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="20" file="0058" n="58" rhead="Apollonij Pergæi"/>
            ſed potius ex vndecima libri primi;
              <lb/>
            </s>
            <s xml:id="echoid-s1300" xml:space="preserve">
              <figure xlink:label="fig-0058-01" xlink:href="fig-0058-01a" number="29">
                <image file="0058-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0058-01"/>
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            eſt enim quadratum H N æquale re-
              <lb/>
            ctangulo contento ſub abſciſſa H C,
              <lb/>
            & </s>
            <s xml:id="echoid-s1301" xml:space="preserve">ſub latere recto, eſtque rectangu-
              <lb/>
            lum ſub H C, & </s>
            <s xml:id="echoid-s1302" xml:space="preserve">ſub ſemierecto C G
              <lb/>
            ſemiſsis illius; </s>
            <s xml:id="echoid-s1303" xml:space="preserve">igitur quadratum H
              <lb/>
            N æquale eſt duplo rectanguli H C G.</s>
            <s xml:id="echoid-s1304" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">d</note>
          <p style="it">
            <s xml:id="echoid-s1305" xml:space="preserve">Hoc autem eſt æquale duobus
              <lb/>
            quadratis I H, H Q, & </s>
            <s xml:id="echoid-s1306" xml:space="preserve">I H in H
              <lb/>
            Q bis, &</s>
            <s xml:id="echoid-s1307" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1308" xml:space="preserve">Poſt hæc verba ſubiun-
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            go claritatis gratia, atque C H in H
              <lb/>
            I bis æquale eſt duplo C Q in H I
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            vna cum duplo Q H in H I.</s>
            <s xml:id="echoid-s1309" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s1310" xml:space="preserve">Ergo quadratum B I æquale eſt
              <lb/>
              <note position="right" xlink:label="note-0058-02" xlink:href="note-0058-02a" xml:space="preserve">e</note>
            I C in I H bis, &</s>
            <s xml:id="echoid-s1311" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1312" xml:space="preserve">Hìc pariter, vt
              <lb/>
            clarior reddatur demõſtratio, ſubiun-
              <lb/>
            go, ſcilicet duplo rectãguli C H I vna
              <lb/>
            cum duplo quadrati H I; </s>
            <s xml:id="echoid-s1313" xml:space="preserve">erat autem
              <lb/>
            quadratum N I æquale duplo rectan-
              <lb/>
            guli C H I, & </s>
            <s xml:id="echoid-s1314" xml:space="preserve">vnico quadrato H I,
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            ergo, &</s>
            <s xml:id="echoid-s1315" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1316" xml:space="preserve"/>
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            <s xml:id="echoid-s1317" xml:space="preserve">Et quia quadratum OR æqua-
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              <note position="right" xlink:label="note-0058-03" xlink:href="note-0058-03a" xml:space="preserve">f</note>
            le eſt C R in I H bis, &</s>
            <s xml:id="echoid-s1318" xml:space="preserve">c.
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            </s>
            <s xml:id="echoid-s1319" xml:space="preserve">
              <figure xlink:label="fig-0058-02" xlink:href="fig-0058-02a" number="30">
                <image file="0058-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0058-02"/>
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            Subiungo hanc declarationem.
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            </s>
            <s xml:id="echoid-s1320" xml:space="preserve">Scilicet duplo rectanguli C H
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            I, & </s>
            <s xml:id="echoid-s1321" xml:space="preserve">duplo quadrati H I cum
              <lb/>
            duplo rectanguli R I H. </s>
            <s xml:id="echoid-s1322" xml:space="preserve">Qua-
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            re quadratum I O æquale eſt
              <lb/>
            quadrato R I, duplo quadrati
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            H I, duplo rectanguli R I H,
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            & </s>
            <s xml:id="echoid-s1323" xml:space="preserve">duplo rectanguli C H I: </s>
            <s xml:id="echoid-s1324" xml:space="preserve">ſed
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            quadratũ H R æquale eſt qua-
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            drato R I, quadrato I H cum
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            duplo rectanguli R I H. </s>
            <s xml:id="echoid-s1325" xml:space="preserve">Ergo
              <lb/>
            quadratum I O æquale eſt qua-
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            drato H R, quadrato H I cum duplo rectanguli C H I; </s>
            <s xml:id="echoid-s1326" xml:space="preserve">erat autem prius qua-
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            dratum I N æquale quadrato I H cum duplo rectanguli C H I. </s>
            <s xml:id="echoid-s1327" xml:space="preserve">Igitur exceßus
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            quadrati I O ſupra quadratum I N eſt quadratum H R.</s>
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