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

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CONICOEUM LIBER I. 63<br />

et quoniam est /iE: AB^^ABi^Zj erit etiam<br />

[Eucl. V def. 9J<br />

JE:JZ = JE' :<br />

est<br />

autem<br />

AB^ = Tz/^ : FB^ [Eucl. V, 15].<br />

rz/2 = nrxrA^nrx fb.<br />

quare etiam<br />

Ezf :^Z = nrxTB: FB^ = E®:@A<br />

[E\iclYI,A] = E®x®^:^®X®A = ni:x2JO:Oi:^<br />

[ib.]. et est<br />

E®x®^ = nz X 2J0.<br />

quare [Eucl. V, 9]<br />

^®X®A = OU^ = H®\<br />

ergo H® quadrata aequalis est rectangulo zfA ad z/Z<br />

adplicato, quod deficit figura ZA rectangulo EJx^Z<br />

simili.<br />

iam dico, @H ad alteram partem sectionis productam<br />

a ^E in duas partes aequales secari.<br />

producatur enim et <strong>cum</strong> sectione in O concurrat,<br />

per ^ autem rectae H^ parallela ducatur ^X, per X<br />

autem rectae AN parallela ducatur X^. et quoniam<br />

est H;e!=0X [Eucl. 1, 34], erit etiam HS^ = ^X^uerum<br />

HIb;^ == AlHlxlEiO,<br />

^X^ = AXXXW [prop. XIII].<br />

itaque [EucL VI, 16]<br />

O^: WX=XA:A^.<br />

et OS'-^X=;s;B:BX [Eucl. VI, 4]. quare etiam<br />

X^:^^=^5:5XetsubtrahendoX^:^^ = X,^:X5<br />

[Eucl. V, 17]. itaque A;sI=XB [Eucl. V, 9]. est<br />

t6 a' St . . . xov

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