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

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CONICORUM LIBER I. 93<br />

etiam BZxZA-. ZA'' = AH X HB :<br />

et permutando<br />

[Eucl. V, 16]<br />

est<br />

autem<br />

BZxZA: AHxHB = z/Z^ :<br />

z/Z^ : H£;2 = Zr^ : EH^<br />

HE\<br />

HE\<br />

[Eucl. VI, 4].<br />

permutando igitur<br />

BZxZA:Zr^^AHxHB: FH^ [Eucl. V, 16].<br />

quare etiam, in ellipsi componendo [Eucl. V, 18], in<br />

oppositis autem e contrario [Eucl. V, 7 coroll.] et conuertendo<br />

[Eucl. Y, 19 coroll.],<br />

Ar^^rz^^^BE^^rw<br />

[Eucl. II, 5]; et permutando. est autem FB^ = AF^.<br />

quare etiam EH^ = ZFl itaque ZF == EH et<br />

^Zj HE parallelae sunt. ergo etiam z/F = FE<br />

[Eucl. VI, 4].<br />

XXXI.<br />

Si in hyperbola in latere transuerso figurae punctum<br />

sumitur ad uerticem sectionis rectam abscindens non<br />

minorem dimidio latere transuerso figurae, et ab eo<br />

recta ad sectionem adcidit,<br />

haec producta intra sectionem<br />

cadet ad partes eius<br />

sequentes.<br />

sit hyperbola, cuius diametrus<br />

sit AB, et in ea<br />

punctum aliquod F sumatur<br />

abscindens FB non minorem dimidia AB^ et ad<br />

sectionem adcidat recta jTz/. dico, FJ productam<br />

intra sectionem cadere.

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