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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            <s xml:id="echoid-s2426" xml:space="preserve">
              <pb o="53" file="0091" n="91" rhead="Conicor. Lib. V."/>
              <figure xlink:label="fig-0091-01" xlink:href="fig-0091-01a" number="68">
                <image file="0091-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0091-01"/>
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            ponendo eadem K G
              <lb/>
            ad G R minorẽ pro-
              <lb/>
            portionem habebit,
              <lb/>
            quãad K M, & </s>
            <s xml:id="echoid-s2427" xml:space="preserve">pro-
              <lb/>
            pterea G R maior e-
              <lb/>
            rit, quàm K M, vnde
              <lb/>
            E I ad G R, ſeu I T
              <lb/>
            ad G B (propter ſi-
              <lb/>
            militudinem trian-
              <lb/>
            gulorum E I T, R G
              <lb/>
            B) minorem propor-
              <lb/>
            tionem habet, quàm
              <lb/>
            E I ad K M, ſeu I C
              <lb/>
            ad C S; </s>
            <s xml:id="echoid-s2428" xml:space="preserve">& </s>
            <s xml:id="echoid-s2429" xml:space="preserve">ideo com-
              <lb/>
            parando homologarũ
              <lb/>
            ſummas in ellipſi, & </s>
            <s xml:id="echoid-s2430" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0091-01" xlink:href="note-0091-01a" xml:space="preserve">Lem. 4.</note>
            eorundem differen-
              <lb/>
            tias in hyperbola C
              <lb/>
            T ad O B, ſiue C H
              <lb/>
            ad H O (propter ſi-
              <lb/>
            militudinem trian-
              <lb/>
            gulorũ) habebit mi-
              <lb/>
            norẽ proportionem,
              <lb/>
            quàm I C ad C S,
              <lb/>
            vel C D ad D F, & </s>
            <s xml:id="echoid-s2431" xml:space="preserve">
              <lb/>
            diuidendo in hyper-
              <lb/>
            bola, & </s>
            <s xml:id="echoid-s2432" xml:space="preserve">componendo in ellipſi C O ad O H habebit minorem proportionem, quàm
              <lb/>
              <note position="right" xlink:label="note-0091-02" xlink:href="note-0091-02a" xml:space="preserve">Ex 9. 10.
                <lb/>
              huius.</note>
            C F ad F D, ſiue quàm latus tranſuerſum habet ad rectum; </s>
            <s xml:id="echoid-s2433" xml:space="preserve">ergo breuiſsima ex
              <lb/>
            B ad axim ducta eum ſecat ſupra punctum H, & </s>
            <s xml:id="echoid-s2434" xml:space="preserve">abſcindit lineam minorem,
              <lb/>
            quàm A H.</s>
            <s xml:id="echoid-s2435" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2436" xml:space="preserve">Rurſus ijſdem poſitis, oſtendendum eſt, ramum E p cadentem ſupra ramum
              <lb/>
            E V verſus verticem, velinfra infimum breuiſecantem E V non eße breuiſecan-
              <lb/>
            tem, & </s>
            <s xml:id="echoid-s2437" xml:space="preserve">abſcindere ex axi minorem lineam, