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-div924" type="section" level="1" n="290">
          <p>
            <s xml:id="echoid-s10898" xml:space="preserve">
              <pb o="302" file="0340" n="341" rhead="Apollonij Pergæi"/>
            ſummam earundem: </s>
            <s xml:id="echoid-s10899" xml:space="preserve">& </s>
            <s xml:id="echoid-s10900" xml:space="preserve">ſumma duorum quadratorum ipſarum æqualis eſt
              <lb/>
            ſummæ duorum quadratorum A C, Q R ( 22. </s>
            <s xml:id="echoid-s10901" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s10902" xml:space="preserve">) ergo ſumma A C,
              <lb/>
            Q R minor eſt, quàm ſumma I L, N O, atque ſic oſtendetur, quod sũ-
              <lb/>
            ma I L, N O minor eſt, quàm ſumma S T, V X. </s>
            <s xml:id="echoid-s10903" xml:space="preserve">Quod erat propoſitũ.</s>
            <s xml:id="echoid-s10904" xml:space="preserve"/>
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        <div xml:id="echoid-div927" type="section" level="1" n="291">
          <head xml:id="echoid-head362" xml:space="preserve">PROPOSITIO XXXXIII.</head>
          <p>
            <s xml:id="echoid-s10905" xml:space="preserve">D Einde in ellipſi quadratum ſummæ A C, Q R minus eſt quadrato
              <lb/>
            ſummæ I L, N O; </s>
            <s xml:id="echoid-s10906" xml:space="preserve">& </s>
            <s xml:id="echoid-s10907" xml:space="preserve">ſumma duorum quadratorum A C, Q R
              <lb/>
              <figure xlink:label="fig-0340-01" xlink:href="fig-0340-01a" number="396">
                <image file="0340-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0340-01"/>
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            æqualis eſt ſummæ duorum quadratorum I L, N O (22. </s>
            <s xml:id="echoid-s10908" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s10909" xml:space="preserve">) igitur
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            remanet A C in Q R minus quàm I L in N O, & </s>
            <s xml:id="echoid-s10910" xml:space="preserve">ſimiliter I L in N O
              <lb/>
              <note position="left" xlink:label="note-0340-01" xlink:href="note-0340-01a" xml:space="preserve">f</note>
            minus erit, quàm S T in V X.</s>
            <s xml:id="echoid-s10911" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s10912" xml:space="preserve">Sed in hyperbola, quia quilibet axium minor eſt homologa diame-
              <lb/>
            tro coniugatarum; </s>
            <s xml:id="echoid-s10913" xml:space="preserve">igitur planum rectangulum ab axibus contentum mi-
              <lb/>
            nus eſt eo quod à duabus coniugatis continetur hoc igitur in hyperbo-
              <lb/>
            le manifeſtum eſt.</s>
            <s xml:id="echoid-s10914" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10915" xml:space="preserve">In ellipſi autem, quia A C ad Q R maiorem proportionem habet;
              <lb/>
            </s>
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              <note position="left" xlink:label="note-0340-02" xlink:href="note-0340-02a" xml:space="preserve">g</note>
            quàm I L ad N O per conuerſionem rationis, & </s>
            <s xml:id="echoid-s10917" xml:space="preserve">permutando maior A C
              <lb/>
            ad minorem I L minorem proportionem habebit, quàm differentia ipſa-
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            rum A C, Q R ad differentiam ipſarum I L & </s>
            <s xml:id="echoid-s10918" xml:space="preserve">N O; </s>
            <s xml:id="echoid-s10919" xml:space="preserve">& </s>
            <s xml:id="echoid-s10920" xml:space="preserve">propterea diffe-
              <lb/>
            rentia ipſarum A C, & </s>
            <s xml:id="echoid-s10921" xml:space="preserve">Q R maior erit differentia reliquarum I L, & </s>
            <s xml:id="echoid-s10922" xml:space="preserve">N
              <lb/>
            O. </s>
            <s xml:id="echoid-s10923" xml:space="preserve">Et ſimiliter oſtendetur, quod exceſſus I L ſuper N O maior ſit, quàm
              <lb/>
            exceſſus S T ſuper V X.</s>
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