Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
300 COMMENTARIA ANTIQUA. 6V^7CL7CT0V6tt tfl FA 6Vll7tCnX£L Xal tfj tOllfj, Ot^TOJg deLXVvtaL. xal ri ZE icpaittie^co tfjg roft^g xata tb E, r} dh 6v^7tt(o6tg tfi FA avcotEQOv tfj ZH. Xeyco, crt 5 expXrjd^etaa 6v^7Ce0ettaL tfj roftg. rjxd^G) yaQ dia tijg E a(prjg 7taQdXXr}Xog tfi FA a0v^7tt(6tG) rj E&' ri E& ccQa xata ftoi/ov tb E teiivei trjv tofiijv, eTtel ovv ri FA tfj E® 7taQdXXr}l6g iotiv^ xal tfi AH 6v^7tL7ttet rj ZH, nal tfj E& ccQa ^vfi- 10 TteGettat' 6)0te xal tfj roft^. El' tCg iattv evd-vyQa^^og yovCa TteQiexovCa trjv v7teQ^okriv etiQa trjg 7teQLexov6rjg tr}v v7teQ- ^oXriv^ ovK e6tLv iXdacov trjg 7teQLexov6rjg trjv vTteQ- ^oXriv. 15 e6tG) v7teQ^olri^ rjg d6v^7tt(otOL at FA, AA, eteQai de tLveg dav^jttcotoL tfi to^fj ecstoaav aC EZH. Xiyo^ otL ovK iXdaoov icftlv rj TtQog rc5 Z yovCa tfjg ^tQog rc5 A. eatoaav yaQ TtQoteQOV aC EZH tatg FA, AA 20 7taQdXXr\\oL, iar\ aQa rj TtQog rc5 Z yovCa tfj 7tQbg t(p A' ovK ildaaov ccQa iatlv rj ^tQog rw Z tijg TtQog rc5 A. ^rj iatoaav drj 7taQdXXr\XoL, xad-cbg i7tl trjg devtiQag 1. FA] rj p. ovTco p, 2. Post 8sLv.vvtai excidit praeparatio; in Wp nulla lacuna. 3. ri Ss av(i7ttcoaig] at dh avfintcaaEis Wp, corr. Halley cum Comm. 4. tfj (alt.)] tfjg Halley. 9. AH] scripsi, AN -g et, A in ras. m. 1, W; AF Halley cum Comm. 15. 175] scripsi, 7} Wp; possis etiam xat coniicere. 16. EZH] scriipsi, EZ Wp; EZ, ZH Halley cum Comm, 18. tc5] p, to W. 20. naQdXXrjXoi. i'ari a^a] p, naQaXXriXoLg ri dqa W.
EUTOCII COMMENTARIA IN CONICA. 301 gentem cum FA concurrat, etiam cum sectione concurrere, sic demonstratur: sint asymptotae ^JT, ^z/, et ZK, ZH cadant ut in quarta figura, ZE autem sectionem contingat in E, et punctum concursus cum FA rectae ZH superius sit. dico, eam productam cum sectione concurrere. ducatur enim per punctum contactus E asymptotae FA parallela E&\ E@ igitur in solo E sectionem secat [prop. XIII]. quoniam igitur FA rectae E® parallela est, et ZH cum AH concurrit, etiam cum E® concurret; ergo etiam cum sectione. Si quis est angulus rectilineus hyperbolam continens alius atque is, qui hyperbolam continet, minor non est angulo hyperbolam continente. j^ sit byperbola, cuius asymptotae ^r sint FAj A/1, aliae autem aliquae sectionis asymptotae sint EZ,ZH. dico, angulum ad Z positum minorem non esse angulo ad A posito. nam primum EZ, ZH rectis FA, AA parallelae sint. itaque L Z = i A. ergo angulus ad Z positus angulo ad A posito minor non est. iam parallelae ne sint, sicut in secunda figura. In fig. 1 r et E om. W; in sectione est. In fig. 2 om. A W, pro z/ hab. A.
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300 COMMENTARIA ANTIQUA.<br />
6V^7CL7CT0V6tt tfl FA 6Vll7tCnX£L Xal tfj tOllfj, Ot^TOJg<br />
deLXVvtaL.<br />
xal ri ZE icpaittie^co tfjg roft^g xata tb E, r}<br />
dh 6v^7tt(o6tg tfi FA avcotEQOv tfj ZH. Xeyco, crt<br />
5 expXrjd^etaa 6v^7Ce0ettaL tfj roftg.<br />
rjxd^G) yaQ dia tijg E a(prjg 7taQdXXr}Xog tfi FA<br />
a0v^7tt(6tG) rj E&' ri E& ccQa xata ftoi/ov tb E teiivei<br />
trjv tofiijv, eTtel ovv ri FA tfj E® 7taQdXXr}l6g iotiv^<br />
xal tfi AH 6v^7tL7ttet rj ZH, nal tfj E& ccQa ^vfi-<br />
10 TteGettat' 6)0te xal tfj roft^.<br />
El' tCg iattv evd-vyQa^^og yovCa TteQiexovCa<br />
trjv v7teQ^okriv etiQa trjg 7teQLexov6rjg tr}v v7teQ-<br />
^oXriv^ ovK e6tLv iXdacov trjg 7teQLexov6rjg trjv vTteQ-<br />
^oXriv.<br />
15 e6tG) v7teQ^olri^ rjg d6v^7tt(otOL at FA, AA, eteQai<br />
de tLveg dav^jttcotoL tfi to^fj ecstoaav aC EZH. Xiyo^<br />
otL ovK iXdaoov icftlv rj TtQog rc5 Z yovCa tfjg ^tQog<br />
rc5 A.<br />
eatoaav yaQ TtQoteQOV aC EZH tatg FA, AA<br />
20 7taQdXXr\\oL, iar\ aQa rj TtQog rc5 Z yovCa tfj 7tQbg<br />
t(p A' ovK ildaaov ccQa iatlv rj ^tQog rw Z tijg<br />
TtQog rc5 A.<br />
^rj iatoaav drj 7taQdXXr\XoL, xad-cbg i7tl trjg devtiQag<br />
1. FA] rj p. ovTco p, 2. Post 8sLv.vvtai excidit<br />
praeparatio; in Wp nulla lacuna. 3. ri Ss av(i7ttcoaig] at<br />
dh avfintcaaEis Wp, corr. Halley <strong>cum</strong> Comm. 4. tfj (alt.)]<br />
tfjg Halley. 9. AH] scripsi, AN -g et, A in ras. m. 1, W;<br />
AF Halley <strong>cum</strong> Comm. 15. 175] scripsi, 7} Wp; possis<br />
etiam xat coniicere. 16. EZH] scriipsi, EZ Wp; EZ, ZH<br />
Halley <strong>cum</strong> Comm, 18. tc5] p, to W. 20. naQdXXrjXoi.<br />
i'ari a^a] p, naQaXXriXoLg ri dqa W.
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