XLVI PROLEGOMENA. p. 158, 26 ') prius ts a librario additum esse ueri simillimum est, de altero constat. p. 2, 9 (^); 26, 17 (a) omissionem huius particulae eidem tribuerim; de rs p. 98, 22 omisso p. 21 dictum est. jtat siue additum siue omissum plurimum habet dubitationis. p. 128, 7; 160, 23; 196, 19 (b); p. 16, 7; 18, 18 (a) Theoni deberi uidetur, librariis p. 68, 14; 98, 8; 132, 16; 212, 1 (b); p. 20, 22; 28, 21 (a). p. 68, 17; 146, 25; 170, 16 (b); p. 8, 5; 60, 5; 174, 13 (a) a Theone omissum esse potest; p. 70, 13; 74, 17; 88, 18; 126, 13; 134, 5; 144, 13; 198, 9; 200, 23; 204, 4 (b); p. 14, 1; ]6, 19; 44, 2, 23 (a) librarii peccauerunt. nai nonnullis locis, inprimis iis, ubi initio demonstrationis ante snsi in Theoninis non legitur (p. 132, 19; 200, 9 (b); p. 226, 5 (a), in archetypo codd. PVat.v facile credideris interpolatum esse. p. 168, 4 (b); 176, 2 (a) omitti non potest. restat locus de articulo in Theoninis uel addito uel omisso. ac primum quidem inter nQog et litteras figurae interpositum est t6 p. 10, 12; 12, 4, 5, 6, 21, 23; 18, 18 (bis), 25; 26, 23; 28, 2 (bis)'; 38, 12, 13, 17 (bis), 18 (bis); 40, 15; 42, 19, 20, 21; 44, 4 (a), rriv p. 102, 25; 136, 16; 150, 23 (bis); 182, 16; 214, 6, 21 (b); p. 200, 4 (bis) (a); post eandem praepositionem omis- 8um inuenitur xo p. 90, 11; 134, 6; 148, 20 (b); p. 10, 8; 20, 18; 22, 15; 26, 22; 44, 5 (a) atque, ubi deesse non potest, p. 136, 6, T^r p. 74, 17 (b); 60, 7 (a)*). iam uero Theonem ipsum puto p. 214, 8 (b); 44, 23 (a) articulum Ti]g post &n6 in quadrato significando ab Euclide omissum offendisse; quamquam p. 124, 21; 218, 26 eum non addidit atque p. 170, 17 omisisse uidetur. in rectangulis autem Euclides zwv raro omisit, u. p. 124, 20; 126, 5; 180, 11; a Theone articulus neque additus neque omissus deprehenditur; nam tav p. 212, 9 additum, p. 210, 13 omissum librario tribuere malim, cui sine dubio p. 180, 11 (a) tfjg debetur; eiusdem incuria p. 156, 15 vnb t&v intercidisse adparet. in angulis significandis cum codices sescentis locia miro consensu articulum post vito praebeant 1) Hoc loco in textu distinguendum non erat, erat p. 160, post fiiarjv. 2) Articulus post JiQ6g etiam in ceteris codicibus saepius uel additur uel omittitur, u. p. 12, 4; 18, 25; 20, 21; 44, 6, 7; 182, 16; 214, 6 et p. 76, 2; 92, 4; 116, 11. 1
PROLEGOMENA. XLVII totidemque omittant, Euclidem mihi persuasi sine uUo discrimine et 17 vnb xwv ABF et 17 vnb ABT dixisse. inTheoninis tibv satis plane additur; u. p. 82, 5, 6 (bis), 15; 112, 13, 14; 118, 4; 136, 22; 144, 8; 146, 25; 198, 8, 10; 202, 6; 210, 9, 12, 26; 212, 1, 20, 25, 26; 214, 1, 2, 3 (bis), 15, 16, 18, 19; 216, 1 (b); p. 54, 16, 18; 78, 16; 194, 5, 6 (a). omittitur p. 72, 6; 82, 15; 86, 15; 88, 11; 212, 22 (b); p. 56, 8 (a). quod in Theo- ninis p. 142, 1; 214, 15, 17 (b); p. 176, 4; 182, 2, 3; 230, 3 (a) T^S, p. 114, 18; 130, 2; 156, 6; 172, 16 xrjv additur, non est ponendus in culpa Theon. reliquos locos, ubi articulus siue a Theone siue a librariis temere uel additus uel omissus est*), praetermitto, neque ad me pertinere arbitror, reliqua exempla neglegentiae et temeritatis librariorum congerere. Exemplis, quae adtuli, luculentissime comprobatur, Theonem non solum in omni genere additamentorum paene dixi delectatum esse, uerum etiam breuitatis cuiusdam studio abreptum non pauca omisisse. restant autem aliae omissiones, quarum magna pars Theoni deleganda est. Euclides quidem ea, quae in propositione uniuerse expressit, in expositione ad certas figurae litteras referre solet. Theon interdum in exposi- tione quoque uniuersam ac minus distinctam significationem ita praetulit, ut aliquid omitteret, uelut p. 134, 15 tag itQhg toLs A, J, p. 22, 24 xb AF et lin. 25 t6 BJ, p. 8, 5 fx xibv AB, BF, p. 46, 18 E. nec dissimiles sunt illae omissiones, quas p. 24, 8 et p. 200, 8; 210,10 in Theoninis deprehendimus. praeterea Theon p. 170, 20 fii&g superuacaneum esse iudicauit; eadem de causa p. 46, 15, 23; 48, 1 tij &fasi deleuit, p. 110, 8, 13; 112, 23; 114, 5, 18 xm £i'dsi. speciei ratus notionem in sequenti sldog satis expressam esse. contra p. 90, 2; 104, 21; 110,24; 150,4; 206,10 librariorum culpa manifesta est. idem dici sane licet de p. 98, 17, ubi Kal to3 (ieys&si. in b deest, cum probabilitate quadam etiam de p. 98, 23. sed p. 106, 1, 22 omissionem Theoni imputauerim. idem nescio an p. 154, 5 xsxQccywvov, p. 120, 24; 184, 22 oQd-oymviov, p. 112, 20; 138, 23 7tccQaXXr]X6yQcc(i(iov , p. 112, 1 sldog omiserit, etsi non ignoro, talia a librariis saepius et interpolari et omitti^). p. 18, 18 1) U. p. 134, 10, 14 ; 138, 18 (b) (cfr. p. 130, 15, 20) ; p. 14, 15 16, 5, 7, 8; 22, 8 (a) et p. 142, 10 (b); p. 40, 25; 42, 2, 14; 48, 4 (cfr. p. 48, 16); 50, 1; 60, 20 (a). 2) Cfr. adp. crit. ad p. 116, 3 et ad uol. I p. 150 sqq. ;
- Page 1: .^ '4*-- . ; ^ ^ "^- :,* ..-:. ii-.
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36 AEAOMENA. 'Eav i] tQia fiEysd^r]
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38 AEAOMENA. ^Eccv fi dvo ^sysd-rj
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40 AEAOMENA. xa'. ^Eav fi 8vo y.sya
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42 AEAOMENA. dvo yccQ ^Eyid^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 d^i^ei. lE
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50 AEAOMENA. tris ^AE 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. fjxO^a 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 B^i 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 %^i6Bi dsdo^svrj
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196 APPENDIX. rrjv ZE svd^sta yQa^^
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198 APPENDIX. xal rj rzl' dod^et^a
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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^st^a,
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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 [isysd^og 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. ^idot
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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 yQafi^ov 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 ^oiotfj 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^ :^.'-