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-div967" type="section" level="1" n="306">
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            <s xml:id="echoid-s11362" xml:space="preserve">
              <pb o="319" file="0357" n="358" rhead="Conicor. Lib. VII."/>
            rectangulum ſub A G E in E H æquale quadrato ex G E, & </s>
            <s xml:id="echoid-s11363" xml:space="preserve">ſi pro-
              <lb/>
            portio illa maior fuerit, erit quoque rectangulum maius quadrato; </s>
            <s xml:id="echoid-s11364" xml:space="preserve">& </s>
            <s xml:id="echoid-s11365" xml:space="preserve">
              <lb/>
            ſi illa proportio minor fuerit, Rectangulum quadrato miuus erit.</s>
            <s xml:id="echoid-s11366" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11367" xml:space="preserve">Et primo, quia A G ad G E ponitur vt G H ad H E; </s>
            <s xml:id="echoid-s11368" xml:space="preserve">componendo A G E
              <lb/>
            ad G E, erit vt G E ad E H, & </s>
            <s xml:id="echoid-s11369" xml:space="preserve">rectangulum ſub extremis contentum, ni-
              <lb/>
            mirum ſub A G E in E H, æquale erit quadrato ex intermedia G E.</s>
            <s xml:id="echoid-s11370" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11371" xml:space="preserve">Secundo, ſi A G ad G E maiorem proportionem habuerit, quàm G H ad H
              <lb/>
            E, componendo A G E ad G E maiorem proportionem habebit, quàm G E ad
              <lb/>
            E H, & </s>
            <s xml:id="echoid-s11372" xml:space="preserve">ideo Rectangulum ſub A G E in E H maius erit quadrato ex G E.
              <lb/>
            </s>
            <s xml:id="echoid-s11373" xml:space="preserve">pari ratione ſi A G ad G E minorem proportionem habuerit, quàm G H ad
              <lb/>
            H E, oſtendetur Rectangulum ex A G E in E H minus quadrato G E.</s>
            <s xml:id="echoid-s11374" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div969" type="section" level="1" n="307">
          <head xml:id="echoid-head380" xml:space="preserve">LEMMA V.</head>
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            <s xml:id="echoid-s11375" xml:space="preserve">IN hyperbola, cuius axis C A, & </s>
            <s xml:id="echoid-s11376" xml:space="preserve">erectus A F, præſecta H A, in-
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            tercepta G A, diameter L I, cuius erectus I K, latus C E, & </s>
            <s xml:id="echoid-s11377" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0357-01" xlink:href="fig-0357-01a" number="425">
                <image file="0357-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0357-01"/>
              </figure>
            diameter Q P, cuius erectus P R, latus C O: </s>
            <s xml:id="echoid-s11378" xml:space="preserve">Dico quod erectus P
              <lb/>
            R ab ipſo erecto I K, vel ab A F atque rectangulum ſub O G E in
              <lb/>
            G H ab ipſo quadrato G E, vel rectangulum ex O G A in A H ab
              <lb/>
            ipſo quadrato G A, vna deficiunt, vel vna æqualia ſunt, aut vna
              <lb/>
            excedunt.</s>
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          <p style="it">
            <s xml:id="echoid-s11380" xml:space="preserve">Et primo ponatur rectangulum ſub O G E in E H æquale quadrato E G, er-
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            go idem rectangulum ſub O G E in E O ad rectangulum ſub E G O in E H,
              <lb/>
            ſeu E O ad E H eandem proportionem habet, quàm ad quadratum G E, & </s>
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              <lb/>
            propterea E O ad E H erit vt rectangulum ſub E G O in E O ad </s>
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