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="359" file="0397" n="398" rhead="Conicor. Lib. VII."/>
            terius homologæ diametri, atque differentia quadrati axis ab
              <lb/>
            eius figura maior erit ſemidifferentia quadratorum duorum late-
              <lb/>
            rum figuræ ſuæ homologæ, & </s>
            <s xml:id="echoid-s12385" xml:space="preserve">minor erit integra differentia eo-
              <lb/>
            rundem quadratorum.</s>
            <s xml:id="echoid-s12386" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12387" xml:space="preserve">In fectione A B N ſit axis A C maior in figura prima, & </s>
            <s xml:id="echoid-s12388" xml:space="preserve">in ſecunda
              <lb/>
            minor, ſintquè I L, P Q duæ aliæ diametri, quæ in ellipſi cadant inter
              <lb/>
            axim, & </s>
            <s xml:id="echoid-s12389" xml:space="preserve">vnã æqualium; </s>
            <s xml:id="echoid-s12390" xml:space="preserve">ducanturque duæ ordinationes A B, A N ad
              <lb/>
              <note position="left" xlink:label="note-0397-01" xlink:href="note-0397-01a" xml:space="preserve">b</note>
            diametros I L, P Q, & </s>
            <s xml:id="echoid-s12391" xml:space="preserve">duas ad axim perpendiculares B E, N M; </s>
            <s xml:id="echoid-s12392" xml:space="preserve">ſit-
              <lb/>
            que A F erectus ipſius A C, & </s>
            <s xml:id="echoid-s12393" xml:space="preserve">A G, C H duæ interceptæ: </s>
            <s xml:id="echoid-s12394" xml:space="preserve">ponaturque
              <lb/>
            in ellipſi X D æqualis E D, habebit E H ad H A minorem proportio-
              <lb/>
              <note position="left" xlink:label="note-0397-02" xlink:href="note-0397-02a" xml:space="preserve">c</note>
            nem in prima hyperbola, & </s>
            <s xml:id="echoid-s12395" xml:space="preserve">maiorem in reliquis, quàm E D ad D A,
              <lb/>
            ſeu quàm E X, quæ eſt ſumma in hyperbola, & </s>
            <s xml:id="echoid-s12396" xml:space="preserve">differentia in ellipſi
              <lb/>
            ipſarum E G, & </s>
            <s xml:id="echoid-s12397" xml:space="preserve">E H ad A C differentiam ipſarum H A, A G; </s>
            <s xml:id="echoid-s12398" xml:space="preserve">& </s>
            <s xml:id="echoid-s12399" xml:space="preserve">qua-
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              <figure xlink:label="fig-0397-01" xlink:href="fig-0397-01a" number="468">
                <image file="0397-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0397-01"/>
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            dratum A C in omnibus figuris ad differentiam quadratorum A C, & </s>
            <s xml:id="echoid-s12400" xml:space="preserve">
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            A F eandem proportionem habet, quàm quadratum A H ad differentiam
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            duorum quadratorum A H, & </s>
            <s xml:id="echoid-s12401" xml:space="preserve">G A: </s>
            <s xml:id="echoid-s12402" xml:space="preserve">atque E H ad H A minorem pro-
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            portionem habet in duabus primis figuris, & </s>
            <s xml:id="echoid-s12403" xml:space="preserve">maiorem proportionem in
              <lb/>
            duabus ſecundis, quàm E G ad G A, comparando homologorum ſum-
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            mas, erit E H ad H A, vt E H cum E G ad H A cum G A, nempe ag-
              <lb/>
            gregatum E H, E G in earundem differentiam ad aggregatum H A, A
              <lb/>
            G in earundem differentiam, quod eſt æquale differentiæ duorum qua-
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            dratorum E H, E G; </s>
            <s xml:id="echoid-s12404" xml:space="preserve">nempe quadratum A C ad differentiam quadrato-
              <lb/>
            rum duorum laterum figuræ I L minorem proportionem habet (in prima
              <lb/>
            ellipſi), & </s>
            <s xml:id="echoid-s12405" xml:space="preserve">maiorem (in ſecunda) quàm quadratum A H ad aggrega-
              <lb/>
            tum H A, A G in earundem differentiam, quod eſt æquale differentiæ
              <lb/>
            quadratorum H A, A G, nempe quadratum A C ad differentiam </s>
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