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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280 COI^IMENTARIA ANTIQUA. iiStLV l6Yi. TCaQccXXrilog ccqk icrlv rj UP^ tij MO, KaC i0tLV, (og ri Z& TCgbg ©K^ ri MS JtQog NS' (og de ri ®K TCgbg &H, ri NS ^Qbg SO' dc' t6ov uQa, ag rj &Z TCQbg 0H, rj MS TCQbg SO' dvccTtaXcv, 6g 5 rj H® jCQbg @Z, rj OS TCQbg SM- 6vv^svtc, 6g rj HZ TCQbg Z0, tovtiatc jCQbg ZE, rj OM jCQbg MS, tovtiatcv rj iJz/ TCQbg z/P. cog ds rj HJ TCQbg ^P, t6 {fjcb HJP TCQbg tb anb z/P, taov 8e tb vnb H^P t^ vTcb AJF' fhg ccQa 7] HZ TCQbg ZE, tb vnb AAT 10 TCQbg xb ccTcb z/P. avaTcaXcv aQa, dtg rj EZ TCQbg ZH^ t6 aTcb z/P TCQog tb vtco A^F, Etg tb vr}\ Kal iTcl tijg AE ysyQacpd^co rj^cKVKXcov tb AEZ, Tcal tfj AA jcaQccXkrj^og TJx^t^ iv avtfp 7] 15 ZH Xoyov TCOLOvda tbv tov cctco ZH iCQog to vTcb AHE tbv trjg FA TCQog trjv diTClaaCav trjg AE] ^CtG) rjfiiKVKXiov tb ABF xal iv avtS evd-std tig rj ABy xal x£C6d^G)6av dvo evd^etac avL(5oc aC A E, EZ, xal iK^B^Xria^o rj EZ inl to H, xal trj JE 20 t6ri KeC0d^G) rj ZH, Kal tetiiri6%^co okrj rj EH 8C%a Katcc tb @, Kal eCXi^cpd^cj tb KsvtQov tov kvkXov tb Ky Koi ccTC avtov Kccd^etog ijcl trjv AB rjx^co Kol dv^paXXetG) trj TCeQccpeQeCcc Kata tb A, Kal dia tov A trj AB TcaQcckkrjXog rjxxtG) rj AM, Kal iK^krj- 1. 71 — 2. ^Gtiv] om. Wp, corr. Halley cum Comm. 3. @H]@N p. ^ 4. 0H] @N p. SO] corr. ex SA W. dvdnccXLv] did ndXtv Wp, corr. Comm. 5. H@] corr. ex 0Z m. 1 W. 0Z] Z in ras. W. OS] O m ras. W. 6. X0VTS6XLV W. OM] 0M Wp, corr. Comm. 11. AJT] jdAF Wp, corr. Comm. 12. vri'] om. Wp. 15. noLovca] 7C01- in ras. W. 16. xov trjg] xov avxbv xat xrjg Halley cum Comm. 19. x6] p, rc5 W. 22. x6] p, xa W. 23. A] e corr. m. 2 W.

EUTOCII COMMENTARIA IN CONICA. 281 itaque UPZl rectae MO parallela^) est [Eucl. YI, 2]. et est Z0:&K^MS:NS', uerum ®K:®H=^NS:SO', ex aequo igitur @Z : == MS - SO^ e contrario ®H H® :®Z= OS: SM'^ componendo HZ :Z@ = OM : MS = HZ:ZE = H/i : JF, uerum 77z/ : z/P = U/1 X z/P : z/P^ et n/ix^P= A^X^r [Eucl. III, 36]. itaque HZ : ZE = Azl ^F: /IP^. ergo e contrario EZ:ZH = ^P^ : AA X AT, Ad prop. LVIII. In AE autem semicirculus describatur y^^Z, et in eo rectae A/1 parallela ducatur ZHy quae jr ifficiat zm : AH xHE^^TA: 2AE I p. 182, 19—22] sit ABF semicirculus et in eo recta aliqua 1) Fort. post MO lin. 1 praeterea addendum: &6xe xal xfi BF. In fig. multae litterae renouatae in W; pro N hab. ^, pro n autem M, pro O 0, pro M N; K et P om.

EUTOCII COMMENTARIA IN CONICA. 281<br />

itaque UPZl rectae MO parallela^) est [Eucl. YI, 2].<br />

et est Z0:&K^MS:NS', uerum ®K:®H=^NS:SO',<br />

ex aequo igitur @Z :<br />

== MS - SO^ e contrario<br />

®H<br />

H® :®Z= OS: SM'^ componendo<br />

HZ :Z@ = OM : MS = HZ:ZE = H/i : JF,<br />

uerum 77z/ : z/P = U/1 X z/P : z/P^ et<br />

n/ix^P= A^X^r [Eucl. III, 36].<br />

itaque HZ : ZE = Azl ^F: /IP^. ergo e contrario<br />

EZ:ZH = ^P^ : AA X AT,<br />

Ad prop. LVIII.<br />

In AE autem semicirculus describatur y^^Z,<br />

et in eo rectae A/1 parallela ducatur ZHy <strong>quae</strong><br />

jr<br />

ifficiat zm : AH xHE^^TA: 2AE I p. 182,<br />

19—22] sit ABF semicirculus et in eo recta aliqua<br />

1) Fort. post MO lin. 1 praeterea addendum: &6xe xal xfi BF.<br />

In fig. multae litterae renouatae in W; pro N hab. ^,<br />

pro n autem M, pro O 0, pro M N; K et P om.

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