Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
. 216 COMMENTARIA ANTIQUA. triv yiCav itXevQav rot> XQiymvov tifivsL xal xriv ^a6Lv, ijtl ds trjg VTiSQPoXrjg ri]V rs JtXsvQav xal trjv i% sv^eCag trj XoLTtfj TtlsvQa ixPaXXo^svrjv TtQog tfj xo- QV(pf], iitl 81 trig iXXsCtl;s(og xal sxatSQav tcav itksv- 5 Q^v xal trjv pd6LV. ro ds dszatov aitlovatSQOv ^sv ttg iTtL^dklcjv lccag av oCrjd^sCrj tavtov slvaL tS dsvtSQG), tovto ^svtOL ovx «g s^SL' ixsL (isv yccQ inl Ttdarjg tijg STtKpavsCag slsys ka^^dvsC^aL td dvo Crj^sta, ivtav^a ds inl trjg ysvo^svrjg yQa^^^g. iv 10 ds totg s^rjg tQLolv dxQL^sCtSQOv sxdatrjv tcov rofitoi/ rot^TCOv dtaxQCvsL (istd tov XsysLV xal td CdLco^ata avtcov zd aQXLxd. Elg tb La' UsTtOL^Gd^a}, d)g ro «jro BF TtQog ro vTto 15 BAF, ovtog rj @Z JtQog Z,A' aacpsg ^sv iatt to Xsyo^svov, Ttkrjv st ttg xal vTtofivrjed^fjvaL ^ovkstaL, s6to t(p VTtb BAF l6ov ro v^jto OflP, rc5 ds aTtb BF L0OV TtaQa trjv IJP jtaQapXrjd^sv nkdtog noLsCto) trjv nU, xal ysyovstc3, (hg rj OII TtQbg IIU, rj AZ 20 TtQog Z@' ysyovsv ccQa ro ^rjtov^svov. iitsl ydQ iettv, d)g rj On itQog IIZ, r\ AZ itQbg Z@, dvditaXLv 6g rj Zn jtQbg nO, ry ®Z TtQog ZA. (hg ds rj ZH jtQog nO, tb XIP TtQog PO, tovts6tL tb ditb BF TtQbg tb imb BAF. tovto xQrjOL^svsL xal totg i^rig 25 dvo d^soQi^^aaLv. 4. 8i] Bupra scr. p. 7. snC] n e corr. m. 1 p. 8. «Aayf Xani-] pW^ (^'Isysv W^). 10. totg fl^Js tgi-] pW^ 14. nsnoLrjad-co] p, t^ in ras. m. 2 W. 15. satLv W. 17. rc5 (pr.)] corr. ex t6 W^ 18. /IP] /I e corr. m. 1 W. 19. 112 (pr.)] Z m ras. m. rec. W. Oil] O corr. ex W. 21. On] O corr. ex @ W. 22. ZU] 2 e corr. W. nO]
EUTOCII COMMENTARIA IN CONICA. 217 uertendum est, diametrum sectionis in parabola alterum latus trianguli basimque secare, in hyperbola autem et latus et rectam in altero latere ad uerticem uersus producto positam, in ellipsi autem et utramque latus et basim. decimam uero, qui obiter intuitus erit, fortasse eandem ac secundam esse putauerit; sed minime ita est; illic enim duo puncta in tota superficie sumi posse dicebat, hic uero in linea orta. in tribus autem deinde sequentibus propositionibus unamquamque harum sectionum diligentius distiuguit proprietates simul principales earum indicans. Ad prop. XI. Fiat Br^:BAxAr=®Z:ZA [I p. 38, 24—25]: manifestum quidem, quod dicitur, nisi si quis admoneri O TL Z ^elit. sit onxnp = BAxAr, et spatium quadrato BF'^ aequale ad IIP adplicatum latitudinem efficiat 7727, fiatque 077 : nZ = AZ : Z@; ® Z A itaque effectum est, quod quaeritur. nam quoniam est OTL: IIZ == AZ : Z&^ e contrario erit [Eucl. V, 7 coroll.] est autem Zn:nO==®Z:ZA. Zn:nO = ZP: PO [Eucl. YI, 1] = BF^ : BA X AR hoc etiam in duabus, quae sequuntur, propositionibus [I p. 44,11; 50,6] utile est. O e corr. W. Un] Z e corr. W. 23. PO'] O e corr. W. tovzEGxiv W. £r] JB e corr. p.
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216 COMMENTARIA ANTIQUA.<br />
triv yiCav itXevQav rot> XQiymvov tifivsL xal xriv ^a6Lv,<br />
ijtl ds trjg VTiSQPoXrjg ri]V rs JtXsvQav xal trjv i%<br />
sv^eCag trj XoLTtfj TtlsvQa ixPaXXo^svrjv TtQog tfj xo-<br />
QV(pf], iitl 81 trig iXXsCtl;s(og xal sxatSQav tcav itksv-<br />
5 Q^v xal trjv pd6LV. ro ds dszatov aitlovatSQOv ^sv<br />
ttg iTtL^dklcjv lccag av oCrjd^sCrj tavtov slvaL tS dsvtSQG),<br />
tovto ^svtOL ovx «g s^SL' ixsL (isv yccQ inl<br />
Ttdarjg tijg STtKpavsCag slsys ka^^dvsC^aL td dvo<br />
Crj^sta, ivtav^a ds inl trjg ysvo^svrjg yQa^^^g. iv<br />
10 ds totg s^rjg tQLolv dxQL^sCtSQOv sxdatrjv tcov rofitoi/<br />
rot^TCOv dtaxQCvsL (istd tov XsysLV xal td CdLco^ata<br />
avtcov zd aQXLxd.<br />
Elg tb<br />
La'<br />
UsTtOL^Gd^a}, d)g ro «jro BF TtQog ro vTto<br />
15 BAF, ovtog rj @Z JtQog Z,A' aacpsg ^sv iatt to<br />
Xsyo^svov, Ttkrjv st ttg xal vTtofivrjed^fjvaL ^ovkstaL,<br />
s6to t(p VTtb BAF l6ov ro v^jto OflP, rc5 ds aTtb<br />
BF L0OV TtaQa trjv IJP jtaQapXrjd^sv nkdtog noLsCto)<br />
trjv nU, xal ysyovstc3, (hg rj OII TtQbg IIU, rj AZ<br />
20 TtQog Z@' ysyovsv ccQa ro ^rjtov^svov. iitsl ydQ iettv,<br />
d)g rj On itQog IIZ, r\ AZ itQbg Z@, dvditaXLv 6g<br />
rj Zn jtQbg nO, ry ®Z TtQog ZA. (hg ds rj ZH<br />
jtQog nO, tb XIP TtQog PO, tovts6tL tb ditb BF<br />
TtQbg tb imb BAF. tovto xQrjOL^svsL xal totg i^rig<br />
25 dvo d^soQi^^aaLv.<br />
4. 8i] Bupra scr. p. 7. snC] n e corr. m. 1 p. 8.<br />
«Aayf Xani-] pW^ (^'Isysv W^). 10. totg fl^Js tgi-] pW^<br />
14. nsnoLrjad-co] p, t^ in ras. m. 2 W. 15. satLv W. 17.<br />
rc5 (pr.)] corr. ex t6 W^ 18. /IP] /I e corr. m. 1 W. 19.<br />
112 (pr.)] Z m ras. m. rec. W. Oil] O corr. ex W.<br />
21. On] O corr. ex @ W. 22. ZU] 2 e corr. W. nO]
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