Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
296 COMMENTARIA ANTIQUA. iyy£yQa(i^8va, aitSQ (hg TtEQitxa aq)TjQ6d"ri v(p' rj^cjv dsdeLy^Evov yaQ tovtov, ort av a^v^Tttcotoi syytov jtQO0dyov6c tfj to^fj xal Ttavtog Tot» dod^evtog stg sXattov dcptxvovvtaL, TtSQtttov iiv tavta ^rjtSLv. diiilst 5 ov8s djtodst^Sig s%ov6C ttvag, dXXd diacpoQag xarayQacpcov. Xva 8s totg ivtvy%dvov6L trjv rj^iQav drjXriv jtOLijao^sVy ixKSLad^c} ivtavd-a td ag TtSQLttd dcprjQri^iva. Et tivig sIglv dovpLTttatOL tfj to^fj stSQaL tcjv TtQOSLQrj^ivcDv , syyLov slGlv at TtQOSLQrj^ivaL tfj tofifj. 10 s6tC3 vitSQ^okri^ rjg dav^TttotOL at FA^ A^. liycj, ort, sl' tLvig slClv dav^Tttcjtot tfj to[ifj, ixsCvcov syytov al(5Lv at FA, A^d. otL ^sv ovv, (hg inl trjg itQcoti^g xatayQacprjg, ov dvvavtat at EZH ddv^TttcotOL sivai, cpavsQov, coCts 15 slvaL TtaQaXXrjkov trjv pbsv EZ tfj FA, trjv dh ZH tfj A^' didsLKtaL yaQ, otL avfiTtsaovvtat tfj to^fj' iv yaQ ta dg)OQL^o^ivG3 toitG) vno tc5v dav^Tttoatcov xal trjg to^rjg sIglv, sl di, 6g iitl trjg dsvtiQag TttmCscog slGLVy dev^- 20 ntcotOL at EZ, ZH naQdkXrjloL ovCaL tatg FA, A^, syyLOv fidXXov sIclv at FA, A^ trjg to^rjg TjitSQ at EZ, ZH. sl di, ag inl trjg tQCtrjg jttcooscogf xal ovtcog at ^sv FA, A^, idv ix^Xrjd^cDCLV sCg djtSLQOv, iyyCt,ov6L 3. yCQOGtxyovGLv W. 6. exov6iv W. 6. ivtvyxccvov- CLv W. rinEQuv'] W, rjfiE seq. lac. p, rniSTsgav yvcofn^v Halley praeeunte Commandino ; sed puto prouerbium esse de opera superflua. 7. ^xxstff-d-co] p, s-asjGd^co W. 10. FA, JJ'\ r^, AA Wp, corr. Comm. 11. oxl st'] in ras. m. 1 W. SLGLV aXXaL Halley cum Comm. 12. FA] FJ Wp, corr. Comm. 13. cog] comp. p, comp. supra scr. m. 1 W. 21. rjnsg] sltcsq p. 24. syyi^ovGL'] scripsi, syyL {l in ras., seq. lac. 1 litt.) aiovGLV W, syyLaL ovgul p.
, omni EUTOCII COMMENTAEIA IN CONICA. 297 sitiones perscriptae reperiebantur, quae ut superfluae a nobis remotae sunt; nam hoc demonstrato, asymptotas ad sectionem propius adcedere et ad distantiam data distantia minorem peruenire, superfluum erat haec quaerere. scilicet ne demonstrationes quidem babent, sed differentias flgurarum. sed ut legentibus lucem claram reddamus, bic coUocentur, quae ut superflua remota sunt. Si quae asymptotae sunt sectionis aliae atque eae, quas diximus supra, hae, quas supra diximus, sectioni propiores sunt. sit hyperbola, cuius asymptotae sint F^, A/l, dico, si quae asymptotae sint sectionis, TA^ AA iis propiores esse. iam ut in prima figura EZ^ ZH asymptotas esse non posse, manifestum, ita scilicet, ut EZ rectae FA parallela sit, ZH autem rectae AA\ nam demonstratum est [prop. XIII], eas cum sectione concurrere; sunt enim in spatio positae, quod asymptotis sectioneque continetur. sin, ut in secundo sunt casu, asymptotae sunt jEZ, ZH rectis TA^ AA parallelae, TA, A/1 sectioni propiores sunt quam EZ, ZH. In fig. 2 r om. W, E in ras. hab.; figuras primas numeris a" §" y" d" notat W.
