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-s2395" xml:space="preserve">
              <pb o="52" file="0090" n="90" rhead="Apollonij Pergæi"/>
            in e M æquale eſt
              <lb/>
              <figure xlink:label="fig-0090-01" xlink:href="fig-0090-01a" number="67">
                <image file="0090-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0090-01"/>
              </figure>
            rectangulo V e M,
              <lb/>
            alterius figuræ, &</s>
            <s xml:id="echoid-s2396" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2397" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2398" xml:space="preserve">Et ponamus re-
              <lb/>
              <note position="right" xlink:label="note-0090-01" xlink:href="note-0090-01a" xml:space="preserve">d</note>
            ctangulum F G cõ-
              <lb/>
            mune, &</s>
            <s xml:id="echoid-s2399" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2400" xml:space="preserve">Scili-
              <lb/>
            cet, addatur in hy-
              <lb/>
            perbola, & </s>
            <s xml:id="echoid-s2401" xml:space="preserve">aufera-
              <lb/>
            ratur in ellipſi com-
              <lb/>
            muniter rectangulis
              <lb/>
            F G.</s>
            <s xml:id="echoid-s2402" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2403" xml:space="preserve">Tandem proſe-
              <lb/>
              <note position="right" xlink:label="note-0090-02" xlink:href="note-0090-02a" xml:space="preserve">e</note>
            quamur ſuperiorẽ
              <lb/>
            demonſtrationem,
              <lb/>
            vt oſtendatur veri-
              <lb/>
            tas reliquarũ pro-
              <lb/>
            poſitionum, &</s>
            <s xml:id="echoid-s2404" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2405" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2406" xml:space="preserve">Demonſtratio ab
              <lb/>
            Apollonio breuitatis
              <lb/>
            gratia neglecta ſic
              <lb/>
            perficietur.</s>
            <s xml:id="echoid-s2407" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2408" xml:space="preserve">Quoniam rectã-
              <lb/>
            gulum E M æquale
              <lb/>
            eſt rectangulo V e
              <lb/>
            M, igitur vt E K ad
              <lb/>
            V e, ſeu K γ ad γ e
              <lb/>
            (propter ſimilitudinem triangulorum E K γ, & </s>
            <s xml:id="echoid-s2409" xml:space="preserve">V e γ) ita erit e M ad M K,
              <lb/>
            & </s>
            <s xml:id="echoid-s2410" xml:space="preserve">componendo, eadem e K habebit ad e γ, atque ad M K eandem proportionem,
              <lb/>
            ideoque e γ æqualis eſt M K; </s>
            <s xml:id="echoid-s2411" xml:space="preserve">quare E I ad K M, ſeu I C ad C S eandem pro-
              <lb/>
            portionem habebit, quàm E I ad e γ, ſeu quàm I X ad e V (propter ſimilitudi-
              <lb/>
            nem triangulorum I E X, & </s>
            <s xml:id="echoid-s2412" xml:space="preserve">e γ V) quare comparando homologorum differentias
              <lb/>
            in hyperbola, & </s>
            <s xml:id="echoid-s2413" xml:space="preserve">eorundem ſummas in ellipſi C X ad c V, vel C Z ad Z c (propter
              <lb/>
              <note position="left" xlink:label="note-0090-03" xlink:href="note-0090-03a" xml:space="preserve">Lem. 3.</note>
            ſimilitudinem triangulorum C Z X, c Z V) habebit eandem proportionem, quàm I
              <lb/>
            C ad C S, vel C D ad D F, & </s>
            <s xml:id="echoid-s2414" xml:space="preserve">diuidendo in hyperbola, & </s>
            <s xml:id="echoid-s2415" xml:space="preserve">componendo in ellipſi C c
              <lb/>
            ad c Z eandem proportionem habebit, quàm C F ad F D, ſeu quàm habet latus
              <lb/>
              <note position="left" xlink:label="note-0090-04" xlink:href="note-0090-04a" xml:space="preserve">9. 10.
                <lb/>
              huius.</note>
            tranſuerſum ad rectum, & </s>
            <s xml:id="echoid-s2416" xml:space="preserve">propterea recta linea V Z eſt breuiſsima omnium,
              <lb/>
            quæ ex V ad axim A D duci poſſunt.</s>
            <s xml:id="echoid-s2417" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2418" xml:space="preserve">Iiſdem prorſus verbis oſtenſum erit, quod recta linea l m ſit breuiſsima om-
              <lb/>
            nium cadentium ex puncto l ad axim, ſi nimirum apponãtur caracteres prioris
              <lb/>
            caſus, vt patet in ſecunda, & </s>
            <s xml:id="echoid-s2419" xml:space="preserve">quarta figura.</s>
            <s xml:id="echoid-s2420" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2421" xml:space="preserve">Iiſdem poſitis oſtendendum eſt, ramum B E, interceptum inter duos breuiſe-
              <lb/>
            cantes E V, non eſſe breuiſecantem, atque lineam breuiſsimam ex B ad axim
              <lb/>
            A D extenſam cadere ſupra ramum B E verſus verticem A.</s>
            <s xml:id="echoid-s2422" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2423" xml:space="preserve">Quoniam rectangulum B G M maius eſt rectangulo O G M, atque oſtenſum ſuit
              <lb/>
            rectangulum E M æquale rectangulo O G M; </s>
            <s xml:id="echoid-s2424" xml:space="preserve">ergo rectangulum B G M maius eſt
              <lb/>
            rectangulo E M, & </s>
            <s xml:id="echoid-s2425" xml:space="preserve">propterea E K ad B G, ſeu K R ad R G (propter ſimilitudi-
              <lb/>
              <note position="left" xlink:label="note-0090-05" xlink:href="note-0090-05a" xml:space="preserve">Lem. 5.</note>
            nem triangulorum) minorem proportionem habet, quàm G M ad M K, & </s>
            <s xml:id="echoid-s2426" xml:space="preserve"/>
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