Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
80 KSiNIK^N S\ Qov TtaQccXXriXoL ccl AK^ ^E' oial tst^i^O&ci) 7] ^E 8i%a xata to A^ aal iTte^svx^ca rj AA. s6tai drj dia- ^stQog 71 AA t^v dvo ev^vycov Tcal ts^vst tccg to^ag ^sta^v tcov A, E xata ta M, N [S^ts rj AAE dCxa 5 tstfirjtat xata to A]. t^x^c^ ccito tov ® Ttaga tr^v AE rj @ZH' s6tai dr} iv ^sv tfj stsQa to^ij l'6rj rj ®S rfj SZ, iv ds tfj stsQa i'6rj rj 0S tfj SH. coCts xal 7] SZ tfj SH iattv l'ar]' oTtsQ ddvvatov. ^r} s0tG)6av §7] at AK^ AE jtaQaHrjloL, dXXa 10 Ov^TtiTttstcaGav xata to K, xal ta XoLitd td avzd ysyovsta^ xal ixpXrjd^staa rj AK av^TttTttsto tfj ZS zatd tb P. 15 o^OLog drj dsC- ^OftfV tOig TtQOtSQ0Vf0tti6tCvy t \ t \ cog to vTto AKE TtQog to 20 aTto AKy iv filv tfj ZAE to^fj to VTtb ZP® TtQbg tb djtb PA, iv dh 25 tfj HAE tb vTtb HP® itQbg tb ditb PA. tb aQa vno HP® i'6ov tcp vTtb ZP@' OTtSQ ddvvatov. ovx ccQa rj EAZ trj EAH xatd TtXsCova arj^sta av^fidk^st rj dvo. 4. mats] insC Halley praeeunte Commandino; ego matB — A lin. 5 deleuerim. 6. ©ZH] p, ©IfZ V. 7. iv — zri ^H] p, om. V. 21. Z^E] ^//E V, Zz/E0 p; corr. Memus. 25. dno\ p, om. V. 27. Ez/Z] p, z/EZ V. E^H] p, JER V.
CONICORUM LIBER IV. 81 posita E/IZ. dico, EAZ cum EzlH in pluribus punctis non concurrere quam in duobus. nam si fieri potest, in tribus concurrat z/, E, ®y ducaturque sectiones ABj AF contingens AK^ et ducta AE producatur^), prius autem sint et parallelae AK, AE', AE in A in duas partes aequales secetur, ducaturque AA» AA igitur diametrus erit sectionum coniugatarum [II, 34] sectionesque inter A, E m M^ N secat. a ® rectae AE parallela ducatur @ZH\ itaque erit [I def. 4] in altera sectione @S= lElZ, in altera autem &^-==SH quare etiam fiZ = SH-^ quod fieri non potest. AKj AE igitur parallelae ne sint, sed in K concurrant, et reliqua eadem comparentur, productaque AK cum Z@ in P concurrat. eodem igitur modo, quo antea, demonstrabimus, esse [III, 19; Eucl. V, 16] in sectione ZAE A KxKEiAK^ = ZPxP®: PA^, in HAE autem AKxKE: AK^ ==HPxP&: PA\ itaque HPxP® = ZPxP® [Eucl. V, 9]; quod fieri non potest. ergo EAZ cum EAH in pluribus punctis non concurrit quam in duobus. 1) Hoc addidit propter secundam figuram. ApolloniuB ed. Heiberg. II.
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80 KSiNIK^N S\<br />
Qov TtaQccXXriXoL ccl AK^ ^E' oial tst^i^O&ci) 7] ^E<br />
8i%a xata to A^ aal iTte^svx^ca rj AA. s6tai drj dia-<br />
^stQog 71 AA t^v dvo ev^vycov Tcal ts^vst tccg to^ag<br />
^sta^v tcov A, E xata ta M, N [S^ts rj AAE dCxa<br />
5 tstfirjtat xata to A]. t^x^c^ ccito tov ® Ttaga tr^v<br />
AE rj @ZH' s6tai dr} iv ^sv tfj stsQa to^ij l'6rj rj<br />
®S rfj SZ, iv ds tfj stsQa i'6rj rj 0S tfj SH. coCts<br />
xal 7] SZ tfj SH iattv l'ar]' oTtsQ ddvvatov.<br />
^r} s0tG)6av §7] at AK^ AE jtaQaHrjloL, dXXa<br />
10 Ov^TtiTttstcaGav xata to K, xal ta XoLitd td avzd ysyovsta^<br />
xal ixpXrjd^staa<br />
rj AK<br />
av^TttTttsto tfj<br />
ZS zatd tb P.<br />
15 o^OLog drj dsC-<br />
^OftfV tOig TtQOtSQ0Vf0tti6tCvy<br />
t \ t \<br />
cog to vTto<br />
AKE TtQog to<br />
20 aTto AKy iv<br />
filv tfj ZAE<br />
to^fj to VTtb<br />
ZP® TtQbg tb<br />
djtb PA, iv dh<br />
25 tfj HAE tb vTtb HP® itQbg tb ditb PA. tb aQa vno<br />
HP® i'6ov tcp vTtb ZP@' OTtSQ ddvvatov. ovx ccQa rj<br />
EAZ trj EAH xatd TtXsCova arj^sta av^fidk^st rj dvo.<br />
4. mats] insC Halley praeeunte Commandino; ego matB<br />
— A lin. 5 deleuerim. 6. ©ZH] p, ©IfZ V. 7. iv —<br />
zri ^H] p, om. V. 21. Z^E] ^//E V, Zz/E0 p; corr.<br />
Memus. 25. dno\ p, om. V. 27. Ez/Z] p, z/EZ V.<br />
E^H] p, JER V.
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