Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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            <s xml:id="echoid-s10459" xml:space="preserve">
              <pb o="285" file="0323" n="323" rhead="Conicor. Lib. VII."/>
            drata H E, & </s>
            <s xml:id="echoid-s10460" xml:space="preserve">ipſius E G, ſiue ad differentiam duorum quadratorum L
              <lb/>
            I, & </s>
            <s xml:id="echoid-s10461" xml:space="preserve">ipſius I P eandem proportionem habebit, quàm quadratum H E
              <lb/>
            ad differentiam duorum quadratorum H E, & </s>
            <s xml:id="echoid-s10462" xml:space="preserve">E G. </s>
            <s xml:id="echoid-s10463" xml:space="preserve">Et iam oſtenſum eſt
              <lb/>
            quod quadratum A C ad quadratum I L eandem proportionem habet,
              <lb/>
            quàm C G in H E ad quadratum H E; </s>
            <s xml:id="echoid-s10464" xml:space="preserve">8. </s>
            <s xml:id="echoid-s10465" xml:space="preserve">ergo ex æqualitate quadratum
              <lb/>
            A C, fiue ad quadratum ſummæ I L, N O eſt, vt C G in H E ad qua-
              <lb/>
            dratum E H V; </s>
            <s xml:id="echoid-s10466" xml:space="preserve">9. </s>
            <s xml:id="echoid-s10467" xml:space="preserve">ſiue ad quadratum differentiæ eius, quæ eſt inter I
              <lb/>
              <note position="left" xlink:label="note-0323-01" xlink:href="note-0323-01a" xml:space="preserve">c</note>
            L, N O eſt vt C G in H E ad quadratum exceſſus E H ſupra H V: </s>
            <s xml:id="echoid-s10468" xml:space="preserve">10.
              <lb/>
            </s>
            <s xml:id="echoid-s10469" xml:space="preserve">
              <note position="left" xlink:label="note-0323-02" xlink:href="note-0323-02a" xml:space="preserve">d</note>
            ſiue ad I L in N O erit, vt C G ad H V: </s>
            <s xml:id="echoid-s10470" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10471" xml:space="preserve">ſiue ad duorum quadrato-
              <lb/>
              <note position="left" xlink:label="note-0323-03" xlink:href="note-0323-03a" xml:space="preserve">e</note>
              <figure xlink:label="fig-0323-01" xlink:href="fig-0323-01a" number="375">
                <image file="0323-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0323-01"/>
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            rum I L, N O ſummam, erit vt
              <lb/>
            C G ad ſummam G E, E H; </s>
            <s xml:id="echoid-s10472" xml:space="preserve">12.
              <lb/>
            </s>
            <s xml:id="echoid-s10473" xml:space="preserve">
              <note position="left" xlink:label="note-0323-04" xlink:href="note-0323-04a" xml:space="preserve">f</note>
            ſiue ad quadratum I P erit, vt
              <lb/>
            C G in H E ad quadratum E G:
              <lb/>
            </s>
            <s xml:id="echoid-s10474" xml:space="preserve">13. </s>
            <s xml:id="echoid-s10475" xml:space="preserve">ſiue ad quadratum differen-
              <lb/>
              <note position="left" xlink:label="note-0323-05" xlink:href="note-0323-05a" xml:space="preserve">g</note>
            tiæ L I, I P erit, vt C G in E
              <lb/>
            H ad quadratum differentiæ H
              <lb/>
            E, E G: </s>
            <s xml:id="echoid-s10476" xml:space="preserve">14. </s>
            <s xml:id="echoid-s10477" xml:space="preserve">ſiue ad quadratum
              <lb/>
              <note position="left" xlink:label="note-0323-06" xlink:href="note-0323-06a" xml:space="preserve">h</note>
            ex recta linea æquali sũmæ dua-
              <lb/>
            rum L I, I P, erit vt C G in
              <lb/>
            E H ad quadratum ex recta li-
              <lb/>
            nea compoſita ex H E, E G:
              <lb/>
            </s>
            <s xml:id="echoid-s10478" xml:space="preserve">
              <note position="left" xlink:label="note-0323-07" xlink:href="note-0323-07a" xml:space="preserve">i</note>
            15. </s>
            <s xml:id="echoid-s10479" xml:space="preserve">ſiue ad L I in I P erit vt C G ad G E: </s>
            <s xml:id="echoid-s10480" xml:space="preserve">16. </s>
            <s xml:id="echoid-s10481" xml:space="preserve">ſiue ad duo quadrata ex
              <lb/>
            L I, & </s>
            <s xml:id="echoid-s10482" xml:space="preserve">ex I P erit vt C G in E H ad duo quadrata E G, & </s>
            <s xml:id="echoid-s10483" xml:space="preserve">E H: </s>
            <s xml:id="echoid-s10484" xml:space="preserve">17.
