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="51" file="0089" n="89" rhead="Conicor. Lib. V."/>
            BG M ſub extremis
              <lb/>
              <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">Lem. 5.</note>
              <figure xlink:label="fig-0089-01" xlink:href="fig-0089-01a" number="66">
                <image file="0089-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0089-01"/>
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            cõtentum maius erit
              <lb/>
            rectãgulo V e M ſub
              <lb/>
            medij s compræhenſo;
              <lb/>
            </s>
            <s xml:id="echoid-s2368" xml:space="preserve">erat autem prius re-
              <lb/>
            ctangulum B G M
              <lb/>
            æquale rectangulo E
              <lb/>
            M; </s>
            <s xml:id="echoid-s2369" xml:space="preserve">ergo rectangulũ
              <lb/>
            E M maius eſt re-
              <lb/>
            ctangulo V e M, & </s>
            <s xml:id="echoid-s2370" xml:space="preserve">
              <lb/>
            propterea E K ad V
              <lb/>
              <note position="right" xlink:label="note-0089-02" xlink:href="note-0089-02a" xml:space="preserve">Lem. 5.</note>
            e, ſeu K γ ad γ e
              <lb/>
            (propter ſimilitudi-
              <lb/>
            nem triangulorum
              <lb/>
            E Y K, & </s>
            <s xml:id="echoid-s2371" xml:space="preserve">V e Y) ma-
              <lb/>
            iorem proportionem
              <lb/>
            habebit, quàm e M
              <lb/>
            ad M K, & </s>
            <s xml:id="echoid-s2372" xml:space="preserve">compo-
              <lb/>
            nendo, eadem K e
              <lb/>
            ad Y e maiorem pro-
              <lb/>
            portionem habebit,
              <lb/>
            quàm ad M K; </s>
            <s xml:id="echoid-s2373" xml:space="preserve">ergo
              <lb/>
            Y e minor eſt, quàm
              <lb/>
            M K, quare E I ad
              <lb/>
            Y e, ſeu I X ad e V
              <lb/>
            (propter ſimilitudi-
              <lb/>
            nem triangulorum I
              <lb/>
            E X, e Y V) habebit
              <lb/>
            maiorem proportio-
              <lb/>
            nem, quàm eadem.
              <lb/>
            </s>
            <s xml:id="echoid-s2374" xml:space="preserve">E I ad M K, ſeu I C ad C S, velad c e; </s>
            <s xml:id="echoid-s2375" xml:space="preserve">& </s>
            <s xml:id="echoid-s2376" xml:space="preserve">propterea comparando homologorum
              <lb/>
              <note position="right" xlink:label="note-0089-03" xlink:href="note-0089-03a" xml:space="preserve">Lem. 4.</note>
            ſummas in ellipſi, & </s>
            <s xml:id="echoid-s2377" xml:space="preserve">earundem differentias in hyperbola C X ad c V, vel C Z
              <lb/>
            ad Z c (propter ſimilitudinem triangulorum C Z X, V c Z) maiorem proportio-
              <lb/>
            nem habebit, quàm S K, ad K M, ſeu C D ad D F, & </s>
            <s xml:id="echoid-s2378" xml:space="preserve">diuidendo in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s2379" xml:space="preserve">componendo in ellipſi C c ad c Z habebit maiorem proportionem, quàm C F
              <lb/>
            ad F D, ſeu quàm latus tranſuerſum ad rectum, & </s>
            <s xml:id="echoid-s2380" xml:space="preserve">propterea breuiſsima linea-
              <lb/>
              <note position="right" xlink:label="note-0089-04" xlink:href="note-0089-04a" xml:space="preserve">ex 9. 10.
                <lb/>
              huius.</note>
            rum cadentium ex puncto V ad axim abſcindet ſegmentum maius, quàm A Z,
              <lb/>
            & </s>
            <s xml:id="echoid-s2381" xml:space="preserve">ramus E V non erit breuiſecans, quod ſuerat oſtendendum.</s>
            <s xml:id="echoid-s2382" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2383" xml:space="preserve">Et demonſtrabitur, quemadmodum dictum eſt, quod G O ad B O mi-
              <lb/>
              <note position="left" xlink:label="note-0089-05" xlink:href="note-0089-05a" xml:space="preserve">b</note>
            norem proportionem habet, quàm F O ad O C, &</s>
            <s xml:id="echoid-s2384" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2385" xml:space="preserve">Nam proportio E D ad
              <lb/>
            B O componitur ex rationibus E D ad D K, & </s>
            <s xml:id="echoid-s2386" xml:space="preserve">D K, ſeu G O ad B O. </s>
            <s xml:id="echoid-s2387" xml:space="preserve">Pariterque
              <lb/>
            proportio Trutinæ Q quæ erat maior quàm E D ad B O componitur ex ratio-
              <lb/>
            nibus C D ad D F, & </s>
            <s xml:id="echoid-s2388" xml:space="preserve">F O ad O C, auferatur communis proportio E D ad D K,
              <lb/>
            vel C D ad D F, remanet proportio G O ad O B minor proportione F O ad O C.</s>
            <s xml:id="echoid-s2389" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2390" xml:space="preserve">Et producamus ex V, l duas perpendiculares V e, l P, quæ, &</s>
            <s xml:id="echoid-s2391" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2392" xml:space="preserve">Et
              <lb/>
              <note position="left" xlink:label="note-0089-06" xlink:href="note-0089-06a" xml:space="preserve">c</note>
            producamus ex V, & </s>
            <s xml:id="echoid-s2393" xml:space="preserve">V duas perpendiculares V e, quæ parallelæ ſint continenti
              <lb/>
            F M, & </s>
            <s xml:id="echoid-s2394" xml:space="preserve">ſecent reliquas lineas in ſignis antea expoſitis; </s>
            <s xml:id="echoid-s2395" xml:space="preserve">Rectangulum ergo V </s>
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