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-div545" type="section" level="1" n="177">
          <p>
            <s xml:id="echoid-s5779" xml:space="preserve">
              <pb o="147" file="0185" n="185" rhead="Conicor. Lib. VI."/>
            ſectioni A C; </s>
            <s xml:id="echoid-s5780" xml:space="preserve">quia ſi eſſet æqualis illi, facta ſuperpoſitione, ſibi mutuò
              <lb/>
            congruerent, & </s>
            <s xml:id="echoid-s5781" xml:space="preserve">caderent puncta E, F, L, I, ſuper B, C, G, K, & </s>
            <s xml:id="echoid-s5782" xml:space="preserve">eſſet
              <lb/>
            F I æqualis C G, atque E L æqualis B K; </s>
            <s xml:id="echoid-s5783" xml:space="preserve">ideoque quadratũ F I ad qua-
              <lb/>
            dratum E L eſſet, vt D I ad D L (19. </s>
            <s xml:id="echoid-s5784" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5785" xml:space="preserve">eſſetque quadratum C G
              <lb/>
              <note position="right" xlink:label="note-0185-01" xlink:href="note-0185-01a" xml:space="preserve">20. lib. 1.</note>
            ad quadratum K B, vt A G ad K A, quod eſt abſurdum; </s>
            <s xml:id="echoid-s5786" xml:space="preserve">quia illius pro-
              <lb/>
            portio ad iſtam eſt, vt H G in G A ad H K in K A (20. </s>
            <s xml:id="echoid-s5787" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s5788" xml:space="preserve">Igitur
              <lb/>
              <note position="right" xlink:label="note-0185-02" xlink:href="note-0185-02a" xml:space="preserve">21. lib. 1</note>
            ſectio parabolica non eſt æqualis ſectioni hyperbolæ, nec ſectio aliqua.
              <lb/>
            </s>
            <s xml:id="echoid-s5789" xml:space="preserve">æqualis eſt ſectioni, quæ non ſit eiuſdem generis; </s>
            <s xml:id="echoid-s5790" xml:space="preserve">Et hoc erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s5791" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div547" type="section" level="1" n="178">
          <head xml:id="echoid-head232" xml:space="preserve">PROPOSITIO VI.</head>
          <p>
            <s xml:id="echoid-s5792" xml:space="preserve">QVælibet duæ ſectiones A B C, & </s>
            <s xml:id="echoid-s5793" xml:space="preserve">D H F, quarum portio
              <lb/>
              <note position="left" xlink:label="note-0185-03" xlink:href="note-0185-03a" xml:space="preserve">a</note>
            vnius ſuperpoſita portioni alterius congruit, ſunt æquales
              <lb/>
            inter ſe.</s>
            <s xml:id="echoid-s5794" xml:space="preserve"/>
          </p>
          <figure number="192">
            <image file="0185-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0185-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s5795" xml:space="preserve">Alioquin congruat portio B C portio-
              <lb/>
              <figure xlink:label="fig-0185-02" xlink:href="fig-0185-02a" number="193">
                <image file="0185-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0185-02"/>
              </figure>
            ni E F, at non cadat portio A B ſuper
              <lb/>
            D E, ſed cadat in ſitu E G, & </s>
            <s xml:id="echoid-s5796" xml:space="preserve">educamus
              <lb/>
            lineam tangentem duas ſectiones in H, & </s>
            <s xml:id="echoid-s5797" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0185-04" xlink:href="note-0185-04a" xml:space="preserve">34. lib. 1.</note>
            educamus E I, D G F parallelas tangen-
              <lb/>
            ti; </s>
            <s xml:id="echoid-s5798" xml:space="preserve">& </s>
            <s xml:id="echoid-s5799" xml:space="preserve">ex H ad ſemipartitionem ipſius E I
              <lb/>
            ducatur H K, quæ occurrat D F in L.
              <lb/>
            </s>
            <s xml:id="echoid-s5800" xml:space="preserve">Et quia H L ſecat bifariam lineam paral-
              <lb/>
            lelam tangenti ab eius termino ductæ; </s>
            <s xml:id="echoid-s5801" xml:space="preserve">
              <lb/>
            ergo eſt diameter vniuerſæ ſectionis (5. </s>
            <s xml:id="echoid-s5802" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0185-05" xlink:href="note-0185-05a" xml:space="preserve">7. lib. 2.</note>
            ex 2.) </s>
            <s xml:id="echoid-s5803" xml:space="preserve">quare bifariam ſecat vnamquan-
              <lb/>
            que ex D F, G F, & </s>
            <s xml:id="echoid-s5804" xml:space="preserve">fiet D L æqualis G
              <lb/>
            L, quod eſt abſurdum: </s>
            <s xml:id="echoid-s5805" xml:space="preserve">igitur ſectio A B
              <lb/>
            C tota congruit ſectioni D H F. </s>
            <s xml:id="echoid-s5806" xml:space="preserve">Quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s5807" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div550" type="section" level="1" n="179">
          <head xml:id="echoid-head233" xml:space="preserve">PROPOSITIO VII.</head>
          <p>
            <s xml:id="echoid-s5808" xml:space="preserve">DVæ ordinationes axis in qualibet coniſectione abſcindunt
              <lb/>
              <note position="left" xlink:label="note-0185-06" xlink:href="note-0185-06a" xml:space="preserve">a</note>
            à ſectione ex vtraque parte axis duas portiones, quarum
              <lb/>
            ſi vna alteri ſuperponatur ſibi mutuò congruent, nec congruunt
              <lb/>
            alicui aliæ portioni ſectionis.</s>
            <s xml:id="echoid-s5809" xml:space="preserve"/>
          </p>
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