Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
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22 KSiNIKOT d'. aTto xov B TtaQcc rrjv TIO dyo^svrj i]^£c dia tmv K, A. di 8L yag ^rj, rjtOL dia tov ivog avtcov elev^staL ^ ovdstSQOv. 5 sQ%sc^(o Slcc ^ovov tov K. s0tLV aQa, ag rj ZzJ TtQog z/H, rj ZX TtQog XH' ojtSQ atOTtov. ovx, aQa 7] ajto rov B TtaQO, tr^v 110 ayo^svri dLo, ^ovov tov K ilsvCstaL' di a^cpotsQCJV aQa. 10 Tav avtdov ovtcov sav to z/ arjfistov snl ^i&g J tc5v ddv^Tttatov , xal rj ^sv /d E ts^vr] tr]v to^rjv Tcata dvo ^rj^sta, 7] ds ^H ocatd /xovov to H jtaQdXXrjXog ov6a tij stsQa tcov davfiTttcotov, xal ysvrjtaL, 6g 7} JE TtQog z/0, ^ EK TtQog K&, tfi ds JH l'
CONICORUM LIBER IV. 23 contingens ducatur ^B. dico, rectam a B rectae ITO parallelam ductam per K, A cadere. nam si per minus, aut alterutrum eorum cadet aut per neutrum. cadat per K solum. itaque [III, 35] cadet ergo per utrumque cadet. quod absurdum est. ergo recta a B rectae 770 parallela ducta per K solum non XIV. lisdem positis si punctum A in alterutra asymptotarum positum est, et ziE sectionem in duobus punctis secat, z/77" autem alteri asymptotarum parallela in 77 solo, et fit EK:K® = AE: z/@, poniturque in JH producta HA = JH, recta per Kj A puncta ducta et asymptotae parallela erit et cum sectione concurret, rectaque a puncto concursus ad z/ ducta sectionem continget. nam eodem modo, quo in praecedenti, ducta ZlB contingenti dico, rectam a jB asymptotae 770 parallelam ductam per puncta K, A cadere. si igitur per K solum cadit, non erit AH =^ HA [III, 34]-, quod absurdum est. sin per A solum cadit, non erit EA : K® [III, 35]. sin neque z/0 = EK : per K neque per A cadit, ergo per utrumque cadet! utrobique absurdum eueniet.
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CONICORUM LIBER IV. 23<br />
contingens ducatur ^B. dico, rectam a B rectae ITO<br />
parallelam ductam per K, A cadere.<br />
nam si<br />
per<br />
minus, aut<br />
alterutrum eorum<br />
cadet aut per neutrum.<br />
cadat per K solum.<br />
itaque [III, 35]<br />
cadet<br />
ergo per utrumque cadet.<br />
quod absurdum est.<br />
ergo recta a B rectae<br />
770 parallela ducta<br />
per K solum non<br />
XIV.<br />
lisdem positis si punctum A in alterutra asymptotarum<br />
positum est, et ziE sectionem in duobus<br />
punctis secat, z/77" autem alteri asymptotarum parallela<br />
in 77 solo, et fit EK:K® = AE: z/@, poniturque<br />
in JH producta HA = JH, recta per Kj A<br />
puncta ducta et asymptotae parallela erit et <strong>cum</strong> sectione<br />
concurret, rectaque a puncto concursus ad z/<br />
ducta sectionem continget.<br />
nam eodem modo, quo in praecedenti, ducta ZlB<br />
contingenti dico, rectam a jB asymptotae 770 parallelam<br />
ductam per puncta K, A cadere.<br />
si igitur per K solum cadit, non erit AH =^ HA<br />
[III, 34]-, quod absurdum est. sin per A solum cadit,<br />
non erit EA : K® [III, 35]. sin neque<br />
z/0 = EK :<br />
per K neque per A cadit,<br />
ergo per utrumque cadet!<br />
utrobique absurdum eueniet.
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