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-div984" type="section" level="1" n="310">
          <pb o="324" file="0362" n="363" rhead="Apollonij Pergæi"/>
          <p>
            <s xml:id="echoid-s11473" xml:space="preserve">Si verò fuerit axis minor parte tertia ſui erecti aſſignari po-
              <lb/>
            terunt ad vtraſque eius partes duo æquales diametri, quarum
              <lb/>
            quælibet pars tertia ſit ſui erecti, atque duo latera figuræ eiuſ-
              <lb/>
            dem minora ſunt duobus lateribus figuræ cuiuslibet alterius dia-
              <lb/>
            metri ad vtraſque eius partes in eadem ſectione cadentis: </s>
            <s xml:id="echoid-s11474" xml:space="preserve">& </s>
            <s xml:id="echoid-s11475" xml:space="preserve">duo
              <lb/>
            latera figuræ diametri ei propinquiores minora ſunt duobus la-
              <lb/>
            teribus figuræ remotioris.</s>
            <s xml:id="echoid-s11476" xml:space="preserve"/>
          </p>
          <figure number="430">
            <image file="0362-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0362-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s11477" xml:space="preserve">In eadem figura ſupponatur prius hyperboles axis A C non minor ſuo
              <lb/>
            erecto, erit P Q maior quàm A C, & </s>
            <s xml:id="echoid-s11478" xml:space="preserve">S T maior quàm P Q: </s>
            <s xml:id="echoid-s11479" xml:space="preserve">ideoquè
              <lb/>
            erectus ipſius A C minor erit erecto ipſius P Q (33. </s>
            <s xml:id="echoid-s11480" xml:space="preserve">ex 7.)</s>
            <s xml:id="echoid-s11481" xml:space="preserve">, & </s>
            <s xml:id="echoid-s11482" xml:space="preserve">erectus
              <lb/>
            ipſius P Q minor eſt erecto ipſius S T; </s>
            <s xml:id="echoid-s11483" xml:space="preserve">igitur duo latera figuræ A C mi-
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            nora ſunt, quàm duo latera figuræ P Q, & </s>
            <s xml:id="echoid-s11484" xml:space="preserve">duo latera figuræ P Q mino-
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            ra, quàm duo latera figuræ S T.</s>
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          <head xml:id="echoid-head386" xml:space="preserve">PROPOSITIO XXXIX.</head>
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            <s xml:id="echoid-s11486" xml:space="preserve">D Einde ſit A C minor quàm A F, ſed non ſit minor tertia parte
              <lb/>
              <note position="right" xlink:label="note-0362-01" xlink:href="note-0362-01a" xml:space="preserve">a</note>
            eius; </s>
            <s xml:id="echoid-s11487" xml:space="preserve">igitur A H non erit minor tertia parte ipſius H C: </s>
            <s xml:id="echoid-s11488" xml:space="preserve">& </s>
            <s xml:id="echoid-s11489" xml:space="preserve">pro-
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            pterea non eſt minor quadrante ipſius A C; </s>
            <s xml:id="echoid-s11490" xml:space="preserve">ideoque C A in A H non.
              <lb/>
            </s>
            <s xml:id="echoid-s11491" xml:space="preserve">eſt minus quarta parte quadrati A C; </s>
            <s xml:id="echoid-s11492" xml:space="preserve">quare C A in A M quater ſum-
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            ptum ad C A in A H quater, nempe M A ad A H non habet maiorem
              <lb/>
            proportionem, quàm quadruplum ipſius A C in A M ad quadratum A
              <lb/>
            C. </s>
            <s xml:id="echoid-s11493" xml:space="preserve">Et ponamus M m æqualem M A, componendo M H, ad H A,
              <lb/>
            nempe M H in H A ad quadratum H A non habebit maiorem </s>
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