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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          <p>
            <s xml:id="echoid-s11261" xml:space="preserve">
              <pb o="315" file="0353" n="354" rhead="Conicor. Lib. VII."/>
            ergo A F minor eſt, quàm I K, & </s>
            <s xml:id="echoid-s11262" xml:space="preserve">I K minor quàm P R. </s>
            <s xml:id="echoid-s11263" xml:space="preserve">Si verò A C
              <lb/>
              <note position="right" xlink:label="note-0353-01" xlink:href="note-0353-01a" xml:space="preserve">21. huins.</note>
            maior eſt, quàm A F eſſet I L maior, quàm I K: </s>
            <s xml:id="echoid-s11264" xml:space="preserve">& </s>
            <s xml:id="echoid-s11265" xml:space="preserve">I L ad I K mino-
              <lb/>
            rem proportionem habebit, quàm A C ad A F (28. </s>
            <s xml:id="echoid-s11266" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s11267" xml:space="preserve">& </s>
            <s xml:id="echoid-s11268" xml:space="preserve">I L ma-
              <lb/>
            ior eſt quàm A C; </s>
            <s xml:id="echoid-s11269" xml:space="preserve">igitur A F minor eſt, quàm I K: </s>
            <s xml:id="echoid-s11270" xml:space="preserve">atquè ſimiliter pa-
              <lb/>
            tebit I K minorem eſſe quàm P R, & </s>
            <s xml:id="echoid-s11271" xml:space="preserve">P R, quàm S Z.</s>
            <s xml:id="echoid-s11272" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div958" type="section" level="1" n="301">
          <head xml:id="echoid-head374" xml:space="preserve">PROPOSITIO XXXIV.</head>
          <p>
            <s xml:id="echoid-s11273" xml:space="preserve">D Einde ſit A C minor, quàm A F, dummodò minor non ſit dimi-
              <lb/>
            dio eius: </s>
            <s xml:id="echoid-s11274" xml:space="preserve">& </s>
            <s xml:id="echoid-s11275" xml:space="preserve">ſecentur duæ præſectæ A H, C G, quæ erunt æqua-
              <lb/>
            les; </s>
            <s xml:id="echoid-s11276" xml:space="preserve">pariterque A G, C H interceptæ æquales; </s>
            <s xml:id="echoid-s11277" xml:space="preserve">ponaturque linea γ æqua-
              <lb/>
            lis ſummæ G E, G A. </s>
            <s xml:id="echoid-s11278" xml:space="preserve">Et quia A G non eſt maior duplo A H, & </s>
            <s xml:id="echoid-s11279" xml:space="preserve">γ maior
              <lb/>
              <figure xlink:label="fig-0353-01" xlink:href="fig-0353-01a" number="419">
                <image file="0353-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0353-01"/>
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            eſt duplo A G, erit γ in A H maius, quàm quadratũ A G; </s>
            <s xml:id="echoid-s11280" xml:space="preserve">igitur γ in A
              <lb/>
            E ad γ in A H, nempe E A ad A H minorem proportionẽ habebit, quã
              <lb/>
            γ in A E ad quadratum A G; </s>
            <s xml:id="echoid-s11281" xml:space="preserve">ideoquè E H ad H A, nẽpe E H in H A ad
              <lb/>
            quadratum A H minorẽ proportionẽ habebit, quàm γ, ſeu eidem æqules
              <lb/>
            E G, G A in A E, cum quadrato A G (quæ ſunt æqualia quadrato G E)
              <lb/>
            ad quadratum A G; </s>
            <s xml:id="echoid-s11282" xml:space="preserve">ergo E H in H A ad quadratum E G, ſeu (vt
              <lb/>
            oſtenſum eſt in 15. </s>
            <s xml:id="echoid-s11283" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s11284" xml:space="preserve">quadratum A C ad quadratum I K minorem
              <lb/>
            proportionem habebit, quàm quadratum A H ad quadratũ A G, ſeu quã
              <lb/>
            quadratum A C ad quadratum A F. </s>
            <s xml:id="echoid-s11285" xml:space="preserve">Igitur A C ad I K minorem pro-
              <lb/>
            portionem habet, quàm ad A F; </s>
            <s xml:id="echoid-s11286" xml:space="preserve">& </s>
            <s xml:id="echoid-s11287" xml:space="preserve">propterea A F minor eſt quàm I K.</s>
            <s xml:id="echoid-s11288" xml:space="preserve"/>
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