Euclidis opera omnia

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24 AEAOMENA. r^toi iGov iGTLV^ r) t6 stsqov tov itsQov do&evtL êi- ôv i0tLV, insl yaQ dod^dv iotiv ixdteQov tav AF^ B/d ^ tk dr] do&ivta ^tOL l'6a idtlv i) uvi6cc. 5 £(?Tco JtQotSQOv i'6a' l'6ov ccQa i6ti t6 AF tc5 5^. xoLvbv d(pr]Q^6^(o t6 BF' XoLTibv aQa t6 AB koina ta r^ l6ov i6tLV. fi^fj £6tG} Srj i6a, dXX' £6ta ^slôv tb AF tov BAy xul x£i6d^(o ta B/d i'6ov t6 FE' do&lv dh t6 BA' 10 do%^£v aQa xal t6 FE. £6tL dh xal oXov tb AF dod-iv xal XoLTcbv tb AE dod-iv i6tLV. xal insl i'6ov i6tl t6 EF ta jBz/, xolvov d(prjQ^6d^(o t6 BF' koinbv ccQa tb BE XoLna ta FA i'6ov i^tCv. xaC i6tL 8o%-£v t6 AE' t6 AB ciQa toi) Jz/ dodîvti (i^ôv i6tLV. 15 ty', 'Edv 17 tQCa ^£y£&r]y xal t6 ^hv nQ&tov nQog t6 d£vt£Qov X6yov i%ri d^Soîvov, t6 Se d£vt£Qov tov 7] iv Adyc), xal tb nQ&tov XQCtov do&ivtL (nftôv fi xov tQCtov Sod-ivtL (i£iôv i^Tûi t) iv k6y(p. 20 i6tG) tQCa ii£yi%-r] td AB^ JTz/, E, xal t6 }i£v AB nQbg t6 Jz/ }.6yov ixitca d^dofiivov^ t6 Sh F^ tov E 6o&£vti (i£tôv £6tC3 rj iv X6yc)' kiy(o, oti xal tb AB tov E dodîyti (i£it,6v i6tiv rj iv X6ya. insl yuQ t6 Fz/ tov E dod-ivtL (i^t^bv i6tLv ri iv 25 Adyc), d(pi^QYi6%ô:) t6 8o%^£v (iiy£&og t6 FZ' koLnov 3. Post infi ras. 3 litt. v. 4. iiviacc] o^ a. 7. iazL codd. 8. &XXd a. rov BJ] om. a. 11. AE] EA a. 14. t6 (alt.)] TM Vat. 16. fiiv] om. ^. 20. fifys^T]] corr. ex ^fyfO'?^ m. 2 v. tk] coit. ex to m. 2 Vat. 22. forat v.
DATA. 25 magnitudmem j4B maguitudini FJ aequalem esse aut alteram data magnitudine maiorem esse altera. nam quoniam data est utraque magnitudo AP^ B^, datae magnitudines aut aequales sunt aut in- ^ g r z/ I 1 prius aeqâles. sint aequales. itaque AF = BJ. communis auferatur B F. itaque reliqua AB reliquae Fz/ aequalis est. ' iam ne TE = BJ. sint aequales, sed data est sed &\i AF^B^, et magnitudo JBz/. data sit est A -£ ^ • r j — ' igi^^^ etiam FE. uerum etiam tota^r" data est. et reliqua AE data est [prop. lY]. et quoniam Er= BA, communis auferatur JB F. itaque reliqua BE reliquae Fz/ aequalis est. et data est magnitudo AE. ergo magnitudo AB data maior est magnitudine Fzf [def. 9]. XIII. Si tres magnitudines propositae sunt et prima ad secundam rationem habet datam et secunda, comparata cum tertia, maior est quam in ratione, etiam prima^ comparata cum tertia, data maior erit quam in ratione. sint tres magnitudines AB, FA, E, et AB ad JTzf rationem liabeat datam, et F^, comparata cum E, data maior sit quam in ratione. dico, etiam magnitudinem AB, comparatam cum E, data maiorem esse quam in ratione. * nam quoniam magnitudo FA, comparata cum E^ data maior est quam in ratione, auferatur data magni- ori] om. a. 24. inti — 25. loycoj om. a. 24. iGtir] -v add. m. 2 V.
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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
Page 39 and 40: PKOLEGOMENA. XXXV p. 200, 12 rjfiiG
Page 41 and 42: PROLEGOMENA. XXXVII Plures Theonis
Page 43 and 44: PROLEGOMENA. XXXIX Restant ii loci,
Page 45 and 46: PEOLEGOMENA. XLI lam ad idem illud
Page 47 and 48: PEOLEGOMENA. XLIII legisse atque ca
Page 49 and 50: PEOLEGOMENA. XLV addenda uel omitte
Page 51 and 52: PROLEGOMENA. XLVII totidemque omitt
Page 53 and 54: PEOLEGOMENA. XLIX periatur, quo The
Page 55 and 56: PROLEGOMENA. LI SiayQdfifiaci.v tco
Page 57 and 58: PEOLEGOMENA. LDI ad Datorum libruin
Page 59 and 60: PROLEGOMENA. LV Datorum partem Lati
Page 61 and 62: ioyco] om. Monac, Zamb. ; p. 58, PE
Page 63 and 64: PROLEGOMENA. LEK Tisus esse uidetur
Page 65 and 66: PROLEGOMENA. LXI (238, 11) TtSQicpi
Page 67 and 68: AEAOMENA. Suclides, edd. Heiberg et
Page 69 and 70: Definitiones. 1. Data magnitudine d
Page 71 and 72: DATA. 5 magnitudine et bases segmen
Page 73 and 74: DATA. 7 nam quoniam data est magnit
Page 75 and 76: DATA. III. Si quotlibet magnitudine
Page 77 and 78: DATA. 1 magnitudo FB [def. 1]. aeqi
Page 79 and 80: DATA. 13 AB ad utramque magiiitudii
Page 81 and 82: DATA. 15 ergo etiam utraque magnitu
Page 83 and 84: DATA. 17 se rationem habeant datam
Page 85 and 86: ' maior ! nam i j ratio ! data I ma
Page 87 and 88: DATA. 21 cum maguitudine BA data es
Page 89: DATA.- 23 tudiue AF, data maior sit
Page 93 and 94: ; DATA. 27 ! tudo JTZ. i [def. 11].
