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-div179" type="section" level="1" n="71">
          <pb o="45" file="0083" n="83" rhead="Conicor. Lib. V."/>
          <p style="it">
            <s xml:id="echoid-s2157" xml:space="preserve">Et ſimiliter patebit, quod L S ſit breuiſſima, &</s>
            <s xml:id="echoid-s2158" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2159" xml:space="preserve">Secundus caſus abſque vllo
              <lb/>
              <note position="left" xlink:label="note-0083-01" xlink:href="note-0083-01a" xml:space="preserve">k</note>
            labore oſtenſus erit ijſdem verbis, & </s>
            <s xml:id="echoid-s2160" xml:space="preserve">caracteribus, quibus caſus primus expoſitus
              <lb/>
            fuit, ſi inſpiciatur ſecunda figura.</s>
            <s xml:id="echoid-s2161" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2162" xml:space="preserve">Et cum B I intercipiatur inter illas patebit etiam, &</s>
            <s xml:id="echoid-s2163" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2164" xml:space="preserve">Et cum B I intercipia-
              <lb/>
              <note position="left" xlink:label="note-0083-02" xlink:href="note-0083-02a" xml:space="preserve">l</note>
            tur inter duos ramos breuiſecantes E K, qui ducuntur ex punctis K, in quibus hy-
              <lb/>
            perbole K T L ſecat parabolen A B L, cadet punctum T hyperboles intra parabolen;
              <lb/>
            </s>
            <s xml:id="echoid-s2165" xml:space="preserve">quare rectangulum B G F maius erit rectangulo T G F, ſeu K M F, quod æquale eſt
              <lb/>
            rectangulo E D F, vt dictum eſt, quare E D ad B G, ſeu D I ad I G (propter ſimili-
              <lb/>
              <note position="right" xlink:label="note-0083-03" xlink:href="note-0083-03a" xml:space="preserve">Lem. 5.
                <lb/>
              præmiſ.</note>
            tudinem triangulorum E D I, B G I) habebit minorem proportionem, quàm G F ad
              <lb/>
            F D, & </s>
            <s xml:id="echoid-s2166" xml:space="preserve">componendo, eadem D G ad G I minorem proportionem habebit, quàm ad
              <lb/>
            F D, ſiue ad A C, & </s>
            <s xml:id="echoid-s2167" xml:space="preserve">ideo I G maior erit, quàm A C.</s>
            <s xml:id="echoid-s2168" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2169" xml:space="preserve">Deinde ex con-
              <lb/>
              <note position="left" xlink:label="note-0083-04" xlink:href="note-0083-04a" xml:space="preserve">m</note>
              <figure xlink:label="fig-0083-01" xlink:href="fig-0083-01a" number="60">
                <image file="0083-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0083-01"/>
              </figure>
            curſu E ad ſectio-
              <lb/>
            nem, &</s>
            <s xml:id="echoid-s2170" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2171" xml:space="preserve">Deinde
              <lb/>
            ex concurſu E ad ſe-
              <lb/>
            ctionem A B parabo-
              <lb/>
            len educantur duo ra-
              <lb/>
            mi E X ſupra breui-
              <lb/>
            ſecantem E K in pri-
              <lb/>
            ma figura, & </s>
            <s xml:id="echoid-s2172" xml:space="preserve">infra
              <lb/>
            eamdem in figura ſe-
              <lb/>
            cunda, & </s>
            <s xml:id="echoid-s2173" xml:space="preserve">ex punct is
              <lb/>
            X ducantur due X Y
              <lb/>
            perpendiculares ad
              <lb/>
            axim, ſecantes axim
              <lb/>
            in Y, & </s>
            <s xml:id="echoid-s2174" xml:space="preserve">hyperbolen K
              <lb/>
            T in a exiſtẽte extra
              <lb/>
            parabolen; </s>
            <s xml:id="echoid-s2175" xml:space="preserve">cumque
              <lb/>
            duæ rectæ a Y, necnõ
              <lb/>
            T G parallelæ ſint cõ-
              <lb/>
            tinenti F V, & </s>
            <s xml:id="echoid-s2176" xml:space="preserve">inter-
              <lb/>
            ponātur inter hyper-
              <lb/>
            bolẽ K T, & </s>
            <s xml:id="echoid-s2177" xml:space="preserve">reliquã
              <lb/>
            continentem F A eritrectangulum a Y F æquale rectangulo T G F, quod factum
              <lb/>
              <note position="right" xlink:label="note-0083-05" xlink:href="note-0083-05a" xml:space="preserve">12. lib. 2.</note>
            eſt æquale rectangulo E D F, eſtque X Y portio ipſius a Y; </s>
            <s xml:id="echoid-s2178" xml:space="preserve">igitur rectangulum E D F
              <lb/>
            maius erit rectangulo X Y F, & </s>
            <s xml:id="echoid-s2179" xml:space="preserve">ideo E D ad X Y, ſeu D b, ad b Y (propter ſimilitu-
              <lb/>
              <note position="right" xlink:label="note-0083-06" xlink:href="note-0083-06a" xml:space="preserve">Lem. 5.
                <lb/>
              præmiſ.</note>
            dinem triangulorum E D b, X Y b) maiorem rationem habet, quàm Y F ad F D, & </s>
            <s xml:id="echoid-s2180" xml:space="preserve">
              <lb/>
            componendo eadem D Y ad Y b maiorem proportionem habebit, quàm ad D F, ſeu
              <lb/>
            C A.</s>
            <s xml:id="echoid-s2181" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2182" xml:space="preserve">Simili modo demonſtrabitur, &</s>
            <s xml:id="echoid-s2183" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2184" xml:space="preserve">Abſquenoua demonſtratione propoſitum
              <lb/>
              <note position="left" xlink:label="note-0083-07" xlink:href="note-0083-07a" xml:space="preserve">n</note>
            oſtendetur inſpiciendo ſecundam ſiguram.</s>
            <s xml:id="echoid-s2185" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div187" type="section" level="1" n="72">
          <head xml:id="echoid-head105" xml:space="preserve">Notæ in Propoſ. LII. LIII.</head>
          <p style="it">
            <s xml:id="echoid-s2186" xml:space="preserve">DIco, quod rami egredientes ex E habent ſuperiùs expoſitas proprieta-
              <lb/>
              <note position="left" xlink:label="note-0083-08" xlink:href="note-0083-08a" xml:space="preserve">a</note>
            tes, &</s>
            <s xml:id="echoid-s2187" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2188" xml:space="preserve">Ideſt eaſdem, quas habent rami in parabola educti iuxta compara-
              <lb/>
            tionem perpendicularis E D ad T rutinam.</s>
            <s xml:id="echoid-s2189" xml:space="preserve"/>
          </p>
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