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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            <s xml:id="echoid-s2628" xml:space="preserve">
              <pb o="58" file="0096" n="96" rhead="Apollonij Pergæi"/>
            vt E L ad L D (propter parallelas I D, H L) pariterque D N ad N I eſt, vt E H
              <lb/>
            ad H I (porpter parallelas E D, N H) quare D N ad N I erit vt E L ad L D,
              <lb/>
            & </s>
            <s xml:id="echoid-s2629" xml:space="preserve">propterea D N ad N I minorem proportionem habebit, quàm latus tranſuer-
              <lb/>
            ſum C A ad eius latus rectum, & </s>
            <s xml:id="echoid-s2630" xml:space="preserve">ideo linea breuiſsima ex puncto H ad axim
              <lb/>
              <note position="left" xlink:label="note-0096-01" xlink:href="note-0096-01a" xml:space="preserve">10. huius.</note>
            A D ducta cadet ſupra ramum H I E verſus verticem A, atq; </s>
            <s xml:id="echoid-s2631" xml:space="preserve">E H non erit bre-
              <lb/>
            uiſecans, quod erat primo loco oſtendendum.</s>
            <s xml:id="echoid-s2632" xml:space="preserve"/>
          </p>
          <figure number="72">
            <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0096-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s2633" xml:space="preserve">Secundo ducatur ramus E O ſecans maiorem axim in P inter verticem A, & </s>
            <s xml:id="echoid-s2634" xml:space="preserve">
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            breuiſecantem E F; </s>
            <s xml:id="echoid-s2635" xml:space="preserve">Dico E O non eſſe breuiſecantem, & </s>
            <s xml:id="echoid-s2636" xml:space="preserve">breuiſsimam ex puncto
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            O ad axim A D ductam cadere infra ramum O P E; </s>
            <s xml:id="echoid-s2637" xml:space="preserve">Ducantur O Q, O R per-
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            pendiculares ad axes, ſecantes eos in Q, R. </s>
            <s xml:id="echoid-s2638" xml:space="preserve">Manifeſtum eſt Q D minorem eſſe,
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            quàm K D, & </s>
            <s xml:id="echoid-s2639" xml:space="preserve">propterea E D ad D Q maiorem proportionem habebit, quàm ad
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            D K, & </s>
            <s xml:id="echoid-s2640" xml:space="preserve">componendo E Q ad Q D maiorem proportionem habebit, quàm E K
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            ad K D: </s>
            <s xml:id="echoid-s2641" xml:space="preserve">oſtenſa autem fuit E K ad K D, vt latus tranſuerſum C A ad eius la-
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            tus rectum; </s>
            <s xml:id="echoid-s2642" xml:space="preserve">igitur E Q ad Q D maiorem proportionem habebit, quàm latus
              <lb/>
            tranſuerſum ad rectum; </s>
            <s xml:id="echoid-s2643" xml:space="preserve">ſed (propter parallelas P D, O Q) vt E Q ad Q D
              <lb/>
            ita eſt E O ad O P, & </s>
            <s xml:id="echoid-s2644" xml:space="preserve">propter parallelas E D, R O, vt E O ad O P, ita eſt D R
              <lb/>
            ad R P; </s>
            <s xml:id="echoid-s2645" xml:space="preserve">ergo D R ad R P eſt, vt E Q ad Q D, & </s>
            <s xml:id="echoid-s2646" xml:space="preserve">propterea D R ad R P ma-
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            iorem proportionem habebit, quàm latus tranuer ſum C A ad eius latus rectum;
              <lb/>
            </s>
            <s xml:id="echoid-s2647" xml:space="preserve">igitur E O non erit breuiſecans, & </s>
            <s xml:id="echoid-s2648" xml:space="preserve">breuiſsima ex puncto O ad axim ducta cadit
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            infra ramum E O verſus D, quod erat oſtendendum.</s>
            <s xml:id="echoid-s2649" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">ex 10.
            <lb/>
          huius.</note>
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        <div xml:id="echoid-div232" type="section" level="1" n="77">
          <head xml:id="echoid-head110" xml:space="preserve">Notæ in Propoſ. LVII.</head>
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            <s xml:id="echoid-s2650" xml:space="preserve">ET dico, quod non repe-
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              <figure xlink:label="fig-0096-02" xlink:href="fig-0096-02a" number="73">
                <image file="0096-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0096-02"/>
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            riatur vllus alius ramus,
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            &</s>
            <s xml:id="echoid-s2651" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2652" xml:space="preserve">Ideſt ſit rurſus linea bre-
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            uiſsima C M, quæ producta,
              <lb/>
            concurrat cum perpendiculari E
              <lb/>
            F in E, quæ ſecet axim in F
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            vltra centrum D ad partes ver-
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            ticis A. </s>
            <s xml:id="echoid-s2653" xml:space="preserve">Dico, quod præter </s>
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