Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
214 COMMENTARIA ANTIQUA. Eiq rb T6 5' d^siDQri^a Tixciaeig sxei Te66aQag' ^ yccQ ov 6v^pdlleL 71 ZH tfj AF ij Ovii^dXkei XQii^g ri ixxog xov xvxkov 7} evxbg 7} eTtl xov F arjfieiov. S'. 5 Mexd xb l\ XQtj e7Ci6xri6aL^ oxl xd T xavxa d^eoQrjfiaxa dklri- Xcov e%ovxaL. dkXd xb JtQcoxov e^eL^ oxl aC ev xri enL- (paveCci. evd^etaL vevov6aL eTtl xrjv xoQvq^rjv ev xavxi] fievov0LV, xb de devxeQOv xb dvdTCalLv, xb de xqlxov 10 exeL trjv dta xrjg xoQvcprjg xov kojvov xo^i]v, xb de xexaQxov xrjv itaQdlXrjlov xfj pdoeL, [xb Tte^jtxov xrjv VTtevavxLav, xb exxov co6avel TtQola^^dvexaL xov £/3- do^ov deLXvvov, oxl zal TtQog OQd^dg ocpeLkeL Jtdvxcog elvaL xfj dLafiexQC) xov xvxXov rj xoLvr] xo^rj avxov 15 Tial xov xe^vovxog iitLTtedov, Kal oxi xovxov ovxcog ^%ovxog ai TtaQdXXrjloL avxy dLxoxoiiovvxaL vitb xov XQLycovov, xb de e^dofiov xdg dklag XQetg xofidg ^deL^e xal xrjv dLd^exQOv Kal xdg en avxr\v xaxayo^evag TtaQaXXriXovg xfj ev xfj pd^et evd^eCa. ev de rc5 oydocp 20 deCzvv6LV, oTteQ ev xotg itQoXeyo^evoLg elno^ev, oxl rj itaQa^oXri xal rj viteQ^oXri xcav elg diteLQov ei0LV av^o^ievcov, iv de xS evdxay, oxl t] eXXeLtjjLg avvvevov6a eig eavtrjv bfioCcog xa tivkXco dLa tb tb xe^vov inCTtedov 6v^7tC7txeLv d^cpoxeQaLg xatg TtXevQatg xov 25 XQLyoovov ovx e6xL xvxXog' KvxXovg yaQ ejtoCovv rj xe VTtevavxCa xofir} Tcal rj itaQdXXrjXog' Kal det i7tL6xrJ6aL, otL ri dtd^exQog xrjg xo^rjg iitl ^hv xrjg itaQapoXrjg 2, rE6aaQocg'] corr. ex TsaaaQBg m. 2 W. 4. F] zqitov Wp, corr. Comm. 7. nQmzov] a' p et similiter saepius.
EUTOCII COMMENTARIA IN CONICA. 215 Ad prop. VII. Propositio YII quattuor casus habet; nam ZH cum AF aut non concurrit aut concurrit et hoc quidem tribus modis, aut extra circulum aut intra aut in puncto r. Post prop. X. Animaduertendum, has X propositiones inter se coniunctas esse. prima autem continet, rectas in superficie positas, quae ad uerticem cadant, in ea manere, secunda contrariam; tertia uero sectionem per uerticem coni continet, quarta sectionem basi parallelam, quinta sectionem contrariam; sexta quasi lemma est septimae demonstrans, communem sectionem circuli planique secantis omnino ad diametrum perpendicularem esse oportere, et si hoc ita sit, rectas ei parallelas a triangulo in binas partes aequales secari; septima reliquas tres sectiones monstrauit et diametrum rectasque ad eam ductas rectae in basi positae parallelas. in octaua autem demonstrat, quod nos in prooemio [p. 176, 12 sq.] diximus, parabolam hyperbolamque earum linearum esse, quae in infinitum crescant; in nona autem ellipsim, quamquam in se recurrat sicut circulus, quia planum secans cum utroque latere trianguli concurrat, circulum non esse; circulos enim et sectio contraria et parallela efficiebant; et animad- 9. To (alt.)] supra scr. m. 1 W. 12. 7tQ06Xa(iBccvstcci W, et p, sed corr. m. 1. sBdofiov] s§S6^ov ov W, ^' ov p; corr. Comm. 13. ocpCXsL W. 14. TOfirn corr. ex TcoftTj in scrib. W. 17. sdei^sv W. 23. to to] scripsi, to' Wp. 25. htiv W. 27. (H mg. m. 1 W.
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214 COMMENTARIA ANTIQUA.<br />
Eiq rb<br />
T6 5' d^siDQri^a Tixciaeig sxei Te66aQag' ^ yccQ ov<br />
6v^pdlleL 71 ZH tfj AF ij Ovii^dXkei XQii^g ri ixxog<br />
xov xvxkov 7} evxbg 7} eTtl xov F arjfieiov.<br />
S'.<br />
5 Mexd xb l\<br />
XQtj e7Ci6xri6aL^ oxl xd T xavxa d^eoQrjfiaxa dklri-<br />
Xcov e%ovxaL. dkXd xb JtQcoxov e^eL^ oxl aC ev xri enL-<br />
(paveCci. evd^etaL vevov6aL eTtl xrjv xoQvq^rjv ev xavxi]<br />
fievov0LV, xb de devxeQOv xb dvdTCalLv, xb de xqlxov<br />
10 exeL trjv dta xrjg xoQvcprjg xov kojvov xo^i]v, xb de<br />
xexaQxov xrjv itaQdlXrjlov xfj pdoeL, [xb Tte^jtxov xrjv<br />
VTtevavxLav, xb exxov co6avel TtQola^^dvexaL xov £/3-<br />
do^ov deLXvvov, oxl zal TtQog OQd^dg ocpeLkeL Jtdvxcog<br />
elvaL xfj dLafiexQC) xov xvxXov rj xoLvr] xo^rj avxov<br />
15 Tial xov xe^vovxog iitLTtedov, Kal oxi xovxov ovxcog<br />
^%ovxog ai TtaQdXXrjloL avxy dLxoxoiiovvxaL vitb xov<br />
XQLycovov, xb de e^dofiov xdg dklag XQetg xofidg ^deL^e<br />
xal xrjv dLd^exQOv Kal xdg en avxr\v xaxayo^evag<br />
TtaQaXXriXovg xfj ev xfj pd^et evd^eCa. ev de rc5 oydocp<br />
20 deCzvv6LV, oTteQ ev xotg itQoXeyo^evoLg elno^ev, oxl<br />
rj itaQa^oXri xal rj viteQ^oXri xcav elg diteLQov ei0LV<br />
av^o^ievcov, iv de xS evdxay, oxl t] eXXeLtjjLg avvvevov6a<br />
eig eavtrjv bfioCcog xa tivkXco dLa tb tb xe^vov<br />
inCTtedov 6v^7tC7txeLv d^cpoxeQaLg xatg TtXevQatg xov<br />
25 XQLyoovov ovx e6xL xvxXog' KvxXovg yaQ ejtoCovv rj xe<br />
VTtevavxCa xofir} Tcal rj itaQdXXrjXog' Kal det i7tL6xrJ6aL,<br />
otL ri dtd^exQog xrjg xo^rjg iitl ^hv xrjg itaQapoXrjg<br />
2, rE6aaQocg'] corr. ex TsaaaQBg m. 2 W. 4. F] zqitov<br />
Wp, corr. Comm. 7. nQmzov] a' p et similiter saepius.
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