Euclidis opera omnia

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YI PRAEFATIO. atque ex illa librorum manu scriptorum multitudine facile mihi persuasi in primis sex plurimum habere ponderis. sunt autem hi: P = cod. Uatic. Gr. 190 Peyrardi, membr. saec. X, duobus constans uoluminibus, de quo u. uol. I p. VIII et uol. V p. XXIV sq.; praeter Elementa, Marini commentarium (uol. II fol. 248—249), Data (fol. 250 —281) continet Theonis vTtofivrjfia sig rovg TtQOiaC- Qovg xavovag IltolsâLOv. de aetate archetypi totius codicis aut eius partis, qua Theonis commentarius continetur, singulari liberaHtate ac benignitate me edocuit Hermamius Usener. in margine enim fol. 298^^ ad Theonis uerba orav 6 t&v tstQasttjQidav ^SQi6^bg tQLcbv stcbv ^cataXsiTtf] uir summus haec repperit scripta: ag vvv Gvvs^r] stcI {s) tov qo%^ ^LOxXrjtiavov (dLoxhtiavov\ tovtsetiv stcI (s^ tov do^ stovg ((ô^£ tovg) xata 'ATcd^siav {anaybiav) tijv xaO'' Tj^&g. cum autem Apameae, in urbe Syriae, anni numerarentur ad aeram quam uocant Seleuci- darum, efficitur, archetypum codicis P aut partis eius Theoninae a. 462 p. Chr., qui est aerae Diocletiani annus 179, in hac urbe ab homine non indocto lectum esse. Vat. == cod. Uatic. Gr. 204, membr. saec. X, cuius de- scriptionem dedi Neue Jahrb. f. Philol. 1886 p. 183sq. Data habet fol. 172"—194, Marinumfol. 195'— 197^ permulta correcta sunt mauu saec. XV (Vat. m. 2), cuius scripturam plenam in prolegomenis adferam. V = cod. Uatic. Gr. 1038, membr. saec. XIII, de quo u. uol. V p. Vsq. Data habet fol. 114"— 129 dua- bus manibus s. XV correcta, Marinum fol. 1 13—114".
PRAEFATIO. Vn commemorat codicem P. Tannery, Rapport sur une mission en Italie p. 43. b = cod. bibliothecae commuualis Bononiensis A l^ 18, 19 sicnatus, membr. saec. XI, duobus constans uoluminibus; u. uol. Y p. XXXIII sq. et Heiberg, Zeitschr. f. Math. u. Phys. hist.-litter. Abt. XXIX p. 6 sq. Data continet uol. II quatern. Xt]— fi inde a p. 64, 22 dx^£t6()c tf] QÊdEL (mg. leLTtsi tj ccqxv) usque ad p. 172, 20 dadotai ta ^syed-SL. titulus est: svxXsl- dov dsdofisva trjg ©savog sxd6as(og. memorabili transmutatione foliorum factum est, ut pro p. 76, 16 tQLyavov — p. 80, 7 stiI triv AF reperiantur uerba p. 56, 14 ysyQKtpQ^c^ — 20 s6xlv^ demonstratio altera propos. 33, propos. 34 usque ad p. 58, 10 do%-lv kqcc. uol.I definitionum et propositionum solarum quasi con- spectum continet, cuius scripturam significaui littera /3. a = cod. Florentin. Laurentianus XXYIII, 1, membr. saec. XIV. Data continet fol. 325^—336. in fine legitur: telog. EvnlsCdov dsdoêva tijg ©savog ix- dodscog, fol. 1": iste liber est (corr. 'erat') Demetrii Chidoni Greci. codex eandem quam b habet foliorum transmutationem. z = cod. Paris. Gr. 2448, bombyc. saec. XIV, de quo u. Omont, Inventaire II p. 263. Data habet fol. 25—56 inde a propos. 24; titulus est d-sd}Qr](ia xd'". His codicibus a me ipso collatis ita usus sum, ut textum potissimum ad codicis P auctoritatem reuocarem neque ad ceteros confugerem nisi iis locis, ubi illum aliquid uitii contraxisse aut constaret aut ueri simillimum esset. coniecturas siue editorum siue meas raro in ordinem uerborum recepi; qua in re si cui
Page 1: .^ '4*-- . ; ^ ^ "^- :,* ..-:. ii-.
Page 6 and 7: EUCLIDIS C^) LGr E8feH OPERA OMNIA.
Page 8 and 9: litPBIAE: TTPIS B. O. THITBKEBT.
Page 12 and 13: Vm PRAEFATIO. nimis caute uel relig
Page 14 and 15: X PRAEFATIO. c = scliolia cod. Laur
Page 17 and 18: De codicibus fatisque Datorum et eo
Page 19 and 20: PROLEGOMENA. XV 23) cod. Paris. Gr.
Page 21 and 22: PROLEGOMENA. XVII ex P cod. 7 totus
Page 23 and 24: PEOLEGOMENA. XIX insi -p. 8%, 2 Azt
Page 25 and 26: PROLEGOMENA. XXI ijtiL 18 So9Eiacc
Page 27 and 28: PROLEGOMENA. XXIII quo codice usa m
Page 29 and 30: PEOLEGOMENA. XXV an Thuano debeatur
Page 31 and 32: PEOLEGOMENA. XXVH rriv EA Xoyog 21
Page 33 and 34: PROLEGOMENA. XXIX rJB 10 BJ 12 tov'
Page 35 and 36: PKOLEGOMENA. XXXI ubi codd. Pv ab V
Page 37 and 38: 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
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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
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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
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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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Euclidis opera omnia

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