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-s2128" xml:space="preserve">
              <pb o="44" file="0082" n="82" rhead="Apollonij Pergæi"/>
            in G, & </s>
            <s xml:id="echoid-s2129" xml:space="preserve">non bifariam in M, ergo (ex lemmate ſexto huius libri) G O ad O M, ſeu
              <lb/>
            G B ad P M (propter ſimilitudinem triangulorum B G O, & </s>
            <s xml:id="echoid-s2130" xml:space="preserve">P M O) & </s>
            <s xml:id="echoid-s2131" xml:space="preserve">multo magis
              <lb/>
            G B ad illius portionem K M habebit maiorem proportionem, quàm M F, ad F G;
              <lb/>
            </s>
            <s xml:id="echoid-s2132" xml:space="preserve">ideoque rectangulum K M F ſub intermedijs contentum minus erit rectangulo B G F
              <lb/>
              <note position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">Lem. 5.
                <lb/>
              pręmiſ.</note>
            contento ſub extremis nõ proportionalium; </s>
            <s xml:id="echoid-s2133" xml:space="preserve">ſed rectangulum B G F æquale eſt rectan-
              <lb/>
            gulo E D F (propterea quod D F, ad F G erat, vt B G ad H, ſeu ad ei æqualæm E D)
              <lb/>
              <note position="left" xlink:label="note-0082-02" xlink:href="note-0082-02a" xml:space="preserve">Lem. 5.
                <lb/>
              pręmiſ.</note>
            igitur rectangulum K M F minus erit rectangulo E D F, & </s>
            <s xml:id="echoid-s2134" xml:space="preserve">propterea E D ad K M,
              <lb/>
            ſeu D R ad R M (propter ſimilitudinem triangulorum E D R, K M R) maiorem ra-
              <lb/>
            tionem habebit, quàm M F ad F D, & </s>
            <s xml:id="echoid-s2135" xml:space="preserve">componendo, eadem D M maiorem rationem
              <lb/>
            habebit ad R M, quàm ad F D, & </s>
            <s xml:id="echoid-s2136" xml:space="preserve">propterea R M minor erit, quàm F D, ſeu quàm
              <lb/>
            A C; </s>
            <s xml:id="echoid-s2137" xml:space="preserve">igitur minimus ramorum ex K ad axim cadentium fertur infra K R; </s>
            <s xml:id="echoid-s2138" xml:space="preserve">Quapro-
              <lb/>
              <note position="left" xlink:label="note-0082-03" xlink:href="note-0082-03a" xml:space="preserve">ex 8. 13.
                <lb/>
              huius.</note>
            pter ramus E K ſupra, vel infra breuiſecantem E B ad ſectionem ductus non eſt bre-
              <lb/>
            uiſecans, & </s>
            <s xml:id="echoid-s2139" xml:space="preserve">abſcindit ex axi ſegmentum A R minus, quàm abſcindat breuiſsima ex
              <lb/>
            K ad axim ducta, quod erat oſtendendum.</s>
            <s xml:id="echoid-s2140" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s2141" xml:space="preserve">Tertio loco ſit E D minor, quàm H, & </s>
            <s xml:id="echoid-s2142" xml:space="preserve">oſtendetur, &</s>
            <s xml:id="echoid-s2143" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2144" xml:space="preserve">Quia H ad B G eſt,
              <lb/>
              <note position="right" xlink:label="note-0082-04" xlink:href="note-0082-04a" xml:space="preserve">h</note>
            vt G F ad F D, eſtque E D minor, quàm H; </s>
            <s xml:id="echoid-s2145" xml:space="preserve">ergo E D ad B G minorem proportionem
              <lb/>
            habet, quàm G F ad F D; </s>
            <s xml:id="echoid-s2146" xml:space="preserve">& </s>
            <s xml:id="echoid-s2147" xml:space="preserve">ideo rectangulum E D F ſub extremis contentum minus
              <lb/>
              <note position="left" xlink:label="note-0082-05" xlink:href="note-0082-05a" xml:space="preserve">Lem. 5.
                <lb/>
              pręmiſ.</note>
            eſt rectangulo B G F, quod ſub intermedijs continetur; </s>
            <s xml:id="echoid-s2148" xml:space="preserve">ponatur iam rectangulum T
              <lb/>
            G F æquale rectangulo E D F, & </s>
            <s xml:id="echoid-s2149" xml:space="preserve">per F ducatur F V perpendicularis ſuper axim
              <lb/>
            A D.</s>
            <s xml:id="echoid-s2150" xml:space="preserve"/>
          </p>
          <figure number="59">
            <image file="0082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0082-01"/>
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            <s xml:id="echoid-s2151" xml:space="preserve">Et componendo, patet, quod D F eſt æqualis R M, &</s>
            <s xml:id="echoid-s2152" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2153" xml:space="preserve">Nam D Rad R M
              <lb/>
              <note position="right" xlink:label="note-0082-06" xlink:href="note-0082-06a" xml:space="preserve">i</note>
            eſt, vt M F ad F D, & </s>
            <s xml:id="echoid-s2154" xml:space="preserve">componendo, eadem D M ad R M, atque ad D F, ſeuad ſemi-
              <lb/>
            erectum A C eandem proportionem habebit, & </s>
            <s xml:id="echoid-s2155" xml:space="preserve">ideo D F eſt æqualis R M.</s>
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