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-div146" type="section" level="1" n="64">
          <head xml:id="echoid-head96" xml:space="preserve">PROPOSITIO LI.</head>
          <p>
            <s xml:id="echoid-s1817" xml:space="preserve">DEindè ſit D A maior quàm A C , ſitque prius ſectio pa-
              <lb/>
            rabole , & </s>
            <s xml:id="echoid-s1818" xml:space="preserve">ſecetur ex D A ipſa D F æqualis A C, & </s>
            <s xml:id="echoid-s1819" xml:space="preserve">A
              <lb/>
            G fiat pars tertia ipſius A F, educaturque B G perpendicularis
              <lb/>
            ad axim, & </s>
            <s xml:id="echoid-s1820" xml:space="preserve">vt D F ad F G, ita fiat B G ad lineam H (& </s>
            <s xml:id="echoid-s1821" xml:space="preserve">hæc
              <lb/>
            eſt Trutina) coniungaturque B E ; </s>
            <s xml:id="echoid-s1822" xml:space="preserve">& </s>
            <s xml:id="echoid-s1823" xml:space="preserve">ſiquidem D E fuerit ma-
              <lb/>
              <note position="right" xlink:label="note-0072-01" xlink:href="note-0072-01a" xml:space="preserve">a</note>
            ior quàm H. </s>
            <s xml:id="echoid-s1824" xml:space="preserve">Dico, quod nullus ramus breuiſecans duci poteſt.</s>
            <s xml:id="echoid-s1825" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1826" xml:space="preserve">Quoniam D E maior eſt, quàm H habebit D E ad B G, nempe D I
              <lb/>
              <note position="right" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">b</note>
            ad I G maiorem rationem , quàm G F ad F D, & </s>
            <s xml:id="echoid-s1827" xml:space="preserve">componatur propor-
              <lb/>
            tio , vt demonſtretur , quod I G minor ſit , quàm D F, quæ æqualis
              <lb/>
            eſt ipſi A C; </s>
            <s xml:id="echoid-s1828" xml:space="preserve">breuiſſima itaque egrediens ex B abſcindit ex ſagitta A
              <lb/>
            D maiorem lineam , quàm A I (13. </s>
            <s xml:id="echoid-s1829" xml:space="preserve">ex quinto) ; </s>
            <s xml:id="echoid-s1830" xml:space="preserve">poſtea ducamus ex E
              <lb/>
            ad ſectionem ramos E K, E L ad vtramque partem B E, & </s>
            <s xml:id="echoid-s1831" xml:space="preserve">duas per-
              <lb/>
            pendiculares
              <lb/>
              <figure xlink:label="fig-0072-01" xlink:href="fig-0072-01a" number="50">
                <image file="0072-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0072-01"/>
              </figure>
            KM, LN, pro-
              <lb/>
            ducamus vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s1832" xml:space="preserve">ad QO tan-
              <lb/>
            gẽtem ſectio-
              <lb/>
            nem in B; </s>
            <s xml:id="echoid-s1833" xml:space="preserve">& </s>
            <s xml:id="echoid-s1834" xml:space="preserve">
              <lb/>
            quoniã ſectio
              <lb/>
            eſt, parabole,
              <lb/>
            & </s>
            <s xml:id="echoid-s1835" xml:space="preserve">OQ tãgens
              <lb/>
            eſt, igitur OG
              <lb/>
              <note position="left" xlink:label="note-0072-03" xlink:href="note-0072-03a" xml:space="preserve">35. lib. 1.</note>
            eſt dupla ip-
              <lb/>
            ſius A G, quę
              <lb/>
            eſt ſemiſſis ip-
              <lb/>
            ſi us F G; </s>
            <s xml:id="echoid-s1836" xml:space="preserve">ergo
              <lb/>
              <note position="right" xlink:label="note-0072-04" xlink:href="note-0072-04a" xml:space="preserve">c</note>
            G F æqualis
              <lb/>
            eſt G O, erit
              <lb/>
            igitur G O ad
              <lb/>
            O M, nempe
              <lb/>
            B G ad P M
              <lb/>
            in maiori pro-
              <lb/>
            portione, quã
              <lb/>
            M F ad F G;
              <lb/>
            </s>
            <s xml:id="echoid-s1837" xml:space="preserve">
              <note position="right" xlink:label="note-0072-05" xlink:href="note-0072-05a" xml:space="preserve">d</note>
            itaque M K in F M minus eſt , quàm B G in G F, quod eſt minus quàm
              <lb/>
            E D in D F propterea quod E D maior eſt quàm H; </s>
            <s xml:id="echoid-s1838" xml:space="preserve">igitur E D in D F
              <lb/>
            multò maius eſt, quàm K M in MF, quare ED ad M K, nempe D R ad
              <lb/>
            R M maiorem rationem habet, quàm M F ad F D, & </s>
            <s xml:id="echoid-s1839" xml:space="preserve">componendo patet,
              <lb/>
              <note position="right" xlink:label="note-0072-06" xlink:href="note-0072-06a" xml:space="preserve">e</note>
            quod D F maior ſit, quàm R M. </s>
            <s xml:id="echoid-s1840" xml:space="preserve">Igitur breuiſſima egrediens ex K (13.
              <lb/>
            </s>
            <s xml:id="echoid-s1841" xml:space="preserve">
              <note position="right" xlink:label="note-0072-07" xlink:href="note-0072-07a" xml:space="preserve">f</note>
            ex quinto) cadit extra R K; </s>
            <s xml:id="echoid-s1842" xml:space="preserve">Et ſimili modo conſtat, quod </s>
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