              <lb/>
            </s>
            <s xml:id="echoid-s10485" xml:space="preserve">
              <note position="left" xlink:label="note-0323-08" xlink:href="note-0323-08a" xml:space="preserve">k</note>
            ſiue ad differentiam duorum quadratorum ex L I, & </s>
            <s xml:id="echoid-s10486" xml:space="preserve">ex I P erit vt C G
              <lb/>
              <note position="left" xlink:label="note-0323-09" xlink:href="note-0323-09a" xml:space="preserve">l</note>
            in E H ad differentiam duorum quadratorum ex H E, & </s>
            <s xml:id="echoid-s10487" xml:space="preserve">ex E G. </s>
            <s xml:id="echoid-s10488" xml:space="preserve">Et
              <lb/>
            hoc erat propoſitum.</s>
            <s xml:id="echoid-s10489" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div881" type="section" level="1" n="270">
          <head xml:id="echoid-head339" xml:space="preserve">Notæ in Propoſit. VIII.</head>
          <p>
            <s xml:id="echoid-s10490" xml:space="preserve">IIſdem figuris manentibus ſit H V potens comparata, &</s>
            <s xml:id="echoid-s10491" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10492" xml:space="preserve">Præter defi-
              <lb/>
              <note position="left" xlink:label="note-0323-10" xlink:href="note-0323-10a" xml:space="preserve">a</note>
            nitiones ſuperius expoſitas hic duæ aliæ declarari debent, ignotum enim eſt
              <lb/>
            quid nam nomine Figuræ comparatæ, & </s>
            <s xml:id="echoid-s10493" xml:space="preserve">Potentis comparatæ intelligi debeat.
              <lb/>
            </s>
            <s xml:id="echoid-s10494" xml:space="preserve">Itaq; </s>
            <s xml:id="echoid-s10495" xml:space="preserve">rectangulum ſub præſecta comparata, & </s>
            <s xml:id="echoid-s10496" xml:space="preserve">intercepta comparata contentum,
              <lb/>
            ideſt rectangulum H E G vocatur Figura comparata: </s>
            <s xml:id="echoid-s10497" xml:space="preserve">& </s>
            <s xml:id="echoid-s10498" xml:space="preserve">ſi quadratum rectæ li-
              <lb/>
            neæ H V æquale fuerit rectangulo H E G vocatur H V Potens comparata.</s>
            <s xml:id="echoid-s10499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10500" xml:space="preserve">Ergo S D in D M ad quadratum D I, nempe E C in C A ad qua-
              <lb/>
              <note position="left" xlink:label="note-0323-11" xlink:href="note-0323-11a" xml:space="preserve">b</note>
            dratũ C E, &</s>
            <s xml:id="echoid-s10501" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10502" xml:space="preserve">AEqualia enim ſpatia, ſcilicet rectangulũ S D M, & </s>
            <s xml:id="echoid-s10503" xml:space="preserve">quadratũ
              <lb/>
              <note position="right" xlink:label="note-0323-12" xlink:href="note-0323-12a" xml:space="preserve">37. lib. I.</note>
            D A ad idem quadratum I D habent eandem proportionem; </s>
            <s xml:id="echoid-s10504" xml:space="preserve">ſed quia triangula
              <lb/>
            M I D, & </s>
            <s xml:id="echoid-s10505" xml:space="preserve">A B C ſimilia ſunt, propterea quod latera homologa ſunt parallela
              <lb/>
            inter ſe; </s>
            <s xml:id="echoid-s10506" xml:space="preserve">pariterquè triangula D S I, & </s>
            <s xml:id="echoid-s10507" xml:space="preserve">C E B ſunt ſimilia, vt oſtenſum eſt
              <lb/>
            in 6. </s>
            <s xml:id="echoid-s10508" xml:space="preserve">& </s>
            <s xml:id="echoid-s10509" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10510" xml:space="preserve">huius; </s>
            <s xml:id="echoid-s10511" xml:space="preserve">ergo S D ad D I erit vt E C ad C B, atquè M D ad D I
              <lb/>
            eſt vt A C ad C B erunt compoſitæ proportiones eædem inter ſe, ſcilicet rectan-
              <lb/>
            gulum S D M ad quadratum D I eandem proportionem habebit, quàm rectan-
              <lb/>
            gulum E C A ad quadratum C B; </s>
            <s xml:id="echoid-s10512" xml:space="preserve">quare vt quadratum A D ad quadratum
              <lb/>
            D I, ſeu vt quadruplum ad quadruplum, ſcilicet vt quadratum A C ad qua-
              <lb/>
            dratum I L, co quod A D, & </s>
            <s xml:id="echoid-s10513" xml:space="preserve">I D ſemiſſes ſunt diametrorum A C, I L.</s>
            <s xml:id="echoid-s10514" xml:space="preserve"/>
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