Euclidis opera omnia

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72 AEAOMENA. ficc'. 'Eav TQLycovov ^Cav e%ri yaviav dsdoiiBvriv^ TteQi de rijv dsdofievrjv ycovtav aC tcIsvquI tiqos aXl^/ias koyov 'e%(o6i dedofievov, dedotai ro TQiycovov ra eldei. 5 exsTG) yaQ tQiycovov xo ABF ^tav ycovtav dedo- êv7]v f^v 'bno xcbv BAF, jieQl de xijv vno xcbv BAF aC nkevQal aC BA, AF jcqos aV.ijXas koyov e%ex(x>6av dedoêvov Xeyco, oxi xb ABF XQiycovov dedoxai xa eldei. 10 exxei6&c3 yaQ xfi d-eaei xal xa (leys&et dedoiievrj ev&eta rj ^Z xal avve6xdxco TtQos xfj ^Z evd-eia xal xa TCQOS avxfj arjêioj xa Z xf] vno xcbv BAF yavCa l'6r} Yj vnb x&v AZE. dodêtaa de rj vnb xcbv BAF' dod-et0a aQa xal rj vnb xcbv ^ZE. mel ovv jiqos 15 d-e0ei dedoêvr] eû&eCa xfi ^Z xal xco TtQos avxfj dsdo- ^svco 0rj^sCc3 x
DATA. 73 XLI. Si triangulus unum angulum datum habet et latera datum angulum comprehendentia rationem inter se habent datam, triangulus datus est specie. habeat enim triangulus ABF unum angulum datum BAF, et latera angulum BAF comprehendentia BA, AF inter se rationem habeant datam. dico, triangulum ABF datum esse specie. ponatur enim recta ziZ positione et magnitudine data, et ad rectam ^Z et punctum in ea positum Z an- gulojB^Faequalis construatur angulus ^Z^ [I;23]. sed datus est angulus BAF. itaque etiam angulus ^ZE datus est [def. 1]. iam quoniam ad rectam positione datam z/Z et datum punctum in ea positum Z recta linea ducta est ZE datum efficiens angulum AZE,ZE data erit positione [prop. XXIX]. et quoniam ratio BA : AF data est, aequalis ei fiat ratio AZ\ZE et iungatur AE. itaque etiam ratio AZ\ZE data est [def. 2]. sed data est AZ. itaque etiam ZE data est [prop. II]. uerum etiam positione data est. et punctum Z datum est; quare etiam E datum est [prop. XXVII]. sed etiam utrumque punctum A , Z datum est. itaque unaquaeque rectarum AZ,ZE, AE positione et magnitudine data est [prop. XXVI]. ergo triangulus AZE datus est specie [prop. XXXIX]. et quoniam duo trianguli ABT, AEZ unum angulum uni angulo aequalem habent, iBAT=iAZE, et
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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
Page 87 and 88: DATA. 21 cum maguitudine BA data es
Page 89 and 90: DATA.- 23 tudiue AF, data maior sit
Page 91 and 92: DATA. 25 magnitudmem j4B maguitudin
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: DATA. 71 XL. Si trianguli singali a
Page 141 and 142: DATA. 70 latera angulos Bî F, zlZE
Page 143 and 144: DATA. 77 rectarum H®, &K, KH magni
Page 145 and 146: DATA. 79 EJ>Z [V,16-, V, 14]. aptet
Page 147 and 148: DATA. 81 sit triangulus ABT unum ha
Page 149 and 150: est [def. 3]. sed ratio AB : etiam
Page 151 and 152: DATA. 85 data est [def. 2]. et datu
Page 153 and 154: DATA. 87 XLVII. Rectilineae figurae
Page 155 and 156: DATA. 89 describantui* ABF, AAB. di
Page 157 and 158: DATA. 91 nam in eadem recta AB duae
Page 159 and 160: \ et f E E A B r J H DATA. 93 sumat
Page 161 and 162: AB : DATA. 95 Jz/ data et in rectis
Page 163 and 164: Bzi : Z& DATA. 97 sint duae figurae
Page 165 and 166: DATA. 99 et simiKs est A figurae B.
Page 167 and 168: 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
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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
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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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