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-div919" type="section" level="1" n="288">
          <pb o="300" file="0338" n="339" rhead="Apollonij Pergæi"/>
          <p>
            <s xml:id="echoid-s10846" xml:space="preserve">XXI. </s>
            <s xml:id="echoid-s10847" xml:space="preserve">Deinde ſit A C æqualis QR in hyperbola fiet A C æqualis ere-
              <lb/>
            cto, & </s>
            <s xml:id="echoid-s10848" xml:space="preserve">conuenient duo puncta H, & </s>
            <s xml:id="echoid-s10849" xml:space="preserve">G in puncto D, eritque A C ad
              <lb/>
              <note position="right" xlink:label="note-0338-01" xlink:href="note-0338-01a" xml:space="preserve">b</note>
              <figure xlink:label="fig-0338-01" xlink:href="fig-0338-01a" number="392">
                <image file="0338-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0338-01"/>
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            Q R vt A D ad ſe ipſam, ſiue vt A C ad ſe ipſam, quæ eſt vt D E ad
              <lb/>
            ſe ipſam, & </s>
            <s xml:id="echoid-s10850" xml:space="preserve">hæc oſtenſa eſt, vt quadratum I L ad quadratum N O; </s>
            <s xml:id="echoid-s10851" xml:space="preserve">igi-
              <lb/>
              <note position="left" xlink:label="note-0338-02" xlink:href="note-0338-02a" xml:space="preserve">Prop. 6.
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              huius.</note>
            tur I L, & </s>
            <s xml:id="echoid-s10852" xml:space="preserve">N O ſunt æquales, & </s>
            <s xml:id="echoid-s10853" xml:space="preserve">ſic demonſtrabitur, quod S T, V X ſunt
              <lb/>
            æquales, & </s>
            <s xml:id="echoid-s10854" xml:space="preserve">hoc erat propoſitum.</s>
            <s xml:id="echoid-s10855" xml:space="preserve"/>
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          <head xml:id="echoid-head360" xml:space="preserve">PROPOSITIO XXVI</head>
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            <s xml:id="echoid-s10856" xml:space="preserve">
              <emph style="sc">At</emph>
            in ellipſi fieri po-
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            teſt, vt H E ſit æ-
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            qualis E G, ſi nimirum
              <lb/>
            punctum B cadat in Q, & </s>
            <s xml:id="echoid-s10857" xml:space="preserve">
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            tunc B E cadetſuper Q D,
              <lb/>
            & </s>
            <s xml:id="echoid-s10858" xml:space="preserve">erit diameter I L æqua-
              <lb/>
            lis ſuæ coniugatæ; </s>
            <s xml:id="echoid-s10859" xml:space="preserve">& </s>
            <s xml:id="echoid-s10860" xml:space="preserve">vo-
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            cabo eas æquales.</s>
            <s xml:id="echoid-s10861" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s10862" xml:space="preserve">Quia C G ad C H, nempe
              <lb/>
            quadratum A C ad ſuam fi-
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            guram maiorem proportionem
              <lb/>
            habet in primis figuris, & </s>
            <s xml:id="echoid-s10863" xml:space="preserve">mi-
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            norem in ſecunda ellipſi, quàm
              <lb/>
            C G ad G E, nempe quàm
              <lb/>
            quadratum A C ad figuram
              <lb/>
            ipſius I L ( 18. </s>
            <s xml:id="echoid-s10864" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s10865" xml:space="preserve">) & </s>
            <s xml:id="echoid-s10866" xml:space="preserve">C
              <lb/>
            G ad G E in primis figurisma-
              <lb/>
            iorem proportionem habet, &</s>
            <s xml:id="echoid-s10867" xml:space="preserve"/>
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