Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
298 COMMENTAEIA ANTIQUA. trjg to^^g xal etg ekattov dLd^trnia navtbg tov dod-evtog atpixvovvtat, avtov ivtbg ovta tijg ai 81 EZH xata ^sv tb Z xal ta iyyvg ycoviag Cvveyyvg el6i tr^g roftijg, ix^Xrid^etaaL de a(pi6tavtaL trig to^rig ^aXXoV Ttavtbg 5 yccQ tov dod^evtog, o vvv a(pe6ti]xa0Lv, e6tLV eXa06ov. e6to6av drj TtdlLV, hg ijcl t^g tetccQtTjg xataygacprjg, d^v^TttcotoL ai EZ, ZH' (paveQov drj xal ovtcog, otL 7] ^ev FA eyyLov iatL trjg to^rjg r]7teQ rj EZ, idv te rj EZ tfj FA TtaQaXXrjkog iotLV, idv te Gv^TtLTtty trj FA. 10 xal idv ^ev rj av^7tto6Lg dvcjteQOV i] trjg dLa rov Z icpaTttoiievrjg trjg to^rjg, te^vet trjv rofn^v, idv de rj 6v^7ttco0Lg iv ta ^eta^v toTtip fi trjg te icpaTtto^evrig xal trjg ycovLag, co(S7teQ xal r] ZH, xatd td avtd ta iitdvco rj @H trjg to^^^g ovx d(pe^eL fAa((o^' dLd6trj^a 15 Ttavxbg tov dod^evtog' S(jte r] FA eyyLov iCtL trjg toiirjg, rjTteQ rj EZ ictLV. rj de ^A eyyLOV trjg to^^g rJTteQ rj ZH d^d td avtd totg iitl tfjg tQLtrjg xatayQacpfjg. rectis otL de 7] dvcoteQco trjg dta tov Z icpaTtto^evrjg In fig. 1 J et H om. W; additae sunt duae rectae EZ, ZH parallelae. In fig. 2 E om. W, pro H hab. 71. 2. di] yccQ Wp, corr. Halley cum Comm. ra syyvg avzov] scripsi, t6 eyyvg avxcov Wp. 3. bIglv W. 6. U.a6-
EUTOCII COMMENTARIA IN CONICA. 299 sin, ut in tertio casu, sic quoque FAj A/1, si productae erunt in infinitum, sectioni adpropinquant et ad distantiam omni data minorem perueniunt, EZy ZH autem ad Z partesque ei propinquas intra angulum positas sectioni propinquae sunt, productae uero magis a sectione distant; nam quam nunc^) habent distantiam, ea omni data est minor. iam rursus, ut in quarta figura, asymptotae sint EZ, ZH. itaque sic quoque manifestum est, FA sectioni propiorem esse quam EZj siue EZ rectae FA parallela est siue cum FA concurrit. et si punctum concursus supra rectam per Z sectionem contingentem ^) positum est, sectionem secat, sin punctum concursus in spatio inter contingentem angulumque positum est, sicut etiam ZHj eodem modo, quo supra, @H^) a sectione non distabit interuallo, quod omni dato minus est. ergo FA sectioni propior erit quam EZ. AA autem sectioni propior est quam ZH eadem de causa, qua in tertia figura. rectam autem, quae supra rectam per Z contin- 1) Sc. TA, AA. 2) Sc. ad d uersus ductam. 3) Haec non satis intellego. Gov\ Halley, ^'XaaGcov Wp. 6. cog] om. Wp, mg. m. 2 U. 7. ZH] HZ p. 8. kyyiov] corr. ex syysLov W. sGtiv W. 17] p, om. W. 9. FA (pr.)] corr. ex FJ m. 1 W. saziv] Wp, 17 Halley. GV(i7tLntsi2 10. GviintcoGLg'] comp. p, GVfi- TttoaGsig W. dvmtSQOv] yicctcotSQov Halley cum Comm. rryg] comp. p, tig W. 11. scpDinto(isvr}g'\ comp. p, scpanto^isvr} W. 14. @H] ZE Halley. 15. SGttv W. 16. sGtiv] om. Halley. ds] om. Wp, corr. Halley.
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298 COMMENTAEIA ANTIQUA.<br />
trjg to^^g xal etg ekattov dLd^trnia navtbg tov dod-evtog<br />
atpixvovvtat,<br />
avtov ivtbg ovta tijg<br />
ai 81 EZH xata ^sv tb Z xal ta iyyvg<br />
ycoviag Cvveyyvg el6i tr^g roftijg,<br />
ix^Xrid^etaaL de a(pi6tavtaL trig to^rig ^aXXoV Ttavtbg<br />
5 yccQ tov dod^evtog, o vvv a(pe6ti]xa0Lv, e6tLV eXa06ov.<br />
e6to6av drj TtdlLV,<br />
hg ijcl t^g tetccQtTjg xataygacprjg,<br />
d^v^TttcotoL ai EZ, ZH' (paveQov drj xal ovtcog, otL<br />
7] ^ev FA eyyLov iatL trjg to^rjg r]7teQ rj EZ, idv te<br />
rj<br />
EZ tfj FA TtaQaXXrjkog iotLV, idv te Gv^TtLTtty trj FA.<br />
10 xal idv ^ev rj av^7tto6Lg dvcjteQOV i] trjg dLa rov Z<br />
icpaTttoiievrjg trjg to^rjg, te^vet trjv rofn^v, idv de rj<br />
6v^7ttco0Lg iv ta ^eta^v toTtip fi trjg te icpaTtto^evrig<br />
xal trjg ycovLag, co(S7teQ xal r] ZH, xatd td avtd ta<br />
iitdvco rj @H trjg to^^^g ovx d(pe^eL fAa((o^' dLd6trj^a<br />
15 Ttavxbg tov dod^evtog' S(jte r] FA eyyLov iCtL trjg<br />
toiirjg, rjTteQ rj EZ ictLV. rj de ^A eyyLOV trjg to^^g<br />
rJTteQ rj ZH d^d td avtd totg iitl tfjg tQLtrjg xatayQacpfjg.<br />
rectis<br />
otL de 7] dvcoteQco trjg dta tov Z icpaTtto^evrjg<br />
In fig. 1 J et H om. W; additae sunt duae rectae<br />
EZ, ZH parallelae.<br />
In fig. 2 E om. W, pro H hab. 71.<br />
2. di] yccQ Wp, corr. Halley <strong>cum</strong> Comm. ra syyvg<br />
avzov] scripsi, t6 eyyvg avxcov Wp. 3. bIglv W. 6. U.a6-
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