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="61" file="0099" n="99" rhead="Conicor. Lib. V."/>
              <figure xlink:label="fig-0099-01" xlink:href="fig-0099-01a" number="76">
                <image file="0099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0099-01"/>
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            ſimiliter C L ad L E, vt proportio figuræ, & </s>
            <s xml:id="echoid-s2706" xml:space="preserve">producamus per L ip-
              <lb/>
            ſam O M parallelam A I F, & </s>
            <s xml:id="echoid-s2707" xml:space="preserve">per F ipſam G M parallelam C E, & </s>
            <s xml:id="echoid-s2708" xml:space="preserve">fa-
              <lb/>
            ciamus ſectionem H C B hyperbolen tranſeuntem per punctum C circa
              <lb/>
              <note position="right" xlink:label="note-0099-01" xlink:href="note-0099-01a" xml:space="preserve">4. lib. 2.</note>
            continentes G M, O M, quæ occurret ſectioni A B (in ellipſi quidem vt
              <lb/>
              <note position="right" xlink:label="note-0099-02" xlink:href="note-0099-02a" xml:space="preserve">56.
                <lb/>
              huius.</note>
            demonſtrauimus) in hyberbola vero eo quod O M parallela axi D A in-
              <lb/>
              <note position="left" xlink:label="note-0099-03" xlink:href="note-0099-03a" xml:space="preserve">b</note>
            clinato ſubtendit, ſi producatur, angulum ſubſequentem continentiæ an-
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            gulum ſecabit A B, & </s>
            <s xml:id="echoid-s2709" xml:space="preserve">corda, ſi producatur, occurret ſectioni; </s>
            <s xml:id="echoid-s2710" xml:space="preserve">Ergo O
              <lb/>
            M ingreditur ſectionem A B, & </s>
            <s xml:id="echoid-s2711" xml:space="preserve">ampliatur ſectio A B per extenſionem,
              <lb/>
            longè à duabus lineis O M, M G, & </s>
            <s xml:id="echoid-s2712" xml:space="preserve">ſectio B C prope illas ducitur (deci-
              <lb/>
              <note position="right" xlink:label="note-0099-04" xlink:href="note-0099-04a" xml:space="preserve">14. lib. 2.</note>
            moſexta, ex ſecundo) igitur duæ ſectiones A B, C B ſibi occurrunt, vt
              <lb/>
            in B, & </s>
            <s xml:id="echoid-s2713" xml:space="preserve">ducamus per B, C lineam occurrentem D F A in I, & </s>
            <s xml:id="echoid-s2714" xml:space="preserve">G F in G;
              <lb/>
            </s>
            <s xml:id="echoid-s2715" xml:space="preserve">Et quia B O æqualis eſt ipſi C G (octaua ex ſecundo) erit O N æqualis
              <lb/>
              <note position="left" xlink:label="note-0099-05" xlink:href="note-0099-05a" xml:space="preserve">c</note>
            ipſi M L, & </s>
            <s xml:id="echoid-s2716" xml:space="preserve">O L ipſi N M; </s>
            <s xml:id="echoid-s2717" xml:space="preserve">ergo O L, nempe N M, ſeu K F ad E I eſt,
              <lb/>
            vt C L ad C E, nempe D F ad D E, ergo K F ad E I eſt, vt D F
              <lb/>
            ad E D comparando homologorum ſummas in hyperbola, & </s>
            <s xml:id="echoid-s2718" xml:space="preserve">eorundem
              <lb/>
              <note position="left" xlink:label="note-0099-06" xlink:href="note-0099-06a" xml:space="preserve">d</note>
              <note position="right" xlink:label="note-0099-07" xlink:href="note-0099-07a" xml:space="preserve">Lem. 3.</note>
            differentias in ellipſi, & </s>
            <s xml:id="echoid-s2719" xml:space="preserve">iterum comparando antecedentes ad differen-
              <lb/>
              <note position="right" xlink:label="note-0099-08" xlink:href="note-0099-08a" xml:space="preserve">Lem. 1.</note>
            tias terminorum
              <lb/>
              <figure xlink:label="fig-0099-02" xlink:href="fig-0099-02a" number="77">
                <image file="0099-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0099-02"/>
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            fiet D K ad K
              <lb/>
            I, vt D F ad F
              <lb/>
            E, quæ eſt vt
              <lb/>
            proportio figu-
              <lb/>
            ræ; </s>
            <s xml:id="echoid-s2720" xml:space="preserve">igitur B I eſt
              <lb/>
            linea breuiſſima
              <lb/>
            (9. </s>
            <s xml:id="echoid-s2721" xml:space="preserve">10. </s>
            <s xml:id="echoid-s2722" xml:space="preserve">ex quin-
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            to) & </s>
            <s xml:id="echoid-s2723" xml:space="preserve">hoc erat
              <lb/>
            probandum.</s>
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