Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
194 COMMENTARIA ANTIQUA. rfi vjtb HKE l'6r}, xal pdetg 7] ZE xij HE l'6ri. ijCBl ovv rj ZE svd^ela rri HE ictiv l'0rj, xoivi] dh xal TCQog OQd^ag ri E^^ ^dCig aQa rj ^Z trj zJH iativ i'6rj. Tcdhv ijtsl l'0r} i6t\v rj BA TteQttpEQSia tfj BF, 5 xal ycovLa ccQa rj vjcb AKB tri vnb FKB ietiv tGrj' Sats xal XoLTCrj sig tdg dvo oQd^dg rj vnb AKE XoLTcij slg tdg dvo OQd-dg trj vjcb FKE iativ l'6rj. insl ovv fj AK sv^sta tfj FK i^tcv iCri' ix xsvtQOv yaQ' Koivr^ ds r] KE, dvo dv6lv t6ai^ xal yavia rj VTcb AKE 10 tfj vTcb FKE' xal ^d^Lg aQa rj AE tfj FE ietLv lar}. iicsl ovv l'6rj rj AE svd^sta tfj FE^ xolvt] ds rj E^ xal TCQbg OQd^dg, pdOLg aQa rj AA tfj AF l'6r]. o^olag ds xal TcdoaL dsL%d"i]6ovtaL au lOov d7ci%ov6aL trig ^B 7] trjg z/@ l'6aL. xal iTCsl rj E® trjg EZ idtLV 15 ikdoGcJV, xoLvrj 6} xal TCQog oQd^dg rj E^, pd6Lg aQu 7] ^® pd6sG)g trjg z/Z i6tLV ild66cov. icdlLV insl rj dnb tov E iipajcto^ivr] tov xvxXov jcaaav tav TCQbg trjv xvQtriv jcsQicpiQSLav 7CQ067CL%tov6c)v ^SL^mv i6tCvj idsLx^rj ds iv ta y' trjg 6t0LxsL0j6s(og tb vicb AE, 20 EA l'6ov ta aTcb trjg EZy otav rj EZ iq^dTctrjtac, sotLV aQa^ G>g rj AE TCQbg EZ, r] EZ TCQbg EA. ^sCt,G)v di i6tLV 7] EZ tfjg EA' dsl ydQ rj syyLov trjg iXaxL6trjg trjg aTCcatSQOV i6tLV iXd66(0V' ^sC^cov aQa xal rj AE trjg EZ. ijcsl ovv r] EZ trjg EA s6tLV 25 iXd66cov^ X0LV7] ds xal JCQbg OQd-dg 7] E^, pd6Lg aQa 7] ^Z tijg ^A i6tLv iXd66ov. Tcdhv ijcsl l6r] i6tlv rj AK Tf/ KB, xoLVT] ds r] KE, dvo aQa at AK^ KE tatg EK, KB, tovts6tLV oXr] tfj EKB, sC6lv l'6aL. dkX^ aC AK, KE tr]g AE ^sC^ovig sl6lv' xal r] BE 1. ZE] Z0 p. HE] H@, H e corr. ni. 1, p. 2. ZE] Z0 p. HE] H@ p. 4. BA] ^dcig Wp, corr. Comm J
; EUTOCII COMMENTARIA IN CONICA. 195 [Eucl. I, 4]. quoniam igitur ZE= HE, et E^ communis perpendicularisque, erit ^Z = AH [EucJ. I, 4]. rursus quoniam arcus BA = Br, erit etiam L AKB = rXB [Eucl. III, 27]. quare etiam qui reliquus est ad duos rectos explendos, /. AKE = FKE, qui reliquus est ad duos rectos explendos. quoniam igitur AK = rK (radii enim sunt), et communis est KE^ duo latera duobus aequalia sunt, et LAKE= FKE-, quare etiam AE=rE. quoniam igitur AE=rE, et E^ communis est perpendicularisque, erit z/^==^jr[Eucl. 1,4]. et similiter demonstrabimus, etiam omnes rectas, quae L AB uel A® aequaliter distent, aequales esse. et quoniam E@ EZ [Eucl. V, 14]. quoniam igitur EZ < EA, EA autem communis et perpendicularis, erit AZ < AA [Eucl. I, 47]. rursus quoniam AK= KB, communis autem KE, duae rectae AK, KE duabus EK, KB siue toti EKB aequales 6. Xomri — AKK^ om. p. 9. AKE] K e corr. p. 10. AE'] E e corr. m. 1 W. 12. JT] AF Wp,^ eorr. Comm. 15. iXXccGGcov W. 20. Tto] pvw, To W. otccv] oTccv 7] in extr. lin. W. 24. EZ] E e corr. p. EA] EA Wp, corr. Halley. 26. sazLv] pvw, ins. m. 2 W. 27. KB] KB iotiv W (fort. recte); sGtiv del. m. 2. 13*
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;<br />
EUTOCII COMMENTARIA IN CONICA. 195<br />
[Eucl. I, 4]. quoniam igitur ZE= HE, et E^ communis<br />
perpendicularisque, erit ^Z = AH [EucJ. I, 4].<br />
rursus quoniam arcus BA = Br, erit etiam<br />
L AKB = rXB<br />
[Eucl. III, 27]. quare etiam qui reliquus est ad duos<br />
rectos explendos, /. AKE = FKE, qui reliquus est<br />
ad duos rectos explendos. quoniam igitur AK = rK<br />
(radii enim sunt), et communis est KE^ duo latera<br />
duobus aequalia sunt,<br />
et LAKE= FKE-, quare etiam<br />
AE=rE. quoniam igitur AE=rE, et E^ communis<br />
est perpendicularisque, erit z/^==^jr[Eucl. 1,4].<br />
et similiter demonstrabimus, etiam omnes rectas,<br />
<strong>quae</strong><br />
L AB uel A® aequaliter distent, aequales esse. et<br />
quoniam E@ EZ [Eucl. V, 14].<br />
quoniam igitur EZ < EA, EA autem communis et<br />
perpendicularis, erit AZ < AA [Eucl. I, 47]. rursus<br />
quoniam AK= KB, communis autem KE, duae rectae<br />
AK, KE duabus EK, KB siue toti EKB aequales<br />
6. Xomri — AKK^ om. p. 9. AKE] K e corr. p. 10. AE']<br />
E e corr. m. 1 W. 12. JT] AF Wp,^ eorr. Comm. 15.<br />
iXXccGGcov W. 20. Tto] pvw, To W. otccv] oTccv 7] in extr.<br />
lin. W. 24. EZ] E e corr. p. EA] EA Wp, corr. Halley.<br />
26. sazLv] pvw, ins. m. 2 W. 27. KB] KB iotiv W (fort.<br />
recte); sGtiv del. m. 2.<br />
13*
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