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296 COMMENTARIA ANTIQUA.<br />
iyy£yQa(i^8va, aitSQ (hg TtEQitxa aq)TjQ6d"ri v(p' rj^cjv<br />
dsdeLy^Evov yaQ tovtov, ort av a^v^Tttcotoi syytov<br />
jtQO0dyov6c tfj to^fj xal Ttavtog Tot» dod^evtog stg<br />
sXattov dcptxvovvtaL, TtSQtttov iiv tavta ^rjtSLv.<br />
diiilst<br />
5 ov8s djtodst^Sig s%ov6C ttvag, dXXd diacpoQag xarayQacpcov.<br />
Xva 8s totg ivtvy%dvov6L trjv rj^iQav drjXriv<br />
jtOLijao^sVy ixKSLad^c} ivtavd-a td ag TtSQLttd dcprjQri^iva.<br />
Et tivig sIglv dovpLTttatOL tfj to^fj stSQaL tcjv<br />
TtQOSLQrj^ivcDv , syyLov slGlv at TtQOSLQrj^ivaL tfj tofifj.<br />
10 s6tC3 vitSQ^okri^ rjg dav^TttotOL at FA^ A^. liycj,<br />
ort, sl' tLvig slClv dav^Tttcjtot tfj to[ifj, ixsCvcov syytov<br />
al(5Lv<br />
at FA, A^d.<br />
otL ^sv ovv, (hg inl trjg itQcoti^g xatayQacprjg, ov<br />
dvvavtat at EZH ddv^TttcotOL sivai, cpavsQov, coCts<br />
15 slvaL TtaQaXXrjkov trjv pbsv EZ tfj FA, trjv dh ZH<br />
tfj A^' didsLKtaL yaQ, otL avfiTtsaovvtat tfj to^fj'<br />
iv yaQ ta dg)OQL^o^ivG3 toitG) vno tc5v dav^Tttoatcov<br />
xal trjg to^rjg sIglv,<br />
sl di, 6g iitl trjg dsvtiQag TttmCscog slGLVy dev^-<br />
20 ntcotOL at EZ, ZH naQdkXrjloL ovCaL tatg FA, A^,<br />
syyLOv fidXXov sIclv at FA, A^ trjg to^rjg TjitSQ at<br />
EZ, ZH.<br />
sl di, ag inl trjg tQCtrjg jttcooscogf xal ovtcog at<br />
^sv FA, A^, idv ix^Xrjd^cDCLV sCg djtSLQOv, iyyCt,ov6L<br />
3. yCQOGtxyovGLv W. 6. exov6iv W. 6. ivtvyxccvov-<br />
CLv W. rinEQuv'] W, rjfiE seq. lac. p, rniSTsgav yvcofn^v<br />
Halley praeeunte Commandino ; sed puto prouerbium esse de<br />
opera superflua. 7. ^xxstff-d-co] p,<br />
s-asjGd^co W. 10. FA, JJ'\<br />
r^, AA Wp, corr. Comm. 11. oxl st'] in ras. m. 1 W.<br />
SLGLV aXXaL Halley <strong>cum</strong> Comm. 12. FA] FJ Wp, corr.<br />
Comm. 13. cog] comp. p, comp. supra scr. m. 1 W. 21.<br />
rjnsg] sltcsq p. 24. syyi^ovGL'] scripsi, syyL {l in ras., seq.<br />
lac. 1 litt.) aiovGLV W, syyLaL ovgul p.