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-div160" type="section" level="1" n="67">
          <p>
            <s xml:id="echoid-s2002" xml:space="preserve">
              <pb o="40" file="0078" n="78" rhead="Apollonij Pergæi"/>
            ad N P erit, vt D G ad G F, quæ eſt proportio figuræ; </s>
            <s xml:id="echoid-s2003" xml:space="preserve">ergo C P eſt li-
              <lb/>
            nea breuiſſima. </s>
            <s xml:id="echoid-s2004" xml:space="preserve">(10. </s>
            <s xml:id="echoid-s2005" xml:space="preserve">ex quinto) Et hoc ſuit ptopoſitum.</s>
            <s xml:id="echoid-s2006" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div163" type="section" level="1" n="68">
          <head xml:id="echoid-head100" xml:space="preserve">PROPOSITIO LVII.</head>
          <p>
            <s xml:id="echoid-s2007" xml:space="preserve">Et dico, quod non reperiatur vllus alius ramus, à quo ab-
              <lb/>
              <note position="right" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">g</note>
            ſcindi poſſit inter ſectionem, & </s>
            <s xml:id="echoid-s2008" xml:space="preserve">D B linea breuiſſima.</s>
            <s xml:id="echoid-s2009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2010" xml:space="preserve">NAm ſi producantur E H, E G ad vtraſque partes ipſius E C ſecan-
              <lb/>
              <note position="right" xlink:label="note-0078-02" xlink:href="note-0078-02a" xml:space="preserve">h</note>
            tes D B in K, I, & </s>
            <s xml:id="echoid-s2011" xml:space="preserve">producamus per D perpendicularem ad A B,
              <lb/>
            quæ occurrat ſectioni ad L,
              <lb/>
              <figure xlink:label="fig-0078-01" xlink:href="fig-0078-01a" number="54">
                <image file="0078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0078-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s2012" xml:space="preserve">ipſi E C ad M, quia iam
              <lb/>
              <note position="right" xlink:label="note-0078-03" xlink:href="note-0078-03a" xml:space="preserve">i</note>
            productæ ſunt ex concurſu
              <lb/>
            M duæ breuiſecantes M C,
              <lb/>
            M L (51. </s>
            <s xml:id="echoid-s2013" xml:space="preserve">ex quinto) igitur
              <lb/>
            linea educta ex M ad H ab-
              <lb/>
            ſcindit ex D B cum B ma-
              <lb/>
            iorem lineam, quàm ſecat
              <lb/>
              <note position="right" xlink:label="note-0078-04" xlink:href="note-0078-04a" xml:space="preserve">k</note>
            breuiſſima egrediens ex H
              <lb/>
            (11. </s>
            <s xml:id="echoid-s2014" xml:space="preserve">ex quinto) & </s>
            <s xml:id="echoid-s2015" xml:space="preserve">linea edu-
              <lb/>
            cta ex M ad G abſcindit ex
              <lb/>
            D B lineam minorem ea,
              <lb/>
            quàm ſecat linea breuiſſima egrediens ex G (51. </s>
            <s xml:id="echoid-s2016" xml:space="preserve">ex quinto) ſed E H, & </s>
            <s xml:id="echoid-s2017" xml:space="preserve">
              <lb/>
            E G efficiunt abſciſſas oppoſito modo; </s>
            <s xml:id="echoid-s2018" xml:space="preserve">ergo non ſunt duæ breuiſecantes,
              <lb/>
            & </s>
            <s xml:id="echoid-s2019" xml:space="preserve">propterea non reperitur alius ramus, cui competat proprietas ipſius E
              <lb/>
            C, & </s>
            <s xml:id="echoid-s2020" xml:space="preserve">hoc erat oſtendendum.</s>
            <s xml:id="echoid-s2021" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div166" type="section" level="1" n="69">
          <head xml:id="echoid-head101" xml:space="preserve">Notæ in Propoſit. IL. L.</head>
          <p>
            <s xml:id="echoid-s2022" xml:space="preserve">SI verò menſura excedit comparatam educatur linea, ad quam com-
              <lb/>
              <note position="right" xlink:label="note-0078-05" xlink:href="note-0078-05a" xml:space="preserve">a</note>
            paratur perpendicularis, & </s>
            <s xml:id="echoid-s2023" xml:space="preserve">vocabo lineam illam Trutinam, &</s>
            <s xml:id="echoid-s2024" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2025" xml:space="preserve">Sic
              <lb/>
            legendum puto: </s>
            <s xml:id="echoid-s2026" xml:space="preserve">Si verò menſura excedit comparatam exponi debet linea certis
              <lb/>
            quibuſdam legibus inuenienda, quæ vocabitur Trutina.</s>
            <s xml:id="echoid-s2027" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2028" xml:space="preserve">Ex E concurſu ſuper perpendicularem, &</s>
            <s xml:id="echoid-s2029" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2030" xml:space="preserve">Ideſt. </s>
            <s xml:id="echoid-s2031" xml:space="preserve">Ex E concurſu per-
              <lb/>
              <note position="right" xlink:label="note-0078-06" xlink:href="note-0078-06a" xml:space="preserve">b</note>
            pendicularis E D ad axim A G, & </s>
            <s xml:id="echoid-s2032" xml:space="preserve">ramoram ſecantium educamus E B ſecantem
              <lb/>
            menſuram, &</s>
            <s xml:id="echoid-s2033" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2034" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2035" xml:space="preserve">Tunc B F non eſt ex minimis, &</s>
            <s xml:id="echoid-s2036" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2037" xml:space="preserve">Dico quod B F non erit recta linea
              <lb/>
              <note position="right" xlink:label="note-0078-07" xlink:href="note-0078-07a" xml:space="preserve">c</note>
            minima earum, quæ inter punctum ſectionis B, & </s>
            <s xml:id="echoid-s2038" xml:space="preserve">axim intercipitur.</s>
            <s xml:id="echoid-s2039" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2040" xml:space="preserve">Et ponatur G I æqualis A H, &</s>
            <s xml:id="echoid-s2041" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2042" xml:space="preserve">Et ponatur G I æqualis A H, iungatur-
              <lb/>
              <note position="right" xlink:label="note-0078-08" xlink:href="note-0078-08a" xml:space="preserve">d</note>
            que B G, cumque A D poſita ſit non maior, quàm H A, erit illius portio F I
              <lb/>
              <note position="left" xlink:label="note-0078-09" xlink:href="note-0078-09a" xml:space="preserve">8. huius.</note>
            minor, quàm A H, ſeu quàm G I, ergo B G eſt breuiſsima, &</s>
            <s xml:id="echoid-s2043" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2044" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2045" xml:space="preserve">Ergo C A ad A H non habet maiorem proportionem, quàm ad A D;
              <lb/>
            </s>
            <s xml:id="echoid-s2046" xml:space="preserve">
              <note position="right" xlink:label="note-0078-10" xlink:href="note-0078-10a" xml:space="preserve">e</note>
            quare D I ad I F, &</s>
            <s xml:id="echoid-s2047" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2048" xml:space="preserve">Ergo G A ad A H non habet maiorem proportionem,
              <lb/>
            quàm ad A D, & </s>
            <s xml:id="echoid-s2049" xml:space="preserve">addatur indirectum recta A L æqualis A H in hyperbola, &</s>
            <s xml:id="echoid-s2050" xml:space="preserve"/>
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