Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
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CONICOKUM LIBER IV. 15 YIL lisdem positis piinctum z/ in angulo positum sit, qui angulo ab asymptotis comprehenso deinceps est positus. dico, sic quoque eadem adcidere. ducatur enim contingens ^0, et ducta 0JB, si fieri potest, per Z ne cadat, sed per H. erit igitur ^E = EH\ quod absurdum est; supposuimus enim, esse ^E = EZ. VIII. lisdem positis punctum z/ in alterutra asymptotarum positum sit, et cetera eadem sint. dico, rectam a puncto contactus ad extremam rectam abscisam ductam ei asymptotae parallelam esse, in qua positum sit punctum z/. sint enim ea, quae diximus, et ponatur EZ = zlE, et a 5 rectae MN parallela ducatur, si fieri potest, BH, itaque JE = EH [III, 34]; quod absurdum est; supposuimus enim, esse /lE = EZ. IX. Si ab eodem puncto duae rectae ducuntur coni sectionem uel arcum circuli singulae in binis punctis secantes, et ut totae se babent ad partes extrinsecus
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CONICOKUM LIBER IV. 15<br />
YIL<br />
lisdem positis piinctum z/ in angulo positum sit,<br />
qui angulo ab asymptotis comprehenso deinceps est<br />
positus. dico, sic quoque eadem adcidere.<br />
ducatur enim contingens ^0, et ducta 0JB, si<br />
fieri potest, per Z ne cadat, sed per H. erit igitur<br />
^E = EH\ quod absurdum est; supposuimus enim,<br />
esse ^E = EZ.<br />
VIII.<br />
lisdem positis punctum z/ in alterutra asymptotarum<br />
positum sit, et cetera eadem sint.<br />
dico, rectam a puncto<br />
contactus ad extremam<br />
rectam abscisam ductam<br />
ei asymptotae parallelam<br />
esse, in qua positum sit<br />
punctum z/.<br />
sint enim ea, <strong>quae</strong><br />
diximus, et ponatur<br />
EZ = zlE,<br />
et a 5 rectae MN parallela<br />
ducatur, si fieri potest, BH, itaque JE = EH<br />
[III, 34]; quod absurdum est; supposuimus enim,<br />
esse /lE = EZ.<br />
IX.<br />
Si ab eodem puncto duae rectae ducuntur coni sectionem<br />
uel ar<strong>cum</strong> circuli singulae in binis punctis<br />
secantes, et ut totae se babent ad partes extrinsecus
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