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-div904" type="section" level="1" n="281">
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              <pb o="294" file="0332" n="333" rhead="Apollonij Pergæi"/>
            habebit, quàm C G ad ipſarum H E, & </s>
            <s xml:id="echoid-s10702" xml:space="preserve">E G differentiam, ſeu ad H G: </s>
            <s xml:id="echoid-s10703" xml:space="preserve">ſed
              <lb/>
            in eadem hyperbola quadratum A C ad quadratorum A C, & </s>
            <s xml:id="echoid-s10704" xml:space="preserve">Q R differen-
              <lb/>
            tiam eandem proportionem habet, quàm C G ad ipſarum C G, & </s>
            <s xml:id="echoid-s10705" xml:space="preserve">C H diffe-
              <lb/>
            rentiam, ſeu ad H G (veluti in principio huius propoſitionis dictum eſt) ergo
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            quadratum A C ad quadratorum ex A C, & </s>
            <s xml:id="echoid-s10706" xml:space="preserve">ex Q R differentiam, eandem
              <lb/>
            proportionem habebit, quàm ad quadratorum ex I L, & </s>
            <s xml:id="echoid-s10707" xml:space="preserve">ex N O differentiam;
              <lb/>
            </s>
            <s xml:id="echoid-s10708" xml:space="preserve">& </s>
            <s xml:id="echoid-s10709" xml:space="preserve">ideo in hyperbola differentiæ quadratorum axium A C, & </s>
            <s xml:id="echoid-s10710" xml:space="preserve">Q R æqualis
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            eſt diffcrentiæ quadratorum I L, & </s>
            <s xml:id="echoid-s10711" xml:space="preserve">N O coniugatarum.</s>
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        <div xml:id="echoid-div907" type="section" level="1" n="282">
          <head xml:id="echoid-head352" xml:space="preserve">Notæ in Propoſit. XIII.</head>
          <p style="it">
            <s xml:id="echoid-s10713" xml:space="preserve">QVoniam in ellipſi quadratum I L ad quadratum N O eandem proportio-
              <lb/>
              <note position="left" xlink:label="note-0332-01" xlink:href="note-0332-01a" xml:space="preserve">7. huius.</note>
            nem habet, quàm H E ad G E; </s>
            <s xml:id="echoid-s10714" xml:space="preserve">comparando antecedentes ad terminorũ
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            ſummas quadratum I L ad quadratorum ex I L, & </s>
            <s xml:id="echoid-s10715" xml:space="preserve">ex N O ſum-
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            mam eandem proportionem habebit, quàm H E ad ipſarum H E, & </s>
            <s xml:id="echoid-s10716" xml:space="preserve">E G ſum-
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            mam: </s>
            <s xml:id="echoid-s10717" xml:space="preserve">ſed quadratum A C ad quadratum I L eſt, vt C G ad H E (vt in octa-
              <lb/>
            ua propoſitione dictum eſt) ergo ex æquali quadratum A C ad quadratorum ex
              <lb/>
              <figure xlink:label="fig-0332-01" xlink:href="fig-0332-01a" number="385">
                <image file="0332-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0332-01"/>
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            I L, & </s>
            <s xml:id="echoid-s10718" xml:space="preserve">ex N O ſummam eandem proportionem habebit, quàm C G ad ſum-
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            mam ipſarum H E, & </s>
            <s xml:id="echoid-s10719" xml:space="preserve">E G, ſeu ad G H: </s>
            <s xml:id="echoid-s10720" xml:space="preserve">ſed in principio præcedentis notæ
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            oſtenſum eſt, quod in ellipſi quadratum A C ad quadratorum ex A C, & </s>
            <s xml:id="echoid-s10721" xml:space="preserve">ex Q
              <lb/>
            R ſummam eandem proportionem habet, quàm C G ad ſummam ipſarum C G,
              <lb/>
            & </s>
            <s xml:id="echoid-s10722" xml:space="preserve">C H, ſeu ad G H: </s>
            <s xml:id="echoid-s10723" xml:space="preserve">quarè quadratum A C eãdem proportionem habet ad ſum-
              <lb/>
            mam quadratorum ex C A, & </s>
            <s xml:id="echoid-s10724" xml:space="preserve">ex Q R, quàm ad ſummam quadratorum ex I
              <lb/>
            L, & </s>
            <s xml:id="echoid-s10725" xml:space="preserve">ex N O; </s>
            <s xml:id="echoid-s10726" xml:space="preserve">& </s>
            <s xml:id="echoid-s10727" xml:space="preserve">propterea in ellipſi quadrata duorum axium A C, & </s>
            <s xml:id="echoid-s10728" xml:space="preserve">Q R
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            ſimul ſumpta æqualia ſunt quadratis duarum coniugatarum diametrorum I L,
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            & </s>
            <s xml:id="echoid-s10729" xml:space="preserve">N O ſimul ſumptis.</s>
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