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Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
294 COMMENTARIA ANTIQUA. ^sd^a dl tavtrjv trjv xata^xsvrjv cog ra avta d£LKvv0av aitXovatEQCog. £iev de Tcal TCtcoCstg s^' tcov yccQ EAZ, aypsiOGiv tb E (Syi^siov ri ^sta^v s6tav tcov 0,B tj stiI tov B 5 i f|(o tov 5, ag yCvovtai tQstg, xal ofioLcog snl Toi) Z aXXai tQstg. Elg to td', "Ev tL0LV avttyQdcpOig rjVQsd^rj allog dstxvv^svov, ott Ttavtbg rot» dod^svtog dtaotrj^atog slg skattov 10 dcptKvovvtat dtd&trj^a. tcov yccQ avtcov vnoKst^svcov sUT^cpd^co tov do^svtog dtaOfij^atog sXattov tb EK, xal 7tS7tot'i]6d'o, cog rj KE JtQog E@, rj ®A TtQog AA, aal dta tov A tfj EZ TtaQdXkriXog ^ MAB. sitsl ovv rj SB ^st^ov i6tl 15 t^g AB, ri SB ccQa TtQbg &Z (ist^ova Xoyov s%st iJTtSQ rj AB JtQbg @Z. ag ds rj SB TtQog @Z, rj @E TtQbg MlSl dtd tb l'0ov slvav tb vitb Z®E ro5 vnb BSM' xal rj @E ccQa TtQbg MS ^st^ova koyov s^st ijTtSQ rj AB TtQbg Z&. dXX' ag ^sv rj AB 7tQb'g Z0, rj 20 AA TtQbg A&, (hg ds rj AA TtQbg A®, rj ®E TtQog EK' ycal rj @E ccQa TtQbg MlSl ^st^ova loyov s%st T^TtSQ rj @E TtQbg EK. sldoCGiv ccQa rj SM trjg KE. HvQsd-riaav ds sv ttOt Tial tavta td d^scjQri^ata 1. Post HataaKSv^v magnam lacunam hab. Wp, fort. propter figuram scholii praecedentis, quam hic hab. W. 3. xat] om. p. Ez/Z] scripsi, EZ rj W, EZH j». 4. EJ scripsi, Wp. 0] scripsi, E Wp. Emendatio litterarum admodum incerta, quia non constat, qaid Eutocius in diuisione secutus sit. 5. ytvsad-ai p. 6. aXXag p. 7. 18'} p, m. rec. W, La' m. 1 W. 8. 8VQ£&i] p. 9. slg] sl p. 11. rilricpQ^(o W. 14. MAB] scripsi, AMB W et, B e corr., p; mxlb Comm. HSL^cov — 15. SB] addidi, om. Wp.
EUTOCII COMMENTARIA IN CONICA. 295 compositionem rationum perficiebatur. elegimus autem hanc constructionem, quia eadem simplicius ostendit. habet autem etiam casus sex; nam ductis rectis E^j z/Z punctum E aut inter 0, B erit positum aut in B aut extra 5, ita ut tres casus oriantur, et similiter in Z aliae tres. Ad prop. XIY. In nonnullis codicibus aliter reperiebatur demonstratum, eas ad distantiam omni data distantia minorem peruenire. nam iisdem suppositis data distantia minor sumatur EK^ fiatque 0A:JA = KE:E@^ et per A rectae ^f EZ parallela MAB. quoniam igitur SB> ABy erit !s;B:0Z> AB:®Z [Eucl. V, 8]. est autem SB:®Z = @E : MS, quia Z@X®E = BSx SM [prop. X]; quare etiam In nonnullis autem codicibus hae quoque propo- @E:MS>AB:Z®. est autem AB : Z® = AA : A® [Eucl. VI, 4] et AA:A® = ®E:EK. itaque etiam ®E:MS>@E:EK. ergo ISIM < KE [Eucl. V, 10]. Fig. in W paullo aliter descripta est ducta inter E Z, MB iis parallela ^iV et ab iV ad MB recta. litt. E, ^, K om. W. 15. ccqk] del. Halley cum Comm. @Z] OZ Wp, corr. Comm. 16. 0Z(alt.)] p, e corr. W. 19. Z0(pr.)] scripsi, ES@ Wp, hf Comm. JB] AB p. 21. xat — 22. EK] om. p. 21. aQu] om. W, corr. Halley. 23. svQid^rjaav p. ticiv W. xai] ccvtiyQcicpois p.
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EUTOCII COMMENTARIA IN CONICA. 295<br />
compositionem rationum perficiebatur.<br />
elegimus autem<br />
hanc constructionem, quia eadem simplicius ostendit.<br />
habet autem etiam casus sex; nam ductis rectis<br />
E^j z/Z punctum E aut inter 0, B erit positum<br />
aut in B aut extra 5, ita ut tres casus oriantur, et<br />
similiter in Z aliae tres.<br />
Ad prop. XIY.<br />
In nonnullis codicibus aliter reperiebatur demonstratum,<br />
eas ad distantiam omni data distantia<br />
minorem peruenire.<br />
nam iisdem suppositis data distantia minor sumatur<br />
EK^ fiatque 0A:JA = KE:E@^ et per A rectae<br />
^f EZ parallela MAB. quoniam<br />
igitur SB> ABy erit<br />
!s;B:0Z> AB:®Z<br />
[Eucl. V, 8]. est autem<br />
SB:®Z = @E : MS,<br />
quia Z@X®E = BSx SM<br />
[prop. X];<br />
quare etiam<br />
In nonnullis autem codicibus hae quoque propo-<br />
@E:MS>AB:Z®.<br />
est autem AB : Z® = AA : A® [Eucl. VI, 4] et<br />
AA:A® = ®E:EK. itaque etiam ®E:MS>@E:EK.<br />
ergo ISIM < KE [Eucl. V, 10].<br />
Fig. in W paullo aliter descripta est ducta inter E Z, MB<br />
iis parallela ^iV et ab iV ad MB recta. litt. E, ^, K om. W.<br />
15. ccqk] del. Halley <strong>cum</strong> Comm. @Z] OZ Wp, corr.<br />
Comm. 16. 0Z(alt.)] p, e corr. W. 19. Z0(pr.)] scripsi,<br />
ES@ Wp, hf Comm. JB] AB p. 21. xat — 22. EK]<br />
om. p. 21. aQu] om. W, corr. Halley. 23. svQid^rjaav p.<br />
ticiv W. xai] ccvtiyQcicpois p.
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