Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
16 KSiNIKSiN d'. ixrbg aTCoXa^Pavo^svag, ovtcog au ivxog ccTtoXa^^avoliBvai dLaLQsd-cj^tv, Scrs rag o^oXoyovg TtQog tw avrcj OriiiEiG) slvai^ rj dia rcov diaiQiceov ayo^svr] svdsta 6v^7t86straL rfj ro^ij xara dvo 6rj^sta, xal at ano rc5v 5 6v^7trc36sc3v STtl to ixrog 6rj^stov ayo^svai icpaipovrat rrjg yQCc^^rjg. s6rco yccQ rav JtQOSiQrjiisvcov yQa^^cjv rig rj AB, xal aito rivog 6r\yisiov rov z/ 8ir\i%Gi6av al AEy AZ rs\ivov6ai rrjv yQa^^rjv rj ^sv Tcara ra ®, E, rj ds 10 xara ra Z, H, xal ov ^sv s%Si Xoyov r] zJE TtQog ®/J, rovtov ixsrco rj EA itQog A&, ov ds r z/Z itQog ^H, rj ZK TtQog KH. Xsyo, ori, ri aito Toi5 A inl ro K iTti^svyvv^svr} 6v^7ts6strai icp' sxdrsQa rfj ro^fj, xal au ccTtb r&v 6v^7trco6saiv iTtl rb z/ i^ti^svyvv^svat 15 ig)dxpovrai rrjg ro^rjg. iTtsl yccQ at EA, Z/1 ixarsQa xara dvo 6rj^sta ts^vsi trjv tofiijv, dvvatov i6tiv aTtb tov z/ did^stQOv dyaystv rrjg ro^rjg' S6rs xal icpaTtro^svag ig>^ sxdrsQa. r\%%co6av icpa7tr6\isvai ai /IB, zlA, xal i7ti^svx^st6a 20 ^ BA, si dvvarov, \irj iQxs6d^c3 dicc rcov A, K, dXl' ijroL did rov srsQOv avrcjv 7] di ovdsrsQov. iQXi^d-o) TtQorsQOv did \i6vov roi} A xal rsinvsro rrjv ZH xara ro M. s6riv ccQa, cog rj Z/i itQog /iH, r\ ZM TtQbg MH' oTtSQ droTtov vTtoxsirat ydQ, cog 25 r\ ZA 7tQbg ^ H, r\ ZK TtQbg KH. idv ds r\ BA \ir\ds dt' srsQOv rov A, K Tto- Qsvr\rai, icp^ sxarsQag rcov AE, /IZ 6v\i^r\6srat rb droTtov. 6. yQcciinfjg] c, corr. ex toiirjg m. 1 V. 12. K] p, KE V. 26. A] p, A V. 27. JE, dZ] p; ^E, EZ V.
CONICORUM LIBER IV. 17 abscisas, ita partes intus abscisae diuiduntur, ita ut partes correspondentes ad idem punctum positae sint, recta per puncta diuisionis ducta cum sectione in duobus punctis concurret, et rectae a punctis concursus ad punctum extrinsecus positum ductae lineam contingent. sit enim AB aliqua linearum, quas diximus, et a puncto aliquo z/ perducantur AE^ /IZ lineam secantes altera in 0, ^, altera autem in Z.jH., sitque AE : ®J = EA\ A®, AZ : AH = ZK : KH. dico, rectam ab ^ ad iiT ductam iu utramque partem ^j^y cum sectione concurrere, et rectas a punctis concursus ad z/ ductas sectionem contingere. quoniam enim E^, Zz/ singulae in binis punctis sectionem secant, fieri potest, ut a z/ diametrus sectionis ducatur. quare etiam contingentes ^^ in utramque partem. ducantur contingentes AB, /iA, et ducta BA, si fieri potest, per A, K ne cadat, sed aut per alterutrum aut per neutrum. prius per A solum cadat rectamque ZH in /1 H = ZM\ MH-, M secet. itaque [III, 37] Z A \ quod absurdum est; nam supposuimus, esse ZA\AH=ZK\KH, sin BA per neutrum punctorum A, K cadit, in utraque ^E, AZ absurdum eueniet. Apollonius, ed. Heiberg. II. 2
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CONICORUM LIBER IV. 17<br />
abscisas, ita partes intus abscisae diuiduntur, ita ut<br />
partes correspondentes ad idem punctum positae sint,<br />
recta<br />
per puncta diuisionis ducta <strong>cum</strong> sectione in duobus<br />
punctis concurret, et rectae a punctis concursus<br />
ad punctum extrinsecus positum ductae lineam contingent.<br />
sit enim AB aliqua linearum, quas diximus, et a<br />
puncto aliquo z/ perducantur AE^ /IZ lineam secantes<br />
altera in 0, ^, altera autem in Z.jH., sitque<br />
AE : ®J = EA\ A®, AZ : AH = ZK :<br />
KH.<br />
dico, rectam ab ^ ad iiT ductam iu utramque partem<br />
^j^y <strong>cum</strong> sectione concurrere,<br />
et rectas a punctis concursus<br />
ad z/ ductas sectionem<br />
contingere.<br />
quoniam enim E^,<br />
Zz/ singulae in binis<br />
punctis sectionem secant,<br />
fieri potest, ut a z/ diametrus<br />
sectionis ducatur.<br />
quare etiam contingentes<br />
^^ in utramque partem. ducantur<br />
contingentes AB, /iA, et ducta BA, si fieri<br />
potest, per A, K ne cadat, sed aut per alterutrum<br />
aut per neutrum.<br />
prius per A solum cadat rectamque ZH in<br />
/1 H = ZM\ MH-,<br />
M secet. itaque [III, 37] Z A \<br />
quod absurdum est;<br />
nam supposuimus, esse<br />
ZA\AH=ZK\KH,<br />
sin BA per neutrum punctorum A, K cadit, in<br />
utraque ^E, AZ absurdum eueniet.<br />
Apollonius, ed. Heiberg. II. 2
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