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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              <pb o="354" file="0392" n="393" rhead="Apollonij Pergæi"/>
            ma C A F. </s>
            <s xml:id="echoid-s12261" xml:space="preserve">Tandem quia rectangulum A H M ad quadratum ex ſumma H
              <lb/>
              <note position="left" xlink:label="note-0392-01" xlink:href="note-0392-01a" xml:space="preserve">ex 16.
                <lb/>
              huius.
                <lb/>
              lbidem.</note>
            M G eandem proportionem habet, quàm quadratum A C ad quadratum ex Q
              <lb/>
            P R, ſed quadratum ex H C G ad rectangulum ex A H C eandem proportionẽ
              <lb/>
            habet, quàm quadratnm ex sũma Y O f ad quadratum A C, (@o quod H C eſt
              <lb/>
            intercepta comparata diametri Y O, cum Y O ſecet bifariam ad eam ordinatim
              <lb/>
            applicatam A C, atque ab eodem pun-
              <lb/>
              <figure xlink:label="fig-0392-01" xlink:href="fig-0392-01a" number="464">
                <image file="0392-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0392-01"/>
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            cto C perpendicularis ad axim ducta
              <lb/>
            cadat ſuper idem punctum C), igitur
              <lb/>
            ex æquali perturbata rectangulum A H
              <lb/>
            M maius ad minus rectangulum ex A
              <lb/>
            H C eandem proportionem habet, quàm
              <lb/>
            quadratum ex ſumma Y O f ad qua-
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            dratum ex ſumma Q P R, & </s>
            <s xml:id="echoid-s12262" xml:space="preserve">propte-
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            rea ſumma laterum Y O f maior erit,
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            quàm ſumma Q P R.</s>
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        <div xml:id="echoid-div1052" type="section" level="1" n="334">
          <head xml:id="echoid-head413" xml:space="preserve">Notæ in Propoſit. XXXXVII.</head>
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            <s xml:id="echoid-s12264" xml:space="preserve">QVia duplum quadrati A C non eſt maius quadrato ex C A F, ergo du-
              <lb/>
            plum quadrati ex A H æquale, aut minus erit quadrato ex ſumma G
              <lb/>
            H, eſtque duplum rectanguli ex E H A, vel ex E H M minus
              <lb/>
            duplo quadrati A H, igitur minus quoque erit quadrato ex G H, igitur du-
              <lb/>
            plum M H ad G H minorem proportionem habet, quàm G H ad E H, ergo
              <lb/>
              <note position="left" xlink:label="note-0392-02" xlink:href="note-0392-02a" xml:space="preserve">Lem. 13.
                <lb/>
              huius.</note>
            duplum rectanguli ex differentia ipſarum E H G M in M H minus eſt duobus
              <lb/>
            quadratis ex G M, & </s>
            <s xml:id="echoid-s12265" xml:space="preserve">ex H M: </s>
            <s xml:id="echoid-s12266" xml:space="preserve">quare duo quadrata ex I L, & </s>
            <s xml:id="echoid-s12267" xml:space="preserve">ex I K minora
              <lb/>
              <note position="left" xlink:label="note-0392-03" xlink:href="note-0392-03a" xml:space="preserve">Lem. 15.
                <lb/>
              huius.</note>
            erunt duobus quadratis ex Q P, & </s>
            <s xml:id="echoid-s12268" xml:space="preserve">ex P R, & </s>
            <s xml:id="echoid-s12269" xml:space="preserve">ſic duo quadrata ex Q P, & </s>
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              <lb/>
            ex P R minora ſunt duobus quadratis ex T S, & </s>
            <s xml:id="echoid-s12271" xml:space="preserve">ex S Z.</s>
            <s xml:id="echoid-s12272" xml:space="preserve"/>
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