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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          <p>
            <s xml:id="echoid-s10638" xml:space="preserve">In eiſdem figuris, quia quadratum A C ad quadratum ſui coniugati
              <lb/>
              <note position="left" xlink:label="note-0330-01" xlink:href="note-0330-01a" xml:space="preserve">a</note>
            (in propoſitione 12. </s>
            <s xml:id="echoid-s10639" xml:space="preserve">13. </s>
            <s xml:id="echoid-s10640" xml:space="preserve">25.) </s>
            <s xml:id="echoid-s10641" xml:space="preserve">nempe C A ad A F erectum ipſius eſt,
              <lb/>
              <note position="left" xlink:label="note-0330-02" xlink:href="note-0330-02a" xml:space="preserve">ex Def. 1.
                <lb/>
              & 2.</note>
            vt Præſecta C G ad Interceptam G A, ſiue ad C H; </s>
            <s xml:id="echoid-s10642" xml:space="preserve">ergo quadratum
              <lb/>
            A C in hyperbola ad differentiam quadratorum axium ipſius, & </s>
            <s xml:id="echoid-s10643" xml:space="preserve">in elli-
              <lb/>
            pſi ad eorundem ſummam eandem proportionem habet, quàm C G ad
              <lb/>
            H G. </s>
            <s xml:id="echoid-s10644" xml:space="preserve">Demonſtratum autem prius fuit, quadratum C A ad quadratum
              <lb/>
              <note position="right" xlink:label="note-0330-03" xlink:href="note-0330-03a" xml:space="preserve">b</note>
            I L eandem proportionem habere, quàm C G ad H E, & </s>
            <s xml:id="echoid-s10645" xml:space="preserve">quadratum
              <lb/>
              <figure xlink:label="fig-0330-01" xlink:href="fig-0330-01a" number="383">
                <image file="0330-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0330-01"/>
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            I L ad quadratum N O eandem proportionem habet, quàm H E ad E
              <lb/>
              <note position="left" xlink:label="note-0330-04" xlink:href="note-0330-04a" xml:space="preserve">6. & 7.
                <lb/>
              huius.</note>
            G; </s>
            <s xml:id="echoid-s10646" xml:space="preserve">Inſuper quudratum I L ad ſummam quadratorum I L, N O in elli-
              <lb/>
            pſi, aut ad eorundem differentiam in hyperbola eandem proportionem
              <lb/>
            habebit, quàm H E ad H G; </s>
            <s xml:id="echoid-s10647" xml:space="preserve">& </s>
            <s xml:id="echoid-s10648" xml:space="preserve">in propoſitione 14. </s>
            <s xml:id="echoid-s10649" xml:space="preserve">vt H E ad exceffum
              <lb/>
            H E, E G, quod eſt duplum D G; </s>
            <s xml:id="echoid-s10650" xml:space="preserve">igitur ex æqualitate quadratum A
              <lb/>
            C, ſiue ad ſummam duorum quadratorum I L, N O, quemadmodum
              <lb/>
            habetur in propoſitione 22. </s>
            <s xml:id="echoid-s10651" xml:space="preserve">& </s>
            <s xml:id="echoid-s10652" xml:space="preserve">30. </s>
            <s xml:id="echoid-s10653" xml:space="preserve">ſiue ad eorundem differentiam, veluti
              <lb/>
            habetur in propoſitionibus 12. </s>
            <s xml:id="echoid-s10654" xml:space="preserve">13. </s>
            <s xml:id="echoid-s10655" xml:space="preserve">14. </s>
            <s xml:id="echoid-s10656" xml:space="preserve">eandem proportionem habebit,
              <lb/>
            quàm C G ad H G, ſiue ad duplum D G, vt in propofitione 14. </s>
            <s xml:id="echoid-s10657" xml:space="preserve">& </s>
            <s xml:id="echoid-s10658" xml:space="preserve">de-
              <lb/>
            monſtratum fuit in eadem proportione eſſe quadratum A C ad ſummam
              <lb/>
            quadratorum A C, & </s>
            <s xml:id="echoid-s10659" xml:space="preserve">eius coniugati, & </s>
            <s xml:id="echoid-s10660" xml:space="preserve">eſt propoſitio 25. </s>
            <s xml:id="echoid-s10661" xml:space="preserve">aut ad eorun-
              <lb/>
            dem differentiam, & </s>
            <s xml:id="echoid-s10662" xml:space="preserve">eſt propoſitio 12. </s>
            <s xml:id="echoid-s10663" xml:space="preserve">quapropter ſumma quadratorum
              <lb/>
            I L, N O coniugatarum in ellipſi, nempe quadratum I L vna cum eius
              <lb/>
            figura eſt æquale aggregato quadrati A C vna cum quadrato eius coniu-
              <lb/>
            gati 30. </s>
            <s xml:id="echoid-s10664" xml:space="preserve">nempe quadrato A C, & </s>
            <s xml:id="echoid-s10665" xml:space="preserve">illius figuræ, & </s>
            <s xml:id="echoid-s10666" xml:space="preserve">in hyperbola diffe-
              <lb/>
            rentia quadratorum I L, N O nempe exceſſus quadrati I L ſuper illius
              <lb/>
            figuram æqualis eſt differentiæ duorum quadratorum A C, & </s>
            <s xml:id="echoid-s10667" xml:space="preserve">recti illius
              <lb/>
            nempe quadrato A C, & </s>
            <s xml:id="echoid-s10668" xml:space="preserve">illius figuræ 27. </s>
            <s xml:id="echoid-s10669" xml:space="preserve">& </s>
            <s xml:id="echoid-s10670" xml:space="preserve">oſtenſum iam eſt, quod I
              <lb/>
              <note position="left" xlink:label="note-0330-05" xlink:href="note-0330-05a" xml:space="preserve">c</note>
            L in hyperbola maior eſt, quàm A C; </s>
            <s xml:id="echoid-s10671" xml:space="preserve">ergo differentia A C & </s>
            <s xml:id="echoid-s10672" xml:space="preserve">illius con-
              <lb/>
            iugati maior quàm differentia I L, & </s>
            <s xml:id="echoid-s10673" xml:space="preserve">N O: </s>
            <s xml:id="echoid-s10674" xml:space="preserve">atquè fic oſtendetur, </s>
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