Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org Apollonii Pergaei quae graece exstant cum ... - Wilbourhall.org
218 COMMENTARIA ANTIQUA. T6 de djto trjg BF itQog t6 vito BAF loyov ^%EL tbv Ovyxsifisvov sk rov ov sxst rj BF jtQog FA xccl 7] BF TtQog BA' dsdsixtaL ^sv sv tc5 sKto) PipXiC) trjg (StOL%SLc60sog sv tc5 Si%o6ta tQctfp d-scoQi]- 5 ^atL, otv ta i^oycDVLa TtaQallrjXoyQa^^a JtQog aXXrjXa Xoyov s%SL tov (SvyxsL^svov sx tcov TtXsvQCOv STtsl ds STtaxtLKcotSQOv ^ccXXov xal ov %ata tbv avayxatov tQOTtov V7tb tcov v7to^vri^atL6tc5v iXsysto^ i^r}trj6a^sv avtb xal ysyQantaL sv totg ixdsdo^svoLg rj^tv stg tb 10 tstaQtov ^scoQrj^a tov dsvtSQOv ^l^Xlov toov 'AQxniri- Sovg TtsQL 6cpaLQag xal xvIlv8qov xal sv totg 0%oXLOLg tov TtQcotov Pl^Xlov trjg TltoXs^aCov 6vvtdi,scog' ov %stQOv 6s xal svtavx^a tovto yQacprjvaL dLcc tb (irj Ttdvtcog tovg avayLvoi^xovtag xdxsCvoLg svtvy%dvsLV, xal ott 0%sdbv 16 TO oXov dvvtay^a t^v xc3vlxc5v xs%QrjtaL avta. Xoyog ix Xoycov GvyxstO^aL XsystaL, otav aC tcBv Xoycov TtrjXtxotritsg icp' savtdg 7toXXa7tXa6La6d-st6aL TtOLm0L tLva, 7tr}XLx6trjtog drjXovotL Xsyo^svrjg tot) dQLd^- ^ov, ov 7taQc6vv(i6g satLV 6 X6yog. iTtl (isv ovv td5v 20 7toXXa7tXa6LC3v dvvat6v idtLv dQL^^ibv bXbxXrjQov slvaL triv 7triXLx6tr}ta, i7tl ds tcov XoL7tc3v 6%s0scjv dvdyxrj tr]v 7trjXLx6trjta dQtd^^ibv slvat xal (i6qlov ^ (i^qlu, sl (iy} ccQa tLg i^iXoL xal dQQr^tovg elvaL 6%s6SLg, olaC sCglv aC xatd td dXoya (isysd^rj. i7tl 7ta6cov ds tcov 6%s6scov 25 dfjXov, otL avtrj rj 7tr}XLx6trjg 7toXXa7tXa6La^ofisvr} i7tl tbv S7t6(isvov oQov Tov X6yov 7tOLst tbv ijyov^isvov. §6tco toCvvv Xbyog 6 tov A 7tQbg tbv B, xal sC- 2. BT] r e corr. m. 1 W. 3. FA — ngog] addidi; om. Wp (pro BA Halley scr. rj). 4. tfjg] ttj W. sv] e corr. p. 6. cri] pw, or seq. ras. 1 litt. W. 10. 'Aqxi(ii]- Sovg] vw, 'AqxI' seq. ras. 5 — 6 litt. W et seq. lac. p. 13.
EUTOCII COMMENTARIA IN CONICA. 219 Et est BF^ :BAxAr= (BF : FA) X (Br:BA) [I p. 40, 8—10]: in propositione XXIII sexti libri Elementorum demonstratum est, parallelogramma aequiangula inter se rationem ex rationibus laterum compositam habere; quoniam autem boc per inductionem magis neque satis stricte a commentatoribus exponebatur, nos de ^a re quaesiuimus et scriptum est in commentariis, quae edidimus ad quartam propositionem libri alterius Arcliimedis de sphaera et cylindro [Archimedis op. III p. 140 sq.] et in scholiis primi libri compositionis Ptolemaei; uerum satius esse duximus hic quoque idem exponere, quia uon omnino iis, qui haec legent, illi quoque libri ad manum sunt, et quia totum paene opus conicorum eo utitur. ratio ex rationibus composita esse dicitur, ubi rationum quantitates inter se multiplicatae rationem quandam efficiunt, quantitas autem is dicitur numerus, a quo ratio denominatur. in multiplis igitur fieri potest, ut quantitas sit totus ahquis numerus, in reliquis uero rationibus necesse est, quantitatem numerum esse cum parte uel partibus, nisi quis etiam irrationales rationes esse statuerit, quales sunt magnitudinum irrationalium. uerum in omnibus rationibus manifestum est, ipsam quantitatem in terminum sequentem proportionis multiplicatam praecedentem efficere. sit igitur proportio A : B, et sumatur medius 5- __ yqatpELvav W. 16— 17. - mg. W. 17. noXXanXaaQ^SLaai VV. T" noi&ai] p, (oaLv post ras. 3 litt. W. 21. r^v] p, om. W.
