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-s8481" xml:space="preserve">
              <pb o="227" file="0265" n="265" rhead="Conicor. Lib. VI."/>
            ipſi C A D circa communem axim A G. </s>
            <s xml:id="echoid-s8482" xml:space="preserve">Et quoniam hyperbolæ H G 1 ſemiaxis
              <lb/>
            tranſuer ſus B G maior eſt tranſuer ſo ſemiaxe B A, hyperboles C A D, pariter-
              <lb/>
            què latus rectum illius maius erit buius latere recto (cum later a figurarum ſint
              <lb/>
              <note position="right" xlink:label="note-0265-01" xlink:href="note-0265-01a" xml:space="preserve">12. huius.</note>
            proportionalia in hyperbolis ſimilibus:) </s>
            <s xml:id="echoid-s8483" xml:space="preserve">igitur hyperbole H G I maior eſt hyper-
              <lb/>
            bola M G N (quod ab alijs oſtenſum eſt), & </s>
            <s xml:id="echoid-s8484" xml:space="preserve">conſiſtunt circa communē axim A G,
              <lb/>
            & </s>
            <s xml:id="echoid-s8485" xml:space="preserve">vertex G eſt communis; </s>
            <s xml:id="echoid-s8486" xml:space="preserve">igitur hyperbole H G I compræbendit hyperbolen M
              <lb/>
            G N; </s>
            <s xml:id="echoid-s8487" xml:space="preserve">& </s>
            <s xml:id="echoid-s8488" xml:space="preserve">ideo hyperbole H G I cadit inter duas hyperbolas G M, & </s>
            <s xml:id="echoid-s8489" xml:space="preserve">A C : </s>
            <s xml:id="echoid-s8490" xml:space="preserve">& </s>
            <s xml:id="echoid-s8491" xml:space="preserve">
              <lb/>
            propterea hyperbole G H multo magis ſucceſſiuè vicinior efficitur hyperbolæ A C,
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            quàm hyperbole G M; </s>
            <s xml:id="echoid-s8492" xml:space="preserve">ſed duæ hyperbole æquales, & </s>
            <s xml:id="echoid-s8493" xml:space="preserve">ſimiliter poſitæ A C, & </s>
            <s xml:id="echoid-s8494" xml:space="preserve">G
              <lb/>
              <note position="right" xlink:label="note-0265-02" xlink:href="note-0265-02a" xml:space="preserve">Propoſ. 7.
                <lb/>
              addit.</note>
            M ſemper magis, ac magis ad inuicem approximantur, igitur multo magis hy-
              <lb/>
            perbolæ concentricæ A C, & </s>
            <s xml:id="echoid-s8495" xml:space="preserve">G H ſemper magis, ac magis ad ſe ſe ipſas appro-
              <lb/>
              <note position="right" xlink:label="note-0265-03" xlink:href="note-0265-03a" xml:space="preserve">lib. 7.
                <lb/>
              prop. 208.
                <lb/>
              29. 30.
                <lb/>
              lib. 5.</note>
            pinquantur, & </s>
            <s xml:id="echoid-s8496" xml:space="preserve">inter ſe non conuenient vt Pappus demonſtrauit. </s>
            <s xml:id="echoid-s8497" xml:space="preserve">Tandem, quoniã
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            lineæ breuiſſimæ, quæ perpendicularis eſt ad tangentem hyperbolem G H portio
              <lb/>
            ab asymptoto E B, & </s>
            <s xml:id="echoid-s8498" xml:space="preserve">ſectione H G compræ henſa effici poteſt minor quacunque
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            recta linea propoſita; </s>
            <s xml:id="echoid-s8499" xml:space="preserve">cadit verò hyperbole A C inter ſectionem G H, & </s>
            <s xml:id="echoid-s8500" xml:space="preserve">continen-
              <lb/>
              <note position="right" xlink:label="note-0265-04" xlink:href="note-0265-04a" xml:space="preserve">Propof. 4.
                <lb/>
              lib. 2.</note>
            tem B E; </s>
            <s xml:id="echoid-s8501" xml:space="preserve">igitur multo magis diſtantia inter hyperbolas G H, & </s>
            <s xml:id="echoid-s8502" xml:space="preserve">A C minor
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            erit quacunque recta linea propofita. </s>
            <s xml:id="echoid-s8503" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s8504" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8505" xml:space="preserve">Si in duobus conis ducta fuerint duo triangula per axes A B C, D E
              <lb/>
              <note position="right" xlink:label="note-0265-05" xlink:href="note-0265-05a" xml:space="preserve">PROP.
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              10. Add.</note>
            F ſimilia, & </s>
            <s xml:id="echoid-s8506" xml:space="preserve">ſimiliter poſita, atq; </s>
            <s xml:id="echoid-s8507" xml:space="preserve">ſectionum I G H, & </s>
            <s xml:id="echoid-s8508" xml:space="preserve">N L M dia-
              <lb/>
            metri G O, L K æque ad baſes inclinatæ intercipiant cũ triangulorum la-
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            teribus A B, D E eiſdem G O, L K parallelis, portiones O B, K E æquales;
              <lb/>
            </s>
            <s xml:id="echoid-s8509" xml:space="preserve">vel cum axibus conorum Aγ, D Z diametris æquidiſtantibus intercipiant
              <lb/>
            portiones O Y, K Z æquales, & </s>
            <s xml:id="echoid-s8510" xml:space="preserve">efficiant angulos A Y C, D Z F
              <lb/>
            aquales : </s>
            <s xml:id="echoid-s8511" xml:space="preserve">erunt conicæ ſectiones inter ſe æquales, & </s>
            <s xml:id="echoid-s8512" xml:space="preserve">in qualibet earum,
              <lb/>
            duplum interceptæ poterit figuram ſectionis.</s>
            <s xml:id="echoid-s8513" xml:space="preserve"/>
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          <figure number="312">
            <image file="0265-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0265-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s8514" xml:space="preserve">Primò in parabolis, quia triangula A B C, D E F ſunt ſimilia, erit B C
              <lb/>
            ad C A vt E F ad F D, & </s>
            <s xml:id="echoid-s8515" xml:space="preserve">G O, L K ſunt parallelæ homologis A B, D E;
              <lb/>
            </s>
            <s xml:id="echoid-s8516" xml:space="preserve">ergo O C ad C G, & </s>
            <s xml:id="echoid-s8517" xml:space="preserve">B O ad G A eandem proportionem habebunt, quàm B C
              <lb/>
            ad C A, ſeu eandem, quàm habet E F ad F D; </s>
            <s xml:id="echoid-s8518" xml:space="preserve">eſtque E K ad L D vt E F
              <lb/>
            ad F D; </s>
            <s xml:id="echoid-s8519" xml:space="preserve">ergo B O ad G A eſt vt E K ad L D; </s>
            <s xml:id="echoid-s8520" xml:space="preserve">ſuntque B O, E K æquales;</s>
            <s xml:id="echoid-s8521" xml:space="preserve"/>
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