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-div471" type="section" level="1" n="145">
          <pb o="128" file="0166" n="166" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div474" type="section" level="1" n="146">
          <head xml:id="echoid-head195" xml:space="preserve">PR OPOSITIO XXXIX.</head>
          <p>
            <s xml:id="echoid-s5035" xml:space="preserve">IN ſectione A B elliptica quælibet
              <lb/>
              <figure xlink:label="fig-0166-01" xlink:href="fig-0166-01a" number="162">
                <image file="0166-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0166-01"/>
              </figure>
            perpendicularis F D ad lineam
              <lb/>
            maximam C D, ab eius termino D
              <lb/>
            in ſectione poſito educta, continget
              <lb/>
            coniſectionem.</s>
            <s xml:id="echoid-s5036" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5037" xml:space="preserve">Alioquin ſecet illam, & </s>
            <s xml:id="echoid-s5038" xml:space="preserve">in eius produ-
              <lb/>
            ctione D G ſumatur punctum G intra ſe-
              <lb/>
              <note position="right" xlink:label="note-0166-01" xlink:href="note-0166-01a" xml:space="preserve">a</note>
            ctionem: </s>
            <s xml:id="echoid-s5039" xml:space="preserve">& </s>
            <s xml:id="echoid-s5040" xml:space="preserve">educamus B G C, igitur G
              <lb/>
            C maior eſt, quàm C D, quia ſubtendit
              <lb/>
            rectum angulum C D G, & </s>
            <s xml:id="echoid-s5041" xml:space="preserve">propterea B C multo maior eſt, quàm C D,
              <lb/>
            quod eſt abſurdum; </s>
            <s xml:id="echoid-s5042" xml:space="preserve">igitur educta illa linea eſt tangens; </s>
            <s xml:id="echoid-s5043" xml:space="preserve">quod erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s5044" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div477" type="section" level="1" n="147">
          <head xml:id="echoid-head196" xml:space="preserve">PROPOSITIO XXXX.</head>
          <p>
            <s xml:id="echoid-s5045" xml:space="preserve">E Contra ſi fuerit F D tangens, erit perpendicularis ſuper
              <lb/>
            maximam D C.</s>
            <s xml:id="echoid-s5046" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5047" xml:space="preserve">Alioquin educamus aliam E D perpendicularem ſuper illam; </s>
            <s xml:id="echoid-s5048" xml:space="preserve">ergo E
              <lb/>
            D tangit ſectionem in puncto D (39. </s>
            <s xml:id="echoid-s5049" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s5050" xml:space="preserve">ſed F D ſuppoſita fuit tan-
              <lb/>
            gens; </s>
            <s xml:id="echoid-s5051" xml:space="preserve">igitur duæ D F, & </s>
            <s xml:id="echoid-s5052" xml:space="preserve">D E tangunt ſectionem in vno puncto, quod
              <lb/>
            eſt abſurdum (36. </s>
            <s xml:id="echoid-s5053" xml:space="preserve">ex I.)</s>
            <s xml:id="echoid-s5054" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div478" type="section" level="1" n="148">
          <head xml:id="echoid-head197" xml:space="preserve">PROPOSITIO XXXXVII.</head>
          <p>
            <s xml:id="echoid-s5055" xml:space="preserve">Q Vælibet linea D E ex puncto
              <lb/>
              <figure xlink:label="fig-0166-02" xlink:href="fig-0166-02a" number="163">
                <image file="0166-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0166-02"/>
              </figure>
            contactus D ad axim alicuius
              <lb/>
            ſectionis A B educta per-
              <lb/>
            pendicularis ad tangentem D C,
              <lb/>
            erit linea breuiſſima, aut maxima.</s>
            <s xml:id="echoid-s5056" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5057" xml:space="preserve">Alioquin educamus D F breuiſſimam,
              <lb/>
              <note position="left" xlink:label="note-0166-02" xlink:href="note-0166-02a" xml:space="preserve">Ex 10. & 20. huius.</note>
            vel maximam; </s>
            <s xml:id="echoid-s5058" xml:space="preserve">ergo D C perpendicularis
              <lb/>
            eſt ſuper D F; </s>
            <s xml:id="echoid-s5059" xml:space="preserve">ſed C D ſuppoſita fuit per-
              <lb/>
              <note position="left" xlink:label="note-0166-03" xlink:href="note-0166-03a" xml:space="preserve">40. huius.</note>
            pendicularis ſuper D E; </s>
            <s xml:id="echoid-s5060" xml:space="preserve">quod eſt abſur-
              <lb/>
            dum: </s>
            <s xml:id="echoid-s5061" xml:space="preserve">quapropter demonſtratũ eſt, quod
              <lb/>
            fuerat propoſitum.</s>
            <s xml:id="echoid-s5062" xml:space="preserve"/>
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