. 317 BF, ovtag rj Ajd TtQog
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SCHOLIA. 319 207. "I67j ccQa^ q)rj6
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Ad prop, XXX demonstr. quart. 1. zl
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APPENDIX SCHOLIOKUM. 325 rfjg nQog
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APPENDIX SCHOLIORUM. 327 aXl^^XoLg
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APPENDIX SCHOLIORUM. 329 AA tfj AA^
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APPENDIX SCHOLIORUM. 331 Ad prop. L
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APPENDIX SCHOLIOKUM. 333 37. Tb A c
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APPENDIX SCHOLIORUM. 335 FBE xfi vn
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1 ^^^li^^^^¥Mi
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0"'-^" *,' VAJrt €'j^ :^.'-
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