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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        <div xml:id="echoid-div1022" type="section" level="1" n="325">
          <p style="it">
            <s xml:id="echoid-s11874" xml:space="preserve">
              <pb o="340" file="0378" n="379" rhead="Apollonij Pergæi"/>
            minus eſt ſemiſſe quadrati G H: </s>
            <s xml:id="echoid-s11875" xml:space="preserve">fiat iam quadratum ex M H æquale ſemiqua-
              <lb/>
            drato ex G H, & </s>
            <s xml:id="echoid-s11876" xml:space="preserve">lateris C M fiant duo diametri Q P, & </s>
            <s xml:id="echoid-s11877" xml:space="preserve">q p, eorumque
              <lb/>
            erecta ſint P R, & </s>
            <s xml:id="echoid-s11878" xml:space="preserve">p r: </s>
            <s xml:id="echoid-s11879" xml:space="preserve">dico ductas diametros æquales eſſe, & </s>
            <s xml:id="echoid-s11880" xml:space="preserve">quadratum
              <lb/>
            ex P Q æquale eſſe quadrato ex differentia ipſarum P Q, & </s>
            <s xml:id="echoid-s11881" xml:space="preserve">P R.</s>
            <s xml:id="echoid-s11882" xml:space="preserve"/>
          </p>
          <figure number="450">
            <image file="0378-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0378-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s11883" xml:space="preserve">Quia vt M H ad G M, ita eſt diameter Q P ad eius erectum P R, ergo
              <lb/>
            comparando antecedentes ad terminorum differentias, erit M H ad H G, vt
              <lb/>
              <note position="left" xlink:label="note-0378-01" xlink:href="note-0378-01a" xml:space="preserve">ex 6. hu.</note>
            P Q ad differentiam ipſarum P Q, & </s>
            <s xml:id="echoid-s11884" xml:space="preserve">P R, & </s>
            <s xml:id="echoid-s11885" xml:space="preserve">pariter eorundem quadrata
              <lb/>
            proportionalia erunt, eſtque quadratum ex H M æquale ſemiquadrato ex
              <lb/>
            G H, ergo quadratum ex P Q æquale erit ſemiquadrato ex differentia P Q,
              <lb/>
            & </s>
            <s xml:id="echoid-s11886" xml:space="preserve">P R, & </s>
            <s xml:id="echoid-s11887" xml:space="preserve">ſic quadratum ex p q æquale erit ſemiquadrato ex differentia ip-
              <lb/>
            ſarum p q & </s>
            <s xml:id="echoid-s11888" xml:space="preserve">p r; </s>
            <s xml:id="echoid-s11889" xml:space="preserve">& </s>
            <s xml:id="echoid-s11890" xml:space="preserve">ſunt diametri P Q, & </s>
            <s xml:id="echoid-s11891" xml:space="preserve">p q æquales, cum æquè rece-
              <lb/>
            dant ab axi, & </s>
            <s xml:id="echoid-s11892" xml:space="preserve">habeant latus commune C M.</s>
            <s xml:id="echoid-s11893" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11894" xml:space="preserve">Secundo dico quod ſumma quadratorum ex Q P, & </s>
            <s xml:id="echoid-s11895" xml:space="preserve">ex P R minor eſt qua-
              <lb/>
            libet alia ſumma quadratorum laterum figuræ alterius diametri.</s>
            <s xml:id="echoid-s11896" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11897" xml:space="preserve">Quia duplum rectanguli M H E minus eſt duplo quadrati M H, ſeu ſingu-
              <lb/>
            lari quadrato ex G H, ergo duplum M H ad H G minorem proportionem ha-
              <lb/>
            bet, quàm G H ad H E, ergo duplum rectanguli ex G E, & </s>
            <s xml:id="echoid-s11898" xml:space="preserve">M H in E H
              <lb/>
              <note position="left" xlink:label="note-0378-02" xlink:href="note-0378-02a" xml:space="preserve">Lem. 10.
