Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
230 COMMENTARIA ANTIQUA. TtQog OQd^ccg ayo^Bvrj aic azQag trjg dia^ixQOV eKrog XB TtiTttBi xal iq)anxBtaL tov kvkIov^ 6 61 ^ATtoXXcoviog iv tovta xad^oXtKov tt dBiKvvGi dvvd^Bvov icpaQ^o- 6ai tatg tQiGl roi) kcovov xal ta kvkIco, 5 to6ovtov diacpBQBi 6 KvxXog tcov tov kcdvov to- ^icjv, oti iit ixBLVOV ^ev at tstay^ivcog zatrjy^ivac JtQog oQd^ag ayovtai tfj dca^itQC)' ovds yccQ aXlai Bvd^Btat TtaQccklriXoi iavtatg vito trig dca^iitQOV tov KvxXov dL%oto^ovvtaL' inl dl tcov tQLcov to^cjv ov 10 Ttdvtcog TtQog OQd^ag dyovzaL, sC ^rj ijtl ^ovovg tovg d^ovag. Elg t6 li]\ "Ev tL6LV dvtLyQacpOLg ro %^BcciQ7i^a tovto iitl ^ovrjg TtaQa^oXfjg Kal vjtSQPoXrjg icttv, KdlXLOv ds xaxtolL- 15 K(6tBQ0v s^SLv triv TtQota^LV, sl ^Tj otL to inl tijg ilXsLipBcog iKSLvoLg Sg dvaiicpC^okov JtaQaXiXsLTttaL' r] yaQ Fz/ ivtog ov6a trjg to^rjg 7ts7tBQa0^ivrjg ov0r]g Kal avtri Kat d^cpotsQa ti^vsL trjv to^rjv. dsL ds i7tLatrJ6aL, oxl, xdv rj AZB ti^vrj tr]v to- 20 ^r^Vj ri avtrj dTtodsL^Lg dQ^o^SL. Elg to K. ^Aito tovtov tov d-sc3Q7]^atog aQXO^svog iq)s^^g iv 7ta6L td av^Tttco^axa xrjg 7taQapolrjg avxfj 8slkvv6lv VTtdQiovta Kal ovk dXXrj xlvl, (og izl xb TtoXv ds xfj 25 v7tSQ^okfi Kal xy iXXsLipsc xal xa kvkIc) xd avxd Sblk- VV0LV v7tdQ%ovxa. i^tscdri ds ovk dxQrj(3Xov (paCvsxaL xotg xd ^rjxcc- 3. Ssi-hvvgl] scripsi praeeunte Comm., SsLv.vvg Wp. 4. raLs'] fort. raig zs. xQiaiv W. kcovov'] v,(qvov xo^atq Halley
EUTOCII COMMENTARIA IN CONICA. 231 diametrum in termino perpendicularis erigatur, extra circulum cadere eumque contingere, Apollonius uero liic propositionem uniuersalem demonstrat, quae simul de tribus coni sectionibus et de circulo ualet. hoc tantum circulus a sectionibus coni differt, quod in eo rectae ordinate ductae ad diametrum perpendiculares ducuntur*, neque enim aliae rectae inter se parallelae a diametro circuli in binas partes aequales secantur; in tribus uero sectionibus non semper perpendiculares ducuntur, sed ad axes solos. Ad prop. XVIII. In nonnullis codicibus haec propositio in sola parabola byperbolaque demonstratur, sed melius est, propositionem uniuersaliorem esse, nisi quod illi de ellipsi, quod ibi res dubia non sit, mentionem non fecerunt. nam T^, quae intra sectionem terminatam posita est, per se sectionem ab utraque parte secat. animaduertendum autem, eandem demonstrationem quadrare, etiam si AZB sectionem secet. Ad prop. XX. Ab hac propositione incipiens deinceps in omnibus proprietates parabolae ei soli adcidere demonstrat nec ulli alii, plerumque uero hyperbolae, ellipsi, circulo eadem adcidere demonstrat. quoniam autem iis, qui mechanica scribunt, propter praeeunte Comin. 6. (h mg. m. 1 W. 13. rovro] supra scr. m. 1 p. 14. iari, p. 15. (ii^] scripsi, kccl Wp. to] om. p in extr. liu. 16. avaiicpi^olov] scripsi, diicpi^oXov Wp, ovy, oc^cpL^oXov Halley cum Comm. 18. avrri] av- e corr. in scrib. p. 19. r£iivrf\ e corr. p, rs(ivsL W. 23. naoiv W. ayr^] p, «vrTy W.
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230 COMMENTARIA ANTIQUA.<br />
TtQog OQd^ccg ayo^Bvrj aic azQag trjg dia^ixQOV eKrog<br />
XB TtiTttBi xal iq)anxBtaL tov kvkIov^ 6 61 ^ATtoXXcoviog<br />
iv tovta xad^oXtKov tt dBiKvvGi dvvd^Bvov icpaQ^o-<br />
6ai tatg tQiGl roi) kcovov xal ta kvkIco,<br />
5 to6ovtov diacpBQBi 6 KvxXog tcov tov kcdvov to-<br />
^icjv, oti iit ixBLVOV ^ev at tstay^ivcog zatrjy^ivac<br />
JtQog oQd^ag ayovtai tfj dca^itQC)' ovds yccQ aXlai<br />
Bvd^Btat TtaQccklriXoi iavtatg vito trig dca^iitQOV tov<br />
KvxXov dL%oto^ovvtaL' inl dl tcov tQLcov to^cjv ov<br />
10 Ttdvtcog TtQog OQd^ag dyovzaL, sC ^rj ijtl ^ovovg tovg<br />
d^ovag.<br />
Elg t6<br />
li]\<br />
"Ev tL6LV dvtLyQacpOLg ro %^BcciQ7i^a tovto iitl ^ovrjg<br />
TtaQa^oXfjg Kal vjtSQPoXrjg icttv, KdlXLOv ds xaxtolL-<br />
15 K(6tBQ0v s^SLv triv TtQota^LV, sl ^Tj otL to inl tijg<br />
ilXsLipBcog iKSLvoLg Sg dvaiicpC^okov JtaQaXiXsLTttaL' r]<br />
yaQ Fz/ ivtog ov6a trjg to^rjg 7ts7tBQa0^ivrjg ov0r]g<br />
Kal avtri Kat d^cpotsQa ti^vsL trjv to^rjv.<br />
dsL ds i7tLatrJ6aL, oxl, xdv rj AZB ti^vrj tr]v to-<br />
20 ^r^Vj ri avtrj dTtodsL^Lg dQ^o^SL.<br />
Elg to K.<br />
^Aito tovtov tov d-sc3Q7]^atog aQXO^svog iq)s^^g iv<br />
7ta6L td av^Tttco^axa xrjg 7taQapolrjg avxfj 8slkvv6lv<br />
VTtdQiovta Kal ovk dXXrj xlvl, (og izl xb TtoXv ds xfj<br />
25 v7tSQ^okfi Kal xy iXXsLipsc xal xa kvkIc) xd avxd Sblk-<br />
VV0LV v7tdQ%ovxa.<br />
i^tscdri ds ovk dxQrj(3Xov (paCvsxaL xotg xd ^rjxcc-<br />
3. Ssi-hvvgl] scripsi praeeunte Comm., SsLv.vvg Wp. 4.<br />
raLs'] fort. raig zs. xQiaiv W. kcovov'] v,(qvov xo^atq Halley
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