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-div898" type="section" level="1" n="278">
          <head xml:id="echoid-head347" xml:space="preserve">Notæ in Propoſit. XVII.</head>
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            <s xml:id="echoid-s10595" xml:space="preserve">SIue ad duo quadrata ex I L, & </s>
            <s xml:id="echoid-s10596" xml:space="preserve">I P erit, vt C G in E H ad duo qua-
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              <note position="left" xlink:label="note-0328-01" xlink:href="note-0328-01a" xml:space="preserve">k</note>
            drata E G, & </s>
            <s xml:id="echoid-s10597" xml:space="preserve">E H, &</s>
            <s xml:id="echoid-s10598" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10599" xml:space="preserve">Quoniam I L ad I P erat vt H E ad E G,
              <lb/>
            & </s>
            <s xml:id="echoid-s10600" xml:space="preserve">quadratum I L ad quadratum I P erit vt quadratum H E ad quadratum
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            E G: </s>
            <s xml:id="echoid-s10601" xml:space="preserve">& </s>
            <s xml:id="echoid-s10602" xml:space="preserve">comparando antecedentes ad terminorũ ſummas quadratum I L ad qua-
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            dratum I L vna cum quadrato I P habebit eandem proportionem, quàm qua-
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            dratum H E ad ſummam quadrati H E cum quadrato E G: </s>
            <s xml:id="echoid-s10603" xml:space="preserve">ſed prius quadra-
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            tum A C ad quadratum I L erat vt rectangulum A H E ad quadratum H E;
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            <s xml:id="echoid-s10604" xml:space="preserve">igitur quadratum A C ad ſummam quadrati I L cum quadrato I P eãdem pro-
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            portionem babebit quàm rectangulum A H E ad quadratum E G vna cum qua-
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            drato E H.</s>
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          <head xml:id="echoid-head348" xml:space="preserve">Notæ in Propoſit. XX.</head>
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            <s xml:id="echoid-s10606" xml:space="preserve">SIue ad differentiam duorum quadratorum I L, I P erit, vt C G in H
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              <note position="left" xlink:label="note-0328-02" xlink:href="note-0328-02a" xml:space="preserve">l</note>
            E ad differentiam duorum quadratorum ex H E, & </s>
            <s xml:id="echoid-s10607" xml:space="preserve">ex E G, &</s>
            <s xml:id="echoid-s10608" xml:space="preserve">c.
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            <s xml:id="echoid-s10609" xml:space="preserve">Quoniam vt dictum eſt quadratum I L ad quadratum I P eandem proportionẽ
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            habet, quàm quadratum H E ad quadratum G E, & </s>
            <s xml:id="echoid-s10610" xml:space="preserve">comparando anteceden-
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            quadrato I P eandem proportionem habebit, quàm quadratum H E ad diffe-
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            rentiam inter quadratum H E, & </s>
            <s xml:id="echoid-s10611" xml:space="preserve">quadratum E G: </s>
            <s xml:id="echoid-s10612" xml:space="preserve">eſtque quadratum C A
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            ad quadratum I L, vt rectangulum A H E ad quadratũ H E; </s>
            <s xml:id="echoid-s10613" xml:space="preserve">ergo ex æquali
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            quadratum A C ad quadratorum ex I L, & </s>
            <s xml:id="echoid-s10614" xml:space="preserve">ex I P differentiam eandem pro-
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            portionem habebit, quàm rectangulum A H E ad quadratorum ex E G, & </s>
            <s xml:id="echoid-s10615" xml:space="preserve">ex
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            E H differentiam.</s>
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