                <lb/>
              huius.</note>
            minus erit ſumma quadratorum ex G E, & </s>
            <s xml:id="echoid-s11899" xml:space="preserve">ex E H & </s>
            <s xml:id="echoid-s11900" xml:space="preserve">propterea ſumma qua-
              <lb/>
            dratorum ex Q P, & </s>
            <s xml:id="echoid-s11901" xml:space="preserve">ex P R minor erit ſumma quadratorum ex I L, & </s>
            <s xml:id="echoid-s11902" xml:space="preserve">ex
              <lb/>
              <note position="left" xlink:label="note-0378-03" xlink:href="note-0378-03a" xml:space="preserve">Lem. 12.
                <lb/>
              huius.</note>
            I K.</s>
            <s xml:id="echoid-s11903" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11904" xml:space="preserve">Tertio, quia duplum rectanguli ex E H A minus eſt duplo quadrati M H,
              <lb/>
            ſeu ſingulari quadrato ex G H, ergo duplum E H ad H G minorem proportio-
              <lb/>
              <note position="left" xlink:label="note-0378-04" xlink:href="note-0378-04a" xml:space="preserve">Lem. 10.
                <lb/>
              huius.</note>
            nem habet, quàm G H ad H A, ergo duplum rectanguli ex G A, E H in A H
              <lb/>
            minus erit ſumma quadratorum ex G A, & </s>
            <s xml:id="echoid-s11905" xml:space="preserve">ex A H: </s>
            <s xml:id="echoid-s11906" xml:space="preserve">quare ſumma quadra-
              <lb/>
              <note position="left" xlink:label="note-0378-05" xlink:href="note-0378-05a" xml:space="preserve">Lem. 12.
                <lb/>
              huius.</note>
            torum ex I L, & </s>
            <s xml:id="echoid-s11907" xml:space="preserve">ex I K minor erit, quàm quadratorum ſumma ex A C, & </s>
            <s xml:id="echoid-s11908" xml:space="preserve">
              <lb/>
            ex A F.</s>
            <s xml:id="echoid-s11909" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11910" xml:space="preserve">Quarto quia duplum rectanguli V H M maius eſt duplo quadrati ex M H,
              <lb/>
            ſeu ſingulari quadrato ex G H, ergo duplum V H ad H G maiorem proportio-
              <lb/>
            nem habet, quàm H G ad H M, & </s>
            <s xml:id="echoid-s11911" xml:space="preserve">propterea duplum rectanguli ex G M, & </s>
            <s xml:id="echoid-s11912" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0378-06" xlink:href="note-0378-06a" xml:space="preserve">Lem 10
                <lb/>
              huius.</note>
            V H in M H maius erit ſumma quadratorum ex G M, & </s>
            <s xml:id="echoid-s11913" xml:space="preserve">ex M H, & </s>
            <s xml:id="echoid-s11914" xml:space="preserve">ideo
              <lb/>
            ſumma quadratorum ex T S, & </s>
            <s xml:id="echoid-s11915" xml:space="preserve">S Z maior erit quadratorum ſumma ex Q
              <lb/>
              <note position="left" xlink:label="note-0378-07" xlink:href="note-0378-07a" xml:space="preserve">Lem. 12.
                <lb/>
              huius.</note>
            P, & </s>
            <s xml:id="echoid-s11916" xml:space="preserve">ex P R, & </s>
            <s xml:id="echoid-s11917" xml:space="preserve">ſic de reliquis: </s>
            <s xml:id="echoid-s11918" xml:space="preserve">quare ſumma quadratorum ex Q P, & </s>
            <s xml:id="echoid-s11919" xml:space="preserve">ex
              <lb/>
            P R minima eſt omnium, vt fuit propoſitum.</s>
            <s xml:id="echoid-s11920" xml:space="preserve"/>
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