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

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

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226 COMMENTARIA ANTIQUA. ayoiievai 7] BE. (pavBQov ovVy ort rj ^ev BF £tg ccTtei,- Qov av^exai dia triv TOftJv, tog dedeixraL ev tg5 oydoa d^ecjQi^fiatc, 7} de 5z/, ^'Ttg e6tlv 7] vnoteCvovGa tr^v eTixoQ xov Slcc xov a^ovog xgvycovov ycovCav TteTteQaC- 5 T«t. xavxYiv drj dtxoxo^ovvxeg xaxa xb Z ical ayayovxeg dno xov A xexay^evog xaxrjy^evriv xriv AH^ dicc de xov Z xfj AH jtaQccXlrjXov xrjv @ZK Tcal itOL- 7]6avxeg xrjv ®Z xfj ZK i'6r}v, exL ^bvxol xal xo dno 0K L0OV x(p vTto ABE, e^o^ev xrjv @K devxegav dLa- 10 iiexQov, xovxo yaQ dvvaxov dLcc xb xrjv ©K exxbg ov6av xrjg xo^ijg eig ccTteLQOV iKpccXKead^aL xal dvvaxbv eivaL ditb xijg aTteCQOv JtQoxed^eC^r] evd^eCa iOrjv dcpeleiv. xb de Z zevxQov xaXet, xrjv de ZB Tcal xdg o^oCoog avxfj dnb xov Z TtQbg xrjv xo^rjv cpeQO^evag eK 15 XOV TCeVXQOV. xavxa ^ev eitl xrjg viteQ^o^ijg xal xc5v dvxixei^evov Tcal (paveQov, oxl neTteQa^iievri eCxlv exaxeQa tcjv Sia^etQOv , 7] fiev TtQcoxr} avxod^ev ix t% yeveCecog xrjg xoy^rjg, rj de devxeQa, Sloxl ^e6rj dvdXoyov icxL 20 7te7teQa6^evGJV evd^eLov tijg xe TtQcoxrjg dLa^exQOv xal xijg TtaQ^ rjv dvvavxaL al xaxayo^evaL iit avxr\v xexay^evcog. inl de xijg iXXeCjpeog ovitco 8i]Xov xb Xeyo^evov. iTteidrj yaQ eCg eavxrjv Cvvvevei, Tcad-aTteQ 6 xvxlog^ 25 xal ivxbg dTtokaii^dvei Ttddag xdg diafiexQOvg xal GiQiOiievag avxdg diteQyd^exai' o6xe ov Jtdvxcog iitl xijg iXXeCtpecog i] ^earj dvdkoyov xov xov eldovg nXev- Qov xal did xov tcbvxqov xijg ro^ijg dyo^evrj xal vnb xijg dtanexQov dL^oxo^o vfievr] vitb xijg xo^fjg TteQaxovxau' 4. a^cavog W. 9. vno] ano p. 19. Igxlv W. 23. ovnoi] ovtco 26. ov] del. Comm.

EUTOCII COMMENTARIA IN CONICA. 227 BF propter sectionem in infinitum crescere, sicut in propositione octaua demonstratum est, B^ autem, quae sub angulo exteriore trianguli per axem positi subtendat, terminatam ^ esse. hac igitur in Z A in duas partes aequales diuisa, ab A autem AH ordinate ducta et per Z rectae ducta &ZK et A H parallela sumpta ®Z rectae ZK aequali praetereaque sumpto &K^ = JBXBE, habebimus alteram diametrum @K, hoc enim fieri potest, quia 0K^ quae extra sectionem est, in infinitum produci potest, et quia ab infinita recta rectam datae aequalem abscindere possumus. Z autem centrum uocat et ZB easque, quae similiter a Z ad sectionem ducuntur, radios. haec quidem in byperbola oppositisque; utramque diametrum terminatam esse, et adparet, priorem statim ex origine sectionis, alteram autem, quod media sit proportionalis inter rectas terminatas, priorem scilicet diametrum et ductarum. parametrum rectarum ad illam ordinate in ellipsi uero nondum constat propositum. quoniam enim sicut circulus in se recurrit, omnes diametros intra se comprehendit et determinat; quare in ellipsi media inter latera figurae proportionalis per centrum sectionis ducta et a diametro in duas partes aequales secta non semper a sectione determinatur. fieri autem 15*

EUTOCII COMMENTARIA IN CONICA. 227<br />

BF propter sectionem in infinitum crescere, sicut in<br />

propositione octaua demonstratum est, B^ autem,<br />

<strong>quae</strong> sub angulo exteriore trianguli per axem positi<br />

subtendat, terminatam<br />

^ esse. hac igitur in Z<br />

A<br />

in duas partes aequales<br />

diuisa, ab A autem AH<br />

ordinate ducta et per Z<br />

rectae<br />

ducta &ZK et<br />

A H parallela<br />

sumpta<br />

®Z rectae ZK aequali<br />

praetereaque<br />

sumpto<br />

&K^ = JBXBE,<br />

habebimus alteram diametrum @K, hoc enim fieri<br />

potest, quia 0K^ <strong>quae</strong> extra sectionem est, in infinitum<br />

produci potest, et quia ab infinita recta rectam datae<br />

aequalem abscindere possumus. Z autem centrum<br />

uocat et ZB easque, <strong>quae</strong> similiter a Z ad sectionem<br />

ducuntur,<br />

radios.<br />

haec quidem in byperbola oppositisque;<br />

utramque diametrum terminatam esse,<br />

et adparet,<br />

priorem statim<br />

ex origine sectionis, alteram autem, quod media sit<br />

proportionalis inter rectas terminatas, priorem scilicet<br />

diametrum et<br />

ductarum.<br />

parametrum rectarum ad illam ordinate<br />

in ellipsi uero nondum constat propositum.<br />

quoniam<br />

enim sicut circulus in se recurrit, omnes diametros<br />

intra se comprehendit et determinat; quare in ellipsi<br />

media inter latera figurae proportionalis per centrum<br />

sectionis ducta et a diametro in duas partes aequales<br />

secta non semper a sectione determinatur. fieri autem<br />

15*

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