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-div890" type="section" level="1" n="274">
          <head xml:id="echoid-head343" xml:space="preserve">Notæ in Propoſit. XV.</head>
          <p style="it">
            <s xml:id="echoid-s10552" xml:space="preserve">SIue ad quadratum I P erit vt C G in E H ad quadratum E G, &</s>
            <s xml:id="echoid-s10553" xml:space="preserve">c.
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              <note position="left" xlink:label="note-0326-01" xlink:href="note-0326-01a" xml:space="preserve">f</note>
            Quoniam I L ad I P erat vt H E ad E G; </s>
            <s xml:id="echoid-s10555" xml:space="preserve">ergo quadratum I L ad qua-
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            dratum I P erit vt quadratum H E ad quadratum E G; </s>
            <s xml:id="echoid-s10556" xml:space="preserve">erat autem quadra-
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            tum A C ad quadratum I L, vt rectangulum C G, ſeu A H in H E ad qua-
              <lb/>
            dratum E H; </s>
            <s xml:id="echoid-s10557" xml:space="preserve">igitur ex æqualitate quadratum A C ad quadratum I P ean-
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            dem proportionem habebit, quàm rectangulum A H E ad quadratum G E.</s>
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        <div xml:id="echoid-div892" type="section" level="1" n="275">
          <head xml:id="echoid-head344" xml:space="preserve">Notæ in Propoſit. XIX.</head>
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            <s xml:id="echoid-s10559" xml:space="preserve">SIue ad quadratum differentiæ L I, & </s>
            <s xml:id="echoid-s10560" xml:space="preserve">I P erit vt C G in E H ad qua-
              <lb/>
              <note position="left" xlink:label="note-0326-02" xlink:href="note-0326-02a" xml:space="preserve">g</note>
            dratum differentiæ H E, E G, &</s>
            <s xml:id="echoid-s10561" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10562" xml:space="preserve">Quia I L ad I P erat vt H E ad
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            E G, comparando antecedentes ad terminorum differentias, ſcilicet I L ad dif-
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            ferentiam ipſarum I L, & </s>
            <s xml:id="echoid-s10563" xml:space="preserve">I P eandem proportionem habebit, quàm E H ad
              <lb/>
              <figure xlink:label="fig-0326-01" xlink:href="fig-0326-01a" number="378">
                <image file="0326-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0326-01"/>
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            differentiam ipſarum E H, & </s>
            <s xml:id="echoid-s10564" xml:space="preserve">E G, & </s>
            <s xml:id="echoid-s10565" xml:space="preserve">quadratum I L ad quadratum ex dif-
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            ferentia ipſarum I L, & </s>
            <s xml:id="echoid-s10566" xml:space="preserve">I P deſcriptum eandem proportionem habebit, quàm
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            quadrætum H E ad quadratum ex differentia ipſarum H E, & </s>
            <s xml:id="echoid-s10567" xml:space="preserve">G E deſcriptũ:
              <lb/>
            </s>
            <s xml:id="echoid-s10568" xml:space="preserve">erat autem quadratum C A ad quadratum I L, vt rectangulum A H E ad
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            quadratum H E; </s>
            <s xml:id="echoid-s10569" xml:space="preserve">ergo ex æqualitate quadratum A C ad quadratum ex diffe-
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            rentia ipſarum I L, & </s>
            <s xml:id="echoid-s10570" xml:space="preserve">I P eandem proportionem habebit, quàm rectangulum
              <lb/>
            A H E ad quadratum ex differentia ipſarum H E, & </s>
            <s xml:id="echoid-s10571" xml:space="preserve">E G.</s>
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