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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          <pb o="338" file="0376" n="377" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s11816" xml:space="preserve">Quia duplum rectanguli ex G E, O H in H E æquale eſt quadratis ex G E
              <lb/>
            & </s>
            <s xml:id="echoid-s11817" xml:space="preserve">ex E H, ergo idem rectangulum, cuius altitudo G E, & </s>
            <s xml:id="echoid-s11818" xml:space="preserve">O H, baſis verò
              <lb/>
            O E bis ſumptum ad duplum rectanguli, cuius altitudo G E, O H, baſis verò
              <lb/>
            H E, ſeu O E ad H E eandem proportionem habet, quàm duplum rectanguli
              <lb/>
            ex G E, & </s>
            <s xml:id="echoid-s11819" xml:space="preserve">O H in O E ad quadrata ex G E, & </s>
            <s xml:id="echoid-s11820" xml:space="preserve">ex E H: </s>
            <s xml:id="echoid-s11821" xml:space="preserve">quare componen-
              <lb/>
            do O H ad E H, ſeu O H A ad E H A eandem proportionem habebit, quàm
              <lb/>
              <note position="left" xlink:label="note-0376-01" xlink:href="note-0376-01a" xml:space="preserve">Lem. 11.
                <lb/>
              huius.</note>
            duo quadrata ex G O, & </s>
            <s xml:id="echoid-s11822" xml:space="preserve">ex O H ad duo quadrata ex G E, & </s>
            <s xml:id="echoid-s11823" xml:space="preserve">ex E H, & </s>
            <s xml:id="echoid-s11824" xml:space="preserve">
              <lb/>
            permutando O H A ad quadrata ex G O, & </s>
            <s xml:id="echoid-s11825" xml:space="preserve">ex O H, ſeu quadratum ex A C
              <lb/>
              <note position="left" xlink:label="note-0376-02" xlink:href="note-0376-02a" xml:space="preserve">17. huius.</note>
            ad quadrata ex Q P, & </s>
            <s xml:id="echoid-s11826" xml:space="preserve">ex P R eandem proportionem habebit, quàm rectan-
              <lb/>
            gulũ E H A ad quadrata ex G E, & </s>
            <s xml:id="echoid-s11827" xml:space="preserve">ex E H, ſeu erit vt quadratum A C ad
              <lb/>
              <note position="left" xlink:label="note-0376-03" xlink:href="note-0376-03a" xml:space="preserve">Ibidem.</note>
            quadrata ex I L, & </s>
            <s xml:id="echoid-s11828" xml:space="preserve">ex I K, vel ad quadrata ex C A & </s>
            <s xml:id="echoid-s11829" xml:space="preserve">ex A F: </s>
            <s xml:id="echoid-s11830" xml:space="preserve">quare
              <lb/>
            duo quadrata ex Q P, & </s>
            <s xml:id="echoid-s11831" xml:space="preserve">ex R P æqualia ſunt duobus quadratis ex I L, & </s>
            <s xml:id="echoid-s11832" xml:space="preserve">
              <lb/>
            ex I K, vel ex C A, & </s>
            <s xml:id="echoid-s11833" xml:space="preserve">A F.</s>
            <s xml:id="echoid-s11834" xml:space="preserve"/>
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          <figure number="448">
            <image file="0376-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0376-01"/>
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            <s xml:id="echoid-s11835" xml:space="preserve">Secundo quia duplum rectanguli ex G E, O H in H E minus ponitur quadratis
              <lb/>
            ex G E, & </s>
            <s xml:id="echoid-s11836" xml:space="preserve">ex E H, igitur idem ſpatium ſcilicet duplum rectanguli ex G E, & </s>
            <s xml:id="echoid-s11837" xml:space="preserve">
              <lb/>
            O H in O E ad duplum rectanguli ex G E, & </s>
            <s xml:id="echoid-s11838" xml:space="preserve">O H in H E, ſiue O E ad H E
              <lb/>
            maiorem proportionem habet, quàm duplum rectanguli ex G E, O H in O E ad
              <lb/>
            quadrata ex G E, & </s>
            <s xml:id="echoid-s11839" xml:space="preserve">O H, & </s>
            <s xml:id="echoid-s11840" xml:space="preserve">vt prius componendo, ex lemmate 11. </s>
            <s xml:id="echoid-s11841" xml:space="preserve">& </s>
            <s xml:id="echoid-s11842" xml:space="preserve">permu-
              <lb/>
            tando, ex 17. </s>
            <s xml:id="echoid-s11843" xml:space="preserve">huius; </s>
            <s xml:id="echoid-s11844" xml:space="preserve">idem quadratum A C ad quadrata ex Q P, & </s>
            <s xml:id="echoid-s11845" xml:space="preserve">ex P R
              <lb/>
            maiorem proportionem habebit quàm ad quadrata ex I L, & </s>
            <s xml:id="echoid-s11846" xml:space="preserve">ex I K, vel ad
              <lb/>
            quadrata, ex C A, & </s>
            <s xml:id="echoid-s11847" xml:space="preserve">ex A F: </s>
            <s xml:id="echoid-s11848" xml:space="preserve">quapropter quadrata ex Q P, & </s>
            <s xml:id="echoid-s11849" xml:space="preserve">ex P R mi-
              <lb/>
            nora erunt quadratis ex I L, & </s>
            <s xml:id="echoid-s11850" xml:space="preserve">ex I K, vel quadratis ex C A, & </s>
            <s xml:id="echoid-s11851" xml:space="preserve">ex A F.</s>
            <s xml:id="echoid-s11852" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11853" xml:space="preserve">Tertio quia duplum rectanguli ex G E, O H in H E maius eſt ſumma qua-
              <lb/>
            dratorum ex G E, & </s>
            <s xml:id="echoid-s11854" xml:space="preserve">ex E H, igitur, eodem progreſſu, habebit quadratum A C
              <lb/>
            ad ſummam quadratorum ex Q P, & </s>
            <s xml:id="echoid-s11855" xml:space="preserve">ex P R minorem proportionem, quàm
              <lb/>
            ad ſummam quadraterum ex I L, & </s>
            <s xml:id="echoid-s11856" xml:space="preserve">ex I K, vel ex C A, & </s>
            <s xml:id="echoid-s11857" xml:space="preserve">ex A F: </s>
            <s xml:id="echoid-s11858" xml:space="preserve">& </s>
            <s xml:id="echoid-s11859" xml:space="preserve">
              <lb/>
            propterea ſumma priorum quadratorum maior erit ſumma poſteriorum, vt fue-
              <lb/>
            rat propoſitum.</s>
            <s xml:id="echoid-s11860" xml:space="preserve"/>
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