Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
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CONICORUM LIBER IV. 55 tingentes non concurrent; quare parallelae sunt^ et ideo JiB diametrus est [II, 27]. ergo per centrum cadit; quod erat demonstrandum. XXXV. Coni sectio uel arcus circuli cum coni sectione uel arcu circuli non concurret in pluribus punctis quam in duobus conuexa ad easdem partes non habens. nam si fieri potest, coni sectio uel arcus circuli^^jT cum coni sectione uel arcu circuli ^z/E^r* concurrat in pluribus punctis quam in duobus ^, B^ F conuexa ad easdem partes non habens. et quoniam in linea ABF sumpta ductae AB, sunt tria puncta A^ B, F et BFj hae ad easdem partes, ad quas sunt concaua lineae ABFy angulum comprehendunt. iam eadem de causa AB, BF eundem angulum comprehendunt ad easdem partes, ad quas sunt concaua lineae A/dBEF, itaque lineae, quas diximus, concaua ad easdem partes habent et ideo etiam conuexa; quod fieri non potest. XXXVI. Si coni sectio uel arcus circuli cum altera oppositarum in duobus punctis concurrit, et lineae inter puncta concursus positae ad easdem partes concaua habent, linea per puncta concursus producta cum altera oppositarum non concurret. i m. 1 V. 15. AB^BT Halley cum Memo. 18. aft^] scripsi, dlXa V. 24. t%(oai] p, hxovai V.
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CONICORUM LIBER IV. 55<br />
tingentes non concurrent; quare parallelae sunt^ et<br />
ideo JiB diametrus est [II, 27]. ergo per centrum<br />
cadit; quod erat demonstrandum.<br />
XXXV.<br />
Coni sectio uel arcus circuli <strong>cum</strong> coni sectione<br />
uel arcu circuli non concurret in pluribus punctis<br />
quam in duobus conuexa ad easdem partes non habens.<br />
nam si fieri potest, coni sectio uel arcus circuli^^jT<br />
<strong>cum</strong> coni<br />
sectione uel arcu circuli ^z/E^r* concurrat<br />
in pluribus punctis quam in duobus ^, B^ F<br />
conuexa ad easdem partes non habens.<br />
et quoniam in linea ABF sumpta<br />
ductae AB,<br />
sunt tria puncta A^ B, F et<br />
BFj hae ad easdem partes, ad quas sunt<br />
concaua lineae ABFy angulum comprehendunt.<br />
iam eadem de causa AB, BF<br />
eundem angulum comprehendunt ad easdem<br />
partes, ad quas sunt concaua lineae A/dBEF,<br />
itaque lineae, quas diximus, concaua ad easdem partes<br />
habent et ideo etiam conuexa; quod fieri non potest.<br />
XXXVI.<br />
Si coni sectio uel arcus circuli <strong>cum</strong> altera oppositarum<br />
in duobus punctis concurrit, et lineae inter<br />
puncta concursus positae ad easdem partes concaua<br />
habent, linea per puncta concursus producta <strong>cum</strong> altera<br />
oppositarum non concurret.<br />
i<br />
m. 1 V. 15. AB^BT Halley <strong>cum</strong> Memo. 18. aft^] scripsi,<br />
dlXa V. 24. t%(oai] p, hxovai V.
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