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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            <s xml:id="echoid-s2068" xml:space="preserve">
              <pb o="42" file="0080" n="80" rhead="Apollonij Pergæi"/>
            pter parallelas D E,
              <lb/>
              <figure xlink:label="fig-0080-01" xlink:href="fig-0080-01a" number="57">
                <image file="0080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0080-01"/>
              </figure>
            B G, & </s>
            <s xml:id="echoid-s2069" xml:space="preserve">ſimilitudinẽ
              <lb/>
            triangulorum E D I,
              <lb/>
            & </s>
            <s xml:id="echoid-s2070" xml:space="preserve">B G I, eſt D I ad I
              <lb/>
            G, vt E D ad B G;
              <lb/>
            </s>
            <s xml:id="echoid-s2071" xml:space="preserve">igitur D I ad I G ma-
              <lb/>
            iorem proportionem
              <lb/>
            habet, quàm G F ad
              <lb/>
            F D, & </s>
            <s xml:id="echoid-s2072" xml:space="preserve">componendo
              <lb/>
            D G ad G I maio rem
              <lb/>
            rationem habebit,
              <lb/>
            quàm eadem G D ad
              <lb/>
            D F; </s>
            <s xml:id="echoid-s2073" xml:space="preserve">& </s>
            <s xml:id="echoid-s2074" xml:space="preserve">Ideo I G mi-
              <lb/>
            nor eſt, quàm D F.</s>
            <s xml:id="echoid-s2075" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">c</note>
          <p style="it">
            <s xml:id="echoid-s2076" xml:space="preserve">Igitur G F æqua-
              <lb/>
            lis eſt GO, ergo G
              <lb/>
            O ad O M, &</s>
            <s xml:id="echoid-s2077" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2078" xml:space="preserve">Igi-
              <lb/>
            tur G F æqualis eſt G
              <lb/>
            O, & </s>
            <s xml:id="echoid-s2079" xml:space="preserve">quia F O ſecatur
              <lb/>
            bifariam in G, & </s>
            <s xml:id="echoid-s2080" xml:space="preserve">non
              <lb/>
            bifariam in M (ex
              <lb/>
            lemmate ſexto huius
              <lb/>
            libri) habebit ſemisſis G O ad vnum ſegmentorum inæqualium M O maiorem pro-
              <lb/>
            portionem, quàm reliquum ſegmentum M F ad alteram medietatem F G, ſed pro-
              <lb/>
            pter parallelas P M, B G, & </s>
            <s xml:id="echoid-s2081" xml:space="preserve">ſimilitudinem triangulorum B G O, P M O eſt G O ad
              <lb/>
            O M, vt B G ad P M, ergo B G ad P M maiorem proportionem habet, quàm M F ad
              <lb/>
            F G: </s>
            <s xml:id="echoid-s2082" xml:space="preserve">habet verò B G ad minorem M K maiorem proportionem, quàm ad M P (cum
              <lb/>
            punctum P tangentis cadat extra ſectionem); </s>
            <s xml:id="echoid-s2083" xml:space="preserve">ergo B G ad K M adhuc maiorem pro-
              <lb/>
            portionem habet, quàm M F ad F G.</s>
            <s xml:id="echoid-s2084" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2085" xml:space="preserve">Itaque K M in M F minus eſt, quàm B G in G F, &</s>
            <s xml:id="echoid-s2086" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2087" xml:space="preserve">Quoniam prima B G
              <lb/>
              <note position="right" xlink:label="note-0080-02" xlink:href="note-0080-02a" xml:space="preserve">d</note>
            ad ſecundam K M maiorem proportionem habet, quàm tertia M F ad quartam F G;
              <lb/>
            </s>
            <s xml:id="echoid-s2088" xml:space="preserve">ergo ex lemmate quinto huius librirectangulum ſub intermedijs contentum K M F
              <lb/>
            minus erit rectangulo B G F ſub extremis cõtento; </s>
            <s xml:id="echoid-s2089" xml:space="preserve">poſtea, quia H ad B G ex hypotheſi
              <lb/>
            erat, vt G F ad F D, poſita autem fuit E D maior, quàm H, quæ eſt prima propor-
              <lb/>
            tionalium; </s>
            <s xml:id="echoid-s2090" xml:space="preserve">ergo E D ad B G maiorem proportionem habet, quàm G F ad F D, & </s>
            <s xml:id="echoid-s2091" xml:space="preserve">pro-
              <lb/>
              <note position="left" xlink:label="note-0080-03" xlink:href="note-0080-03a" xml:space="preserve">Lem. 5.</note>
            pterea rectangulum ſub extremis E D F maius erit rectangulo ſub intermedijs con-
              <lb/>
            tento B G F; </s>
            <s xml:id="echoid-s2092" xml:space="preserve">fuit autem rectangulum B G F maius rectangulo K M F; </s>
            <s xml:id="echoid-s2093" xml:space="preserve">igitur rectan-
              <lb/>
            gulum E D F multò maius eſt, quàm rectangulum K M F, & </s>
            <s xml:id="echoid-s2094" xml:space="preserve">ideo, ex eodem lemma-
              <lb/>
            te quinto, E D ad M K, nempe D R ad R M (propter ſimilitudinem triangulorum
              <lb/>
            E D R, & </s>
            <s xml:id="echoid-s2095" xml:space="preserve">K M R) maiorem rationem habet, quàm M F ad F D.</s>
            <s xml:id="echoid-s2096" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2097" xml:space="preserve">Et componendo patet, quod D F, &</s>
            <s xml:id="echoid-s2098" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2099" xml:space="preserve">Quoniam D R ad R M maiorem ratio-
              <lb/>
              <note position="right" xlink:label="note-0080-04" xlink:href="note-0080-04a" xml:space="preserve">e</note>
            nem habet, quàm M F ad F D, componendo D M ad M R habebit maiorem propor-
              <lb/>
            tionem, quàm eadem M D ad D F, & </s>
            <s xml:id="echoid-s2100" xml:space="preserve">propterea D F mator eſt, quàm R M, eſt verò
              <lb/>
            ſemisſis erecti A C æqualis D F ex conſtructione, igitur M R minor eſt A C medieta-
              <lb/>
            te lateris recti, & </s>
            <s xml:id="echoid-s2101" xml:space="preserve">propterea breuiſsima educta ex K ſecat ex axi ſegmentum maius,
              <lb/>
              <note position="left" xlink:label="note-0080-05" xlink:href="note-0080-05a" xml:space="preserve">8. huius.</note>
            quàm M R; </s>
            <s xml:id="echoid-s2102" xml:space="preserve">ideoque cadit extra, ſcilicet infra ramum K R E.</s>
            <s xml:id="echoid-s2103" xml:space="preserve"/>
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