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

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CONICORUM LIBER I. 143<br />

strata sunt, EAzi = BM et EZH = BK, erit<br />

HM== AZH^.<br />

auferatur, quod commune est, pentagonum MzlHZN'^<br />

itaque KZN = AMN. est autem KZ rectae AM<br />

parallela. ergo ZN = AN [Eucl. VI, 22 coroll.].<br />

Si<br />

XLVII.<br />

recta hyperbolam uel ellipsim uel ambitum circuli<br />

contingens <strong>cum</strong> diametro concurrit, et per punctum<br />

contactus centrumque recta ad partes sectionis<br />

uersus ducitur, rectas in sectione contingenti parallelas<br />

ductas in binas partes aequales secabit.<br />

sit hyperbola uel ellipsis uel ambitus circuli, cuius<br />

diametrus sit AB. centrum autem F, et sectionem<br />

A<br />

contingens ducatur AE, ducaturque TE et producatur,<br />

et in sectione sumatur punctum aliquod iV, et per N<br />

parallela ducatur SNOH dico, esse NO = OH.<br />

ordinate enim ducantur ^NZ, BA, HMK. itaque<br />

propter ea, <strong>quae</strong> in propositione XLIII demonstrata<br />

sunt, erit ®NZ = ABZ;^, H@K = ABKM. quare<br />

etiam NHKZ = MKZlH^. auferatur, quod commune<br />

COIT. p.<br />

corr. p.<br />

16. GNOHd V; corr. p.<br />

ABSZ V; corr. p.<br />

20. QNZ] BNZ Y;

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