Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
30 KSiNIKSiN 8'. TCQog 6v^7ts6SitaL tfi to^rj, xccl a[ CLTtb tov A ijtl tccg 0v^- trj A M. Tcccl ov ^sv b%bi Xoyov ^ AA Ttgbg z/5, ixhco 7} AKjtQog KB, ov ds exeu loyov rj F^ TtQog z/0, sxsto m rj HS. XsyG), oti tj dicc tcjv K, H 5 TttcoOSLg itpd-tljovtai trjg to^^g. iitsl yccQ tb z/ ivtog i
CONICOEUM LIBER IV. 31 ^ que AJ^^Bj rz/>^@, (\m2i, BN=AM. sit AA:AB==AK: KB, FA :A® = TH: H0. autem dico, rectam per K^ H ductam cum sectione concurrere, rectasque a z/ ad puncta concursus ductas sectionem contingere. quoniam enim A intra angulum ab asymptotis comprehensum positum est, fieri potest, ut a ^ duae rectae contingentes ducantur [II, 49]. ducantur AE, z/Z, et ducatur EZ\ ea igitur per puncta K^ H ueniei^) nam si per unum solum eorum ueniet, altera rectarum in alio puncto secundum eandem rationem secabitur [III, 37];^) quod fieri non potest. sin per neutrum ueniet, in utraque absurdum eueniet. XIX. lam punctum A in angulo sumatur, qui angulo ab asymptotis comprebenso deinceps est positus, rectaeque sectiones seoantes producantur et, ut dictum est, diuidantur. dico, rectam per iJT, H productam cum utraque 1) Quae sequuntur lin. 10—11, et inutilia sunt et propter ydq lin. 11 non ferenda. 2) Cf. supra p. 27 not.
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CONICOEUM LIBER IV. 31<br />
^<br />
que AJ^^Bj rz/>^@, (\m2i, BN=AM. sit<br />
AA:AB==AK: KB, FA :A® = TH: H0.<br />
autem<br />
dico, rectam per K^ H ductam <strong>cum</strong> sectione concurrere,<br />
rectasque a z/ ad puncta concursus ductas sectionem<br />
contingere.<br />
quoniam enim A intra angulum ab asymptotis<br />
comprehensum positum est, fieri potest, ut a ^ duae<br />
rectae contingentes ducantur [II, 49].<br />
ducantur AE, z/Z,<br />
et ducatur EZ\ ea igitur per puncta K^ H ueniei^)<br />
nam si per unum solum eorum ueniet, altera rectarum<br />
in alio puncto secundum eandem rationem secabitur<br />
[III, 37];^) quod fieri non potest. sin per neutrum<br />
ueniet, in utraque absurdum eueniet.<br />
XIX.<br />
lam punctum A in angulo sumatur, qui angulo<br />
ab asymptotis comprebenso deinceps est positus, rectaeque<br />
sectiones seoantes producantur et, ut dictum est,<br />
diuidantur.<br />
dico, rectam per iJT, H productam <strong>cum</strong> utraque<br />
1) Quae sequuntur lin. 10—11, et inutilia sunt et propter<br />
ydq lin. 11 non ferenda.<br />
2) Cf. supra p. 27 not.
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