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-s8342" xml:space="preserve">
              <pb o="222" file="0260" n="260" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0260-01" xlink:href="fig-0260-01a" number="304">
                <image file="0260-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0260-01"/>
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            nor eadem G N; </s>
            <s xml:id="echoid-s8343" xml:space="preserve">igitur diſtantia ſectionum G D minor erit quacunque recta
              <lb/>
            linea propoſita. </s>
            <s xml:id="echoid-s8344" xml:space="preserve">Quia verò (vt conſtat ex demonſtratione caſus 2. </s>
            <s xml:id="echoid-s8345" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s8346" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s8347" xml:space="preserve">addit. </s>
            <s xml:id="echoid-s8348" xml:space="preserve">huius) quælibet recta linea G D intercepta inter hyperbolas conueniens
              <lb/>
            cum axi intra ſectiones maior eſt portione eiuſdem rectæ lineæ C D G inter æ-
              <lb/>
            quidiſtantes asymptotos E P, & </s>
            <s xml:id="echoid-s8349" xml:space="preserve">K Q intercepta; </s>
            <s xml:id="echoid-s8350" xml:space="preserve">igitur interuallum inter duas
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            hyperbolas, licet ſucceſſiuè ſemper magis, ac magis diminuatur, nunquàm ta-
              <lb/>
            men minor effici poterit interuallo duarum æquidiſtantium hyperbolas continen-
              <lb/>
            tium E P, & </s>
            <s xml:id="echoid-s8351" xml:space="preserve">K Q; </s>
            <s xml:id="echoid-s8352" xml:space="preserve">Quod quidem eſt perpendiculare ad vtramque rectam con-
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            tinentem E P, & </s>
            <s xml:id="echoid-s8353" xml:space="preserve">K Q; </s>
            <s xml:id="echoid-s8354" xml:space="preserve">eſtque prædicta perpendicularis minima omnium in-
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            terceptarum inter eas.</s>
            <s xml:id="echoid-s8355" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s8356" xml:space="preserve">Duarum parabolarum, vel hyperbolarum A B, D E æqualium, & </s>
            <s xml:id="echoid-s8357" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0260-01" xlink:href="note-0260-01a" xml:space="preserve">PROP. 8.
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              Addit.</note>
            ſimilium, quarum axes A O, D Y, nec non asymptoti H I K, L M N
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            ſint parallelæ inter ſe, & </s>
            <s xml:id="echoid-s8358" xml:space="preserve">ſimiliter poſitæ: </s>
            <s xml:id="echoid-s8359" xml:space="preserve">Sectionum diſtantia maxima
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            parallela erit vertices coniungenti, & </s>
            <s xml:id="echoid-s8360" xml:space="preserve">ei propinquiores ex vtraq; </s>
            <s xml:id="echoid-s8361" xml:space="preserve">parte
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            maiores ſunt remotioribus vſq; </s>
            <s xml:id="echoid-s8362" xml:space="preserve">ad concurſum: </s>
            <s xml:id="echoid-s8363" xml:space="preserve">ſi veró diſtantiam ma-
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            ximam non habent ſemper augentur quo magis à concurſu recedunt.</s>
            <s xml:id="echoid-s8364" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8365" xml:space="preserve">Cadat concurſus ſectionum Z
              <lb/>
              <figure xlink:label="fig-0260-02" xlink:href="fig-0260-02a" number="305">
                <image file="0260-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0260-02"/>
              </figure>
            inter axes A G, & </s>
            <s xml:id="echoid-s8366" xml:space="preserve">D Y, & </s>
            <s xml:id="echoid-s8367" xml:space="preserve">aſym-
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            ptoti I K, M N coincidant, aut
              <lb/>
            ſibi ſint viciniores, quàm I H; </s>
            <s xml:id="echoid-s8368" xml:space="preserve">M
              <lb/>
            L. </s>
            <s xml:id="echoid-s8369" xml:space="preserve">Et primò angulus Y D A ab
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            axe Y D, & </s>
            <s xml:id="echoid-s8370" xml:space="preserve">D A vertices con-
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            iungente contentus ſemirecto minor
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            non ſit in hyperbola, ſitque rectus
              <lb/>
            in parabola, & </s>
            <s xml:id="echoid-s8371" xml:space="preserve">vltra concurſum.
              <lb/>
            </s>
            <s xml:id="echoid-s8372" xml:space="preserve">Z, ad partes axis D Y, & </s>
            <s xml:id="echoid-s8373" xml:space="preserve">asym-
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            ptotorum magis diſſitorum H I,
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            L M: </s>
            <s xml:id="echoid-s8374" xml:space="preserve">ſumantur in compræhenſa ſectione A B quælibet puncta, B, P, à </s>
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