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-div232" type="section" level="1" n="77">
          <p style="it">
            <s xml:id="echoid-s2653" xml:space="preserve">
              <pb o="59" file="0097" n="97" rhead="Conicor. Lib. V."/>
            mum E C nullus alius ramus breuiſecans ex concurſu E ad ſectionem duci poteſt,
              <lb/>
            qui cadat in eodem quadrante B L, quem breuiſecans interſecat.</s>
            <s xml:id="echoid-s2654" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2655" xml:space="preserve">Nam ſi producantur E H, E G, &</s>
            <s xml:id="echoid-s2656" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2657" xml:space="preserve">Ducantur quilibet rami E H, E G ad
              <lb/>
              <note position="left" xlink:label="note-0097-01" xlink:href="note-0097-01a" xml:space="preserve">h</note>
            vtraſque partes breuiſecantis E C intra quadrantem B L, qui ſecent D B in K,
              <lb/>
            & </s>
            <s xml:id="echoid-s2658" xml:space="preserve">I, & </s>
            <s xml:id="echoid-s2659" xml:space="preserve">producatur per centrum D recta M D L perpendicularis ad axim B A,
              <lb/>
            quæ ſecet ſectionem in L, & </s>
            <s xml:id="echoid-s2660" xml:space="preserve">ramum E C in M.</s>
            <s xml:id="echoid-s2661" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2662" xml:space="preserve">Et quia iam productæ ſunt ex concurſu M duæ breuiſecantes, &</s>
            <s xml:id="echoid-s2663" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s2664" xml:space="preserve">
              <note position="left" xlink:label="note-0097-02" xlink:href="note-0097-02a" xml:space="preserve">i</note>
            Quia C M breuiſsima ex hypotheſi occurrit ſemiaxi minori recto L D breuiſsi-
              <lb/>
            mæ pariter (ex 11. </s>
            <s xml:id="echoid-s2665" xml:space="preserve">huius) in M, ſequitur (non quidem ex 51. </s>
            <s xml:id="echoid-s2666" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2667" xml:space="preserve">huius, ſed
              <lb/>
            ex lemmate 8. </s>
            <s xml:id="echoid-s2668" xml:space="preserve">præmiſſo) quod linea recta ex M ad H coniuncta cadat infra
              <lb/>
            breuiſsimam ex puncto H ad axim B A ductam, & </s>
            <s xml:id="echoid-s2669" xml:space="preserve">coniuncta recta M G cadit
              <lb/>
            ſupra breuiſsimam ex puncto G ad axim ductam.</s>
            <s xml:id="echoid-s2670" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2671" xml:space="preserve">Sed E H, & </s>
            <s xml:id="echoid-s2672" xml:space="preserve">E G efficiunt abſciſsas oppoſito modo, &</s>
            <s xml:id="echoid-s2673" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2674" xml:space="preserve">Quia ab eodem
              <lb/>
              <note position="left" xlink:label="note-0097-03" xlink:href="note-0097-03a" xml:space="preserve">k</note>
            puncto H ſectionis ducuntur tres rectæ lineæ. </s>
            <s xml:id="echoid-s2675" xml:space="preserve">H E, H M, & </s>
            <s xml:id="echoid-s2676" xml:space="preserve">breuiſsima ex H ad
              <lb/>
            axim B A ducta, quarum intermedia eſt H M, eo quod breuiſsima ex H ad
              <lb/>
            axim A B cadit ſupra H M ad partes B, vt dictum eſt, & </s>
            <s xml:id="echoid-s2677" xml:space="preserve">H E cadit
              <lb/>
              <note position="right" xlink:label="note-0097-04" xlink:href="note-0097-04a" xml:space="preserve">Lem 8.</note>
            infra H M ad partes A; </s>
            <s xml:id="echoid-s2678" xml:space="preserve">ergo H E cadit infra breuiſsimam ex
              <lb/>
            H ad A B ductam, & </s>
            <s xml:id="echoid-s2679" xml:space="preserve">propterea E H nan erit breuiſecans:
              <lb/>
            </s>
            <s xml:id="echoid-s2680" xml:space="preserve">Similiter breuiſsimaex G ad A B extenſa cadit infra
              <lb/>
            G M ad partes A, vt dictum eſt; </s>
            <s xml:id="echoid-s2681" xml:space="preserve">at E G cadit
              <lb/>
              <note position="right" xlink:label="note-0097-05" xlink:href="note-0097-05a" xml:space="preserve">1 bidem.</note>
            ſupra G M ad partes B; </s>
            <s xml:id="echoid-s2682" xml:space="preserve">ergo E G cadit
              <lb/>
            ſupra breuiſsimam ex G ad axim
              <lb/>
            A B ductam, quare E G non
              <lb/>
            eſt breuiſecans.</s>
            <s xml:id="echoid-s2683" xml:space="preserve"/>
          </p>
          <figure number="74">
            <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-01"/>
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