Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
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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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. 340 COMMENTARIA ANTIQUA. t6 vjtb HSO' Kccl dL* l'0ov i6tiv, (Dg to ano EA Ttgbg tb anb AA^ tb vTtb &Sn jtQog tb vTtb HSO, "AXXcog, €6tL dl Kal ovtog det^at,' 5 eTtso, iav trig EZ to^rjg aiQ-fi i7ttil)avov6a, 7ia%^ o avn^dlkEt rj AZ dLcifistQog tfj EZ tofifj, yCvstai TtaQakXriXog r] dx%£t6a tfj AT, xal tbv avtbv Xoyov S1BL ri d%%^eL6a Tt^bg trjv dTtote^voiisvrjv VTt avtfjg TtQbg Tc5 E dTtb tfjg E^ ta ov sxsl rj AA itQbg AE, 10 xal td koLTtd b^oiog toig stg tb Ld^\ Eig tb %%'' 'Ejtsl yaQ tari i6t\v r] AS trj ON, td dnb AHN tSv djtb SHO v7tSQS%SL ta 8\g vTtb NSA] s6tG} svd^sta r} AN, xa\ dq^rjQi^Cd-coGav dit avtijg l'6aL 15 aC ASf NO tb 6xwa. cpavsQbv drj ix, trjg b^OLOtrj- ON, otL td A^^ZN, tog xa\ Toi; i'6rjv slvaL trjv AS tfj AT, 0B tstQayova l'6a i6t\v dXXriloLg. iitsi ovv td d%b AHN td AM, MN i6tLv, td ds d%b SHO i6tL 1. NSO p. ioriv] p, V supra scr. m. 1 W. wg] s e corr. m. 1 W. 2. vno] vno to Wp, corr. Halley. 0£7iT] corr. ex O p. HSIO] HS® W et, Jf e corr., p; corr. Comm. 4. ^Gxiv W. ovxto p. 6. fTTEt, fay] bclv ydcQ Halley. 6. AZ] AB ]p. 9. AA] AA Wp, corr. Hailey. 11. M% xo x^'] f^g xo X' p et mg. m. 1 W; corr. Comm. 12. AS] ^fi/ Wp, corr. Comm. 13. AHN] scripsi, AMN Wp, Ig gn Comm. S HO — d£g] SH xdov Wp, corr. Halley cum Comm. {xg go). 15. AS] Als; Wp, corr. Comm, NO] N@, e corr., p. Deinde magnam lacunam hab. Wp; tial ysvEGd-co suppleuit Halley; sed debuit nal naxayEyQocq^&o) uel Kal avfinBnlrjQcoG&cOf et multo plura desunt {et figiira describatur Comm.). oxl ^x U. 16. xijv AISJ] xfiv yf^ p, xTj NASi W. oxC] addidi, om. Wp. 18. AHN] scripsi, J HM Wp; AH, HN m. 2 U. :s;H0] ISJHG Wp; SH, HO Comm. ioxiv W.

: EUTOCII COMMENTARIA IN CONICA. 341 iam eadem de causa etiam et ex aequo est EA^ :AA^ = @Ib;x SH : Aliter. Potest autem etiam sic demonstrari H^El X SO. quoniam, si recta ducitur sectionem EZ contingens in eo puncto, in quo AZ diametrus cum sectione EZ concurrit^ recta ita ducta rectae AT parallela fit [Eutocius ad I, 44], recta ducta etiam ad rectam de jE^ ad jB ab ea abscisam eandem rationem habet, quam AA : AE [supra p. 335 not. 2], et cetera eodem modo, quo ad prop. XIX dictum est [supra p. 334]. Ad prop. XXIX. Nam quoniam est AS = ON^ erit AH' + HN^ = SH' + HO' + 2N;b; X SA I p. 384, 25— 26] sit recta AN^ et ab ea auferantur aequales AS, NO [et perpendiculares ducantur AA^ NBf sitque Ar=AS, AI = HN, lA = AH, ea = a;b:', et expleatur] figura. manifestum igitur quod A^ = ON, esse In fig. litt. B om. W, pro q hab. /ia, pro A' B' autem to^. % scribitur 7^.

:<br />

EUTOCII COMMENTARIA IN CONICA. 341<br />

iam eadem de causa etiam<br />

et ex aequo est EA^ :AA^ = @Ib;x SH :<br />

Aliter.<br />

Potest autem etiam sic<br />

demonstrari<br />

H^El X SO.<br />

quoniam, si recta ducitur sectionem EZ contingens<br />

in eo puncto, in quo AZ diametrus <strong>cum</strong> sectione<br />

EZ concurrit^ recta ita ducta rectae AT parallela<br />

fit [Eutocius ad I, 44], recta ducta etiam ad rectam<br />

de jE^ ad jB ab ea abscisam eandem rationem habet,<br />

quam AA : AE [supra p. 335 not. 2], et cetera eodem<br />

modo, quo ad prop. XIX dictum est [supra p. 334].<br />

Ad prop. XXIX.<br />

Nam quoniam est AS = ON^ erit<br />

AH' + HN^ = SH' + HO' + 2N;b; X SA<br />

I p. 384, 25— 26] sit<br />

recta AN^ et<br />

ab ea<br />

auferantur aequales<br />

AS, NO [et perpendiculares<br />

ducantur<br />

AA^ NBf sitque<br />

Ar=AS,<br />

AI = HN,<br />

lA = AH,<br />

ea = a;b:',<br />

et expleatur] figura.<br />

manifestum<br />

igitur<br />

quod A^ = ON, esse<br />

In fig. litt. B om. W, pro q hab. /ia, pro A' B' autem to^.<br />

% scribitur 7^.

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