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Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org

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CONICORUM LIBER IV. 41<br />

concurrat igitur in 0, P, ducanturque 0Aj AP\ eae<br />

igitur contingent. itaque EA utramque sectionem secat.<br />

quoniam m-<br />

ter Bj r nullum<br />

est punctum concursus.<br />

secet in<br />

M, H. itaque<br />

propter<br />

aliud est punctum concursus praeter A, Bj F, A.<br />

i<br />

alteram<br />

sectionem erit<br />

EA : AH<br />

==EN:NH,<br />

propter alteram<br />

autem EA : AM= EN : NM [III, 37]. lioc autem fieri<br />

non potest ; ergo ne illud quidem, quod ab initio posuimus.<br />

sin ABf ^r parallelae sunt, sectiones erunt ellipses<br />

nel altera arcus circuli. secentur AB, F^ in O, H<br />

in binas partes<br />

aequales, ducaturque<br />

no et in<br />

utramque partem<br />

producatur ; <strong>cum</strong><br />

sectionibus igitur<br />

concurret.<br />

concurrat<br />

igitur in<br />

©, P. itaque @P<br />

diametrus<br />

erit<br />

sectionum [11,28],<br />

et ad eam ordinate ductae AB^ Tz/. ducatur igitur<br />

ab E rectis AB, Tz/ parallela ENMH. EMH igitur<br />

rectam @P et utramque lineam secat,<br />

quoniam nullum<br />

prop-

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