Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
266 COMMENTARIA ANTIQUA. avtl tov B Xcc^Pavoiisvov Orj^sTov rj tavtov h^ti ta A tj tavtbv Tc5 F' tote yccQ avii^aLVSL tb ditb trjs AS tQCycovov 0^0Lov ta F^A tavtbv alvai ta dnots^vo^svc) tQiycovG) vTtb t^v JtaQaXXi^Xcov tatg ^ AF. 5 iav ds ^sta^v Xrjcpd^fj tb B (jtj^lov tav A^ F, Kal ta A, A dvoTSQd) co6l tSv TtSQatov trjg dsvtsQag dia^stQOv, yCvovtav 7Ctc60SLg tQstg' td yaQ Z, E rj dvcotSQCj tcav TtSQcitcov q)SQOvtaL ^ S7i avta rj TiatotSQCJ. sdv ds td A, A STtl td TtsQata co6l tfig 10 dsvtSQag dLa^stQov, td Z, E aatcjtSQCJ svsx^ri6ovtac, b^OLCog ds xal + idv s^cotsQco Xricpd-rj roi; F tb B, [xal] rj 0r STtl tb F ixpXrjd-riastaL, av^paCvsL ds ovtcog yCvsOxt^aL dXXag TttcScsLg tQstg' tov ydQ A 0ri^sCov r} dvotsQco cpsQOfisvov roi' nsQatog trjg dsvtsQag dLa^s- 15 tQOv rj iit avtb ri xatotsQCO xal tb Z b^oCcog (psQolisvov TtOLYiCsL tdg tQstg 7ttco6sLg. idv ds ijtl td etSQa ^SQrj trjg to^rjg Xricpd^fj tb B Crj^stovy rj ^sv F® iK^Xri^Yi0staL ijtl tb ® d^d trjv djtodsL^LV, al ds BZ, BE 7tOLOv0L 7ttc66sLg tQstg, ijtSLdrj tb A i7tl tb 7tSQag 20 (psQStaL trjg dsvtsQag dLa^stQOv r] dvcotsQco ^ xatcotsQoo. i7tl ds trjg iXXsCifjsoog zal trjg tov %vkIov 7tSQLCpsQsCag ovdsv 7tOLKCXov iQov^sv, dXXd o0a iv to 7tQoXa^6vtL d^sooQi^^atL ils%%-ri' 6g slvaL tdg 7ttco6SLg tov ^soQri' ^atog tovtov Qd. 2. J] Bcripsi, z/ Wp. tots yccQ] xai tots Halley cuni Comm.; fort. tots di. 6. A] Z Wp, corr. Comm. (aGiv W. 7. E] E, H Wp, corr. Comm. 8. ij (tert.)] om. Wp, corr. Comm. 9. aGiv W. 11. B] corr. ex W. 12. yicci] deleo. r] Wp, H Halley. ovtoa p. 13. z/] corr. ex A W. 18. 0] H Halley. 19. noiovGiv W. to A] tcc Z, E Halley cum Comm. 21. inl ds] addidi, om. Wp. 23. iXex^r}] scripsi, XEx^f/ Wp. 24. Qd] scripsi, q Wp.
EUTOCn COMMENTARIA IN CONICA. 267 nam punctum, quod pro B sumitur, aut idem est ac A aut idem ac T; ita^) enim sequitur, triangulum in A® descriptum triangulo F^A similem eundem esse ac triangulum a rectis abscisum rectis ^A, AF parallelis. sin punctum B inter Aj F sumitur, et puncta A, A supra terminos alterius diametri posita sunt, tres casus efficiuntur; nam Z, E aut supra terminos cadunt aut in eos aut infra. sin z/, A in terminis alterius diametri posita sunt, Z, E infra cadent. similiter uero . . . .^) si B extra F sumitur, ®r ad r uersus producetur; ita autem adcidit, ut tres alii efficiantur casus; nam puncto z/ aut supra terminum alterius diametri cadente aut in eum aut infra eum etiam Z similiter cadens tres illos casus efficiet. sin ad alteram partem sectionis sumitur punctum Bj F® propter demonstrationem ad ® uersus producetur, BZ, BE autem tres casus efficiunt, quoniam A in terminum alterius diametri cadit aut supra aut infra. in ellipsi uero et ambitu circuli singula non dicemus, sed ea tantum, quae in propositione praecedenti^) dicta sunt. quare casus huius propositionis CIY sunt. 1) H. e. si JB in ^ cadit. quare litteras A, T lin. 2 permutauerunt Comm. Halley. 2) Hic deest casus, ubi z/, A infra terminos cadunt; tum etiam Z, E infra cadunt. omnino omnes XX casus non enumerantur nec probabiliter restitui possunt, quia diuisiones Eutocii parum perspicuae sunt. 3) Immo prop. XLIII, cum ibi in ellipsi XLII casus enumerentur, bic quoque in ellipsi circuloque LXXXIV statuendi 8unt. quare, si numerus XX supra p. 264, 26 in byperbola propositus uerus est, adparet bic lin. 24 q8 scribendum esse.
