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="329" file="0367" n="368" rhead="Conicor. Lib. VII."/>
          <figure number="436">
            <image file="0367-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0367-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s11595" xml:space="preserve">Et primo rectangulum ſub O D E in E H æquale ſit quadrato D E, ergo
              <lb/>
            ad hæc duo ſpatia æqualia eandem proportionem habebit idem rectangulum ſub
              <lb/>
            E D O in O E, ſed vt rectangulum ſub E D O in O E ad rectangulum ſub E
              <lb/>
            D O in E H, ita eſt O E ad E H, (propterea quod æquales altitudines ha-
              <lb/>
            bent), igitur vt O E ad E H, ita eſt rectangulum ſub E D O in O E ad
              <lb/>
            quadratum D E, & </s>
            <s xml:id="echoid-s11596" xml:space="preserve">componendo O H ad E H, ſiue rectangulum O H A ad
              <lb/>
            rectangulum E H A eandem proportionẽ habebit, quàm rectangulum ſub E D
              <lb/>
            O in O E vna cum quadrato D E, ſeu quàm quadratum D O ad quadratum
              <lb/>
            D E, vel potius vt quadratum ex dupla D O ad quadratum ex dupla D E,
              <lb/>
            nempe vt quadratum ex G O H ad quadratum ex G E H, quare permutando
              <lb/>
            rectangulum O H A ad quadratum ex G O H eandem proportionem habebit,
              <lb/>
            quàm rectangulum ex E H A ad quadratum ex G E H, ſeu vt quadratum ex
              <lb/>
              <note position="right" xlink:label="note-0367-01" xlink:href="note-0367-01a" xml:space="preserve">Prop. 16.
                <lb/>
              huius.
                <lb/>
              Ibidem.</note>
            A C ad quadratum ex C A F, vel ex L I K; </s>
            <s xml:id="echoid-s11597" xml:space="preserve">ſed vt rectangulum A H O ad
              <lb/>
            quadratum ex G O H, ita eſt quadratum ex A C ad quadratum ex Q P R:
              <lb/>
            </s>
            <s xml:id="echoid-s11598" xml:space="preserve">quare idem quadratum A C eandem proportionem habet ad quadratum ex Q P
              <lb/>
            R, quàm ad quadratum ex C A F, vel ex I R L, & </s>
            <s xml:id="echoid-s11599" xml:space="preserve">propterea quadrata ipſa
              <lb/>
            æqualia ſunt, & </s>
            <s xml:id="echoid-s11600" xml:space="preserve">ſumma laterum Q P R æqualis eſt ſummæ laterum C A F,
              <lb/>
            vel I L K.</s>
            <s xml:id="echoid-s11601" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s11602" xml:space="preserve">Secundo ſit rectangulũ ſub E D O in E H maius quadrato D E, tunc quidem
              <lb/>
            idem rectangulum ſub E D O in O E ad rectangulum ſub O D E in E H mi-
              <lb/>
            norem proportionẽ habebit, quàm ad quadratum ex D E, ſeu O E ad E H mi-
              <lb/>
            norem proportionem habebit, quàm ad quadratum ex D E; </s>
            <s xml:id="echoid-s11603" xml:space="preserve">& </s>
            <s xml:id="echoid-s11604" xml:space="preserve">componendo
              <lb/>
            ſumpta eadem altitudine H A, quadruplicando poſtrema quadrata, & </s>
            <s xml:id="echoid-s11605" xml:space="preserve">permu-
              <lb/>
            tando, & </s>
            <s xml:id="echoid-s11606" xml:space="preserve">ex 16. </s>
            <s xml:id="echoid-s11607" xml:space="preserve">huius, idem quadratum A C ad quadratum ex Q P R mi-
              <lb/>
            norem proportionem habebit, quàm ad quadratum ex C A F, vel ex L I K,
              <lb/>
            & </s>
            <s xml:id="echoid-s11608" xml:space="preserve">propterea ſumma Q P R maior erit, quàm C A F, ſeu quàm L I K.</s>
            <s xml:id="echoid-s11609" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11610" xml:space="preserve">Tertio ſit rectangulum ſub E D O in E H minus quadrato D E, patet quod
              <lb/>
            idem rectangulum ſub E D O in O E ad rectangulum ſub E D O in E H, ſeu
              <lb/>
            O E ad E H maiorem proportionem habet, quàm ad quadratum D E, & </s>
            <s xml:id="echoid-s11611" xml:space="preserve">com-
              <lb/>
            ponendo ductis prioribus terminis in A H, quadruplicando poſtrema </s>
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