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218 COMMENTARIA ANTIQUA.<br />
T6 de djto trjg BF itQog t6 vito BAF loyov<br />
^%EL tbv Ovyxsifisvov sk rov ov sxst rj<br />
BF jtQog<br />
FA xccl 7] BF TtQog BA' dsdsixtaL ^sv sv tc5 sKto)<br />
PipXiC) trjg (StOL%SLc60sog sv tc5 Si%o6ta tQctfp d-scoQi]-<br />
5 ^atL, otv ta i^oycDVLa TtaQallrjXoyQa^^a JtQog aXXrjXa<br />
Xoyov s%SL tov (SvyxsL^svov sx tcov TtXsvQCOv STtsl ds<br />
STtaxtLKcotSQOv ^ccXXov xal ov %ata tbv avayxatov<br />
tQOTtov V7tb tcov v7to^vri^atL6tc5v iXsysto^ i^r}trj6a^sv<br />
avtb xal ysyQantaL sv totg ixdsdo^svoLg rj^tv stg tb<br />
10 tstaQtov ^scoQrj^a tov dsvtSQOv ^l^Xlov toov 'AQxniri-<br />
Sovg TtsQL 6cpaLQag xal xvIlv8qov xal sv totg 0%oXLOLg tov<br />
TtQcotov Pl^Xlov trjg TltoXs^aCov 6vvtdi,scog' ov %stQOv<br />
6s xal svtavx^a tovto yQacprjvaL dLcc tb (irj Ttdvtcog tovg<br />
avayLvoi^xovtag xdxsCvoLg svtvy%dvsLV, xal ott 0%sdbv<br />
16 TO oXov dvvtay^a t^v xc3vlxc5v xs%QrjtaL avta.<br />
Xoyog ix Xoycov GvyxstO^aL XsystaL, otav aC tcBv<br />
Xoycov TtrjXtxotritsg icp' savtdg 7toXXa7tXa6La6d-st6aL TtOLm0L<br />
tLva, 7tr}XLx6trjtog drjXovotL Xsyo^svrjg tot) dQLd^-<br />
^ov, ov 7taQc6vv(i6g satLV 6 X6yog. iTtl (isv ovv td5v<br />
20 7toXXa7tXa6LC3v dvvat6v idtLv dQL^^ibv bXbxXrjQov slvaL<br />
triv 7triXLx6tr}ta, i7tl ds tcov XoL7tc3v 6%s0scjv dvdyxrj<br />
tr]v 7trjXLx6trjta dQtd^^ibv slvat xal (i6qlov ^ (i^qlu, sl (iy}<br />
ccQa tLg i^iXoL xal dQQr^tovg elvaL 6%s6SLg, olaC sCglv<br />
aC xatd td dXoya (isysd^rj. i7tl 7ta6cov ds tcov 6%s6scov<br />
25 dfjXov, otL avtrj rj 7tr}XLx6trjg 7toXXa7tXa6La^ofisvr} i7tl<br />
tbv S7t6(isvov oQov Tov X6yov 7tOLst tbv ijyov^isvov.<br />
§6tco toCvvv Xbyog 6 tov A 7tQbg tbv B, xal sC-<br />
2. BT] r e corr. m. 1 W. 3. FA — ngog] addidi;<br />
om. Wp (pro BA Halley scr. rj). 4. tfjg] ttj W. sv] e<br />
corr. p. 6. cri] pw, or seq. ras. 1 litt. W. 10. 'Aqxi(ii]-<br />
Sovg] vw, 'AqxI' seq. ras. 5 — 6 litt. W et seq. lac. p. 13.