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266 COMMENTARIA ANTIQUA.<br />
avtl tov B Xcc^Pavoiisvov Orj^sTov rj tavtov h^ti ta<br />
A tj tavtbv Tc5 F' tote yccQ avii^aLVSL tb ditb trjs AS<br />
tQCycovov 0^0Lov ta F^A tavtbv alvai ta dnots^vo^svc)<br />
tQiycovG) vTtb t^v JtaQaXXi^Xcov tatg ^ AF.<br />
5 iav ds ^sta^v Xrjcpd^fj tb B (jtj^lov tav A^ F, Kal<br />
ta A, A dvoTSQd) co6l tSv TtSQatov trjg dsvtsQag<br />
dia^stQOv, yCvovtav 7Ctc60SLg tQstg' td yaQ Z, E<br />
rj dvcotSQCj tcav TtSQcitcov q)SQOvtaL ^ S7i avta rj<br />
TiatotSQCJ. sdv ds td A, A STtl td TtsQata co6l tfig<br />
10 dsvtSQag dLa^stQov, td Z, E aatcjtSQCJ svsx^ri6ovtac,<br />
b^OLCog ds xal + idv s^cotsQco Xricpd-rj roi; F tb B,<br />
[xal] rj 0r STtl tb F ixpXrjd-riastaL, av^paCvsL ds ovtcog<br />
yCvsOxt^aL dXXag TttcScsLg tQstg' tov ydQ A 0ri^sCov r}<br />
dvotsQco cpsQOfisvov roi' nsQatog trjg dsvtsQag dLa^s-<br />
15 tQOv rj iit avtb ri xatotsQCO xal tb Z b^oCcog (psQolisvov<br />
TtOLYiCsL tdg tQstg 7ttco6sLg. idv ds ijtl td etSQa<br />
^SQrj trjg to^rjg Xricpd^fj tb B Crj^stovy rj ^sv F®<br />
iK^Xri^Yi0staL ijtl tb ® d^d trjv djtodsL^LV, al ds BZ,<br />
BE 7tOLOv0L 7ttc66sLg tQstg, ijtSLdrj tb A i7tl tb 7tSQag<br />
20 (psQStaL trjg dsvtsQag dLa^stQOv r] dvcotsQco ^ xatcotsQoo.<br />
i7tl<br />
ds trjg iXXsCifjsoog zal trjg tov %vkIov 7tSQLCpsQsCag<br />
ovdsv 7tOLKCXov iQov^sv, dXXd o0a iv to 7tQoXa^6vtL<br />
d^sooQi^^atL ils%%-ri' 6g slvaL tdg 7ttco6SLg tov ^soQri'<br />
^atog tovtov Qd.<br />
2. J] Bcripsi, z/ Wp. tots yccQ] xai tots Halley cuni<br />
Comm.; fort. tots di. 6. A] Z Wp, corr. Comm. (aGiv W.<br />
7. E] E, H Wp, corr. Comm. 8. ij (tert.)] om. Wp, corr.<br />
Comm. 9. aGiv W. 11. B] corr. ex W. 12. yicci]<br />
deleo. r] Wp, H Halley. ovtoa p. 13. z/] corr. ex<br />
A W. 18. 0] H Halley. 19. noiovGiv W. to A] tcc<br />
Z, E Halley <strong>cum</strong> Comm. 21. inl ds] addidi, om. Wp. 23.<br />
iXex^r}] scripsi, XEx^f/ Wp. 24. Qd] scripsi, q Wp.