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-div774" type="section" level="1" n="240">
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            <s xml:id="echoid-s9180" xml:space="preserve">
              <pb o="245" file="0283" n="283" rhead="Conicor. Lib. VI."/>
            igitur duo æqualia latera tranſuerſa K L ad ſua latera recta eandem proportio-
              <lb/>
            nem habent, & </s>
            <s xml:id="echoid-s9181" xml:space="preserve">ideo huiuſmodi latera recta æqualia ſunt inter ſe; </s>
            <s xml:id="echoid-s9182" xml:space="preserve">ideoque duæ
              <lb/>
            hyperbole genitæ, habentes vertices in eodem latere F H, æquales ſunt inter ſe,
              <lb/>
            quas vocat Mydorgius ſubcontrarias. </s>
            <s xml:id="echoid-s9183" xml:space="preserve">Simili modo duæ aliæ hyperbole inter ſe,
              <lb/>
              <note position="right" xlink:label="note-0283-01" xlink:href="note-0283-01a" xml:space="preserve">10. huius.</note>
            & </s>
            <s xml:id="echoid-s9184" xml:space="preserve">prioribus æquales in eodem cono duci poßunt, vertices habentes in latere
              <lb/>
            F I.</s>
            <s xml:id="echoid-s9185" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9186" xml:space="preserve">Nec reperitur tertia, cuius vertex ſit ſuper aliqua duarum linearum
              <lb/>
              <note position="left" xlink:label="note-0283-02" xlink:href="note-0283-02a" xml:space="preserve">e</note>
            H F.</s>
            <s xml:id="echoid-s9187" xml:space="preserve">, F I, & </s>
            <s xml:id="echoid-s9188" xml:space="preserve">ſit æqualis ſectioni A B, quia, & </s>
            <s xml:id="echoid-s9189" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9190" xml:space="preserve">Immutaui particulam,
              <lb/>
            quæ propoſitionem reddebat falſam, id quod colligitur ex conſtructione, & </s>
            <s xml:id="echoid-s9191" xml:space="preserve">progreßu
              <lb/>
            demonſtrationis: </s>
            <s xml:id="echoid-s9192" xml:space="preserve">Quælibet enim alia ſectio, præter quatuor aſſignatas, habebit
              <lb/>
            axem æquidiſtantem alicui rectæ vt F Z, quæ cadit inter F N, & </s>
            <s xml:id="echoid-s9193" xml:space="preserve">F S; </s>
            <s xml:id="echoid-s9194" xml:space="preserve">& </s>
            <s xml:id="echoid-s9195" xml:space="preserve">
              <lb/>
            hæc oſtendetur inæqualis prædictis ſectionibus, & </s>
            <s xml:id="echoid-s9196" xml:space="preserve">ipſi A B.</s>
            <s xml:id="echoid-s9197" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9198" xml:space="preserve">Deinde ponamus quadratum F G ad GH maius, quàm D B ad B E.
              <lb/>
            </s>
            <s xml:id="echoid-s9199" xml:space="preserve">
              <note position="left" xlink:label="note-0283-03" xlink:href="note-0283-03a" xml:space="preserve">f</note>
            Dico, non reperiri in cono H F I ſectionem æqualem ſectioni A B: </s>
            <s xml:id="echoid-s9200" xml:space="preserve">nam,
              <lb/>
            ſi reperiretur, eſſet vel æqualis parallela ſuo axi, & </s>
            <s xml:id="echoid-s9201" xml:space="preserve">erit quadratum N
              <lb/>
            F ad I N in N H, &</s>
            <s xml:id="echoid-s9202" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9203" xml:space="preserve">Legendum eße vt in textu dixi conſtat ex progreſſis
              <unsure/>
              <lb/>
            totius propoſitionis. </s>
            <s xml:id="echoid-s9204" xml:space="preserve">I am facili negotio demonſtratio perfici poteſt, nam axis F
              <lb/>
            G minor eſt quàm F N, quæ ſubtendit angulum rectum G, quadratum vero
              <lb/>
            G H ſemiſſius totius H I maius eſt rectangulo I N H, ſub inæqualibus ſegmen-
              <lb/>
            tis contentum; </s>
            <s xml:id="echoid-s9205" xml:space="preserve">propterea quadratum F N ad rectangulum I N H maiorem pro-
              <lb/>
            portionem habebit, quàm quadratum G F ad quadratum G H: </s>
            <s xml:id="echoid-s9206" xml:space="preserve">eſtque D B ad
              <lb/>
            B E, vt quadratum F N ad rectangulum I N H; </s>
            <s xml:id="echoid-s9207" xml:space="preserve">propterea quod F N paral-
              <lb/>
              <note position="right" xlink:label="note-0283-04" xlink:href="note-0283-04a" xml:space="preserve">12. lib. I.</note>
            lela eſt axi illius ſectionis, quæ poſita fuit æqualis A B; </s>
            <s xml:id="echoid-s9208" xml:space="preserve">igitur D B ad B E
              <lb/>
            maiorem proportionem habet, quàm quadratum F G ad quadratum G H; </s>
            <s xml:id="echoid-s9209" xml:space="preserve">quod
              <lb/>
            eſt contra hypotheſin: </s>
            <s xml:id="echoid-s9210" xml:space="preserve">habebat enim quadratum F G ad quadratum G H maio-
              <lb/>
            rem proportionem, quàm D B ad B E. </s>
            <s xml:id="echoid-s9211" xml:space="preserve">Non ergo reperitur in cono; </s>
            <s xml:id="echoid-s9212" xml:space="preserve">&</s>
            <s xml:id="echoid-s9213" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s9214" xml:space="preserve"/>
          </p>
          <figure number="330">
            <image file="0283-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0283-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s9215" xml:space="preserve">Sicutì in præcedenti propoſitione factum eſt, nedum in cono recto, ſed etiam
              <lb/>
            in quolibet cono ſcaleno, quomodolibet per axim ſectio à triangulo H F I deter-
              <lb/>
            minari poßet, quando, & </s>
            <s xml:id="echoid-s9216" xml:space="preserve">quomodo in eo deſignari poſſet ſectio æqualis datæ hy-
              <lb/>
            perbole A B. </s>
            <s xml:id="echoid-s9217" xml:space="preserve">Quod ab alijs factum eſt.</s>
            <s xml:id="echoid-s9218" xml:space="preserve"/>
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