Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org

EUTOCII COMMENTARIA IN CONICA. 305
commune adiiciatur tSl®] itaque totum
A;sl==;s;® + MO==0O + nP. etAS=AMxMK,
®0 = SKxKE, nP=n;ElxSP=&MxME.
potest autem aliter quoque demonstrari.
MN in U in duas partes aequales secetur. manifestum
igitur, etiam AK in U in duas partes aequales
secari, et esse &Kx KE = AEx EK-^ nam
&K = AE. et quoniam AK in 2J in partes aequales
secta est, in E autem in inaequales, erit [Eucl. II, 5]
uerum
AEXEK+ UE^ = KS\
EE^ = &Mx ME + HM^ [Eucl. II, 6J.
quare UK^ = AE X EK + ®M X ME + EM^
= 0KX KE + @M X ME + 2JMK eadem de
causa [Eucl. II, 5] igitur UK^ = AMx MK+HMK
quare
0KxKE+®MxME+UM^=AMxMK+2]MK
auferatur, quod commune est, UM^, erit igitur reliquum
0KxKE + GMxME = AM x MK.
Ad prop. XXIV.
Notandum, eum 6v^7trcod6i,g adpellare puncta, in
quibus rectae ABj FA cum sectione concurrant. et
AFK m.l W. 12. 86t^v W. KZ] SK2 Wp, corr. Halley,
sk Comm. 13. iaxLv W. tc5] p, x6 W. @ME] O&ME
Wp, corr. Comm. SK] EKYfip, corr. Comm. 14. savLvW.
xovtsativ W. ta>] supra scr. m. 1 p. 15. @ME] EME
Wp, corr. Comm. ZM] SN Wp, ' corr. Comm. tavtcc]
ravra W, tcc ccvtcc p. 16. eativ W. AMK] NHK Wp,
corr. Comm. t