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="49" file="0087" n="87" rhead="Conicor. Lib. V."/>
            mas in ellipſi, & </s>
            <s xml:id="echoid-s2313" xml:space="preserve">eo-
              <lb/>
              <figure xlink:label="fig-0087-01" xlink:href="fig-0087-01a" number="64">
                <image file="0087-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0087-01"/>
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            rundem differentias
              <lb/>
            in hyperbola C X ad
              <lb/>
              <note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">Lem. 4.</note>
            c V, vel (propter
              <lb/>
            ſimilitudinem triã-
              <lb/>
            gulorum X C Z, V c
              <lb/>
            Z) C Z ad Z c ma-
              <lb/>
            iorem proportionem
              <lb/>
            habet, quàm I C ad
              <lb/>
            C S, vel C D ad D
              <lb/>
            F; </s>
            <s xml:id="echoid-s2314" xml:space="preserve">& </s>
            <s xml:id="echoid-s2315" xml:space="preserve">componendo
              <lb/>
            in ellipſi, & </s>
            <s xml:id="echoid-s2316" xml:space="preserve">diui-
              <lb/>
            dendo in hyperbola
              <lb/>
            C c ad c Z maiorẽ
              <lb/>
            proportionem habe-
              <lb/>
            bit, quàm C F ad
              <lb/>
              <note position="right" xlink:label="note-0087-02" xlink:href="note-0087-02a" xml:space="preserve">9. 10.
                <lb/>
              huius.</note>
            F D, & </s>
            <s xml:id="echoid-s2317" xml:space="preserve">ideo breuiſ-
              <lb/>
            ſima egrediens ex V
              <lb/>
            abſcindit lineã ma-
              <lb/>
            iorem, quàm A Z.</s>
            <s xml:id="echoid-s2318" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2319" xml:space="preserve">Simili modo cõ-
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            ſtat, quod breuiſ-
              <lb/>
              <note position="left" xlink:label="note-0087-03" xlink:href="note-0087-03a" xml:space="preserve">t</note>
            ſima egrediens ex
              <lb/>
            l eiuſdem ſit ratio-
              <lb/>
            nis, &</s>
            <s xml:id="echoid-s2320" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2321" xml:space="preserve">Abſque no-
              <lb/>
            ua demonſtratione
              <lb/>
            in ſecunda, & </s>
            <s xml:id="echoid-s2322" xml:space="preserve">quar
              <lb/>
            ta figura propoſitum oſtenſum erit.</s>
            <s xml:id="echoid-s2323" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2324" xml:space="preserve">Deinde ſit E D æqualis Q, inde demonſtrabitur (quemadmodum ſu-
              <lb/>
              <note position="left" xlink:label="note-0087-04" xlink:href="note-0087-04a" xml:space="preserve">a</note>
            pra factum eſt) quod B H tantum ſit linea breuiſſima, &</s>
            <s xml:id="echoid-s2325" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2326" xml:space="preserve"/>
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        <div xml:id="echoid-div208" type="section" level="1" n="73">
          <head xml:id="echoid-head106" style="it" xml:space="preserve">Secunda pars buius propoſitionis, quam Apollonius non expoſuit hac
            <lb/>
          ratione ſuppleri poteſt.</head>
          <p style="it">
            <s xml:id="echoid-s2327" xml:space="preserve">Sit E D æqualis Trutinæ Q habebunt E D, atque Q eandem proportionem
              <lb/>
            ad B O, componitur verò proportio E D ad B O ex rationibus E D ad D K, & </s>
            <s xml:id="echoid-s2328" xml:space="preserve">
              <lb/>
            D K ad B O, ſeu O G ad B O; </s>
            <s xml:id="echoid-s2329" xml:space="preserve">componebatur autem proportio Trutinæ Q ad B O
              <lb/>
            ex rationibus C D ad D F, & </s>
            <s xml:id="echoid-s2330" xml:space="preserve">F O ad O C; </s>
            <s xml:id="echoid-s2331" xml:space="preserve">ergo ablata communiter proportione
              <lb/>
            E D ad D K, vel C D ad D F, relinquetur proportio G O ad O B eadem propor-
              <lb/>
            tioni F O ad O C; </s>
            <s xml:id="echoid-s2332" xml:space="preserve">ergo rectangulum G O C ſub extremis contentum æquale erit
              <lb/>
            rectangulo B O F ſub intermedijs compræbenſo, addatur in hyperbola, & </s>
            <s xml:id="echoid-s2333" xml:space="preserve">aufe-
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            ratur in ellipſi communiter rectangulum F G, erit rectangulum F S æquale re-
              <lb/>
            ctangulo B G M; </s>
            <s xml:id="echoid-s2334" xml:space="preserve">Et quia I S ad S C, vel E K ad K D, velad F M erat, vt C
              <lb/>
            F ad F D, vel vt S M ad M K; </s>
            <s xml:id="echoid-s2335" xml:space="preserve">ergo rectangulum E M æquale eſt rectangulo
              <lb/>
            F S; </s>
            <s xml:id="echoid-s2336" xml:space="preserve">& </s>
            <s xml:id="echoid-s2337" xml:space="preserve">propterea rectangulum E M æquale erit rectangulo B G M; </s>
            <s xml:id="echoid-s2338" xml:space="preserve">quapropter
              <lb/>
            vt E K ad B G, ſeu K R ad R G, ita erit G M ad M K, & </s>
            <s xml:id="echoid-s2339" xml:space="preserve">componendo, </s>
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