Page 95 and 96: DATA. 29 iam ne sit eadem et fiat A
Page 97 and 98: DATA. . 31 {AH.rZ data est. data es
Page 99 and 100: DATA. 33 €rgo magnitudo ZB, compa
Page 102 and 103: 36 AEAOMENA. 'Eav i] tQia fiEysd^r]
Page 104 and 105: 38 AEAOMENA. Êccv fi dvo ^sysd-rj
Page 106 and 107: 40 AEAOMENA. xa'. Êav fi 8vo y.sya
Page 108 and 109: 42 AEAOMENA. dvo yccQ Êyid^ri xa A
Page 110 and 111: 44 AEAOMENA. ^B TCQog ixdtSQOv t&v
Page 112 and 113: 46 AEAOMENA. yCQog t6 VTcb r&v A^ F
Page 114 and 115: 48 AEAOMENA. i'(?rco Trj dîêi. lE
Page 116 and 117: 50 AEAOMENA. tris ÂE rj d-e6Lg. dc
Page 118 and 119: 52 AEAOMENA. l'. 'Eccv anb dedofisv
Page 120 and 121: 54 AEAOMENA. svd^sia. iav de dvo yQ
Page 122 and 123: 56 AEAOMENA. A/. 'Eav etg naQaXXyjX
Page 124 and 125: 58 AEAOMENA. £ig yocQ TtaQaXliqlov
Page 126: 60 AEAOMENA. fjxOâ yccQ ajtb rov A
Page 129 and 130: DATA. 63 rectae BF parallela clucat
Page 131 and 132: DATA. 65 sumatur enim iii recta AB
Page 133 and 134: A E N M DATA. 67 EH rationem Sid EZ
Page 135 and 136: DATA. 69 ponatur enim recta positio
Page 137 and 138: DATA. 71 XL. Si trianguli singali a
Page 139 and 140: 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
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DATA. 103 latera aequales angulos F
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DATA. 105 datus est, qui relinquitu
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DATA. 107 ^r data est magnitudine (
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DATA. 109 [I, 36; I, 43]. itaque KA
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DATA. 111 nam quomam datum est AH,
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DATA. 113 [I, 34; def. 3]. sed figu
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f I grammum ; nam ' beant ' angulo
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DATA. 117 LXIII. Si triangulus spec
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DATA. 119 pendicularis AA. dico, sp
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DATA. 121 minus est quadratis later
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DATA. 123 sit triangulus ABF datum
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DATA. 125 AA = AT, erit etiam z/5 =
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DATA. 127 uerum ratio AzJ^ : ^F^ da
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— DATA. 129 ratio j4B : EH data e
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DATA. 131 tt expleatur parallelogra
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DATA. 133 sit enim jTz/ aequiangulu
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DATA. 135 reliquus L^KF datus est [
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DATA. 137 rationem habebunt datam [
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DATA, 139 data est^ et anguli ad pu
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DATA. 141 AF ai KF in eadem recta s
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FB : ZH= FM : DATA. 143 ZE : FA. et
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DATA. 145 quoniam JT© parallelogra
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DATA. 147 sint duo trianguli ABF, A
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DATA. 149 datus est. quare etiam re
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DATA. 151 Lxxvni. Si data figura ad
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DATA. 153 datam esse. quare etiam r
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DATA. 155 struatur ad rectam @H et
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DATA. 157 positum, et BAx AF ad BF^
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DATA. 159 perpendicularis HK. quare
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DATA. 161 quus extremus* ad reliquu
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DATA. 163 Lxxxn. Si quattuor rectae
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DATA. 165 positarum rationeni habet
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DATA. 167 sit data quam BJ[. dico,
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DATA. 169 J E, et expleatur A^. et
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DATA. 171 et quoniam AB X BF datum
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DATA. et data est BzJ). et datum es
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DATA. 175 Lxxxvni. Si m circulum ma
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DATA. 177 jr. quoniam datum est utr
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DATA. 179 positione datus est. datu
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UATA. 181 nam intra circulum positi
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DATA. 183 ducatur B F abscindens se
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DATA. .185 permutando [V/ 16] BA-{-
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DATA. 187 tur EZ. dico, datum esse
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DEMONSTRATIONES ALTERAE. 1. Ad prop
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.5 ->; A 1 92 • APPENDIX. 2. Ad p
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194 APPENDIX. naQU %î6Bi dsdo^svrj
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196 APPENDIX. rrjv ZE svd^sta yQa^^
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198 APPENDIX. xal rj rzl' dodêtâ
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200 APPENDIX. Twv ©, K 0r]^si(ov.
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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
Page 327 and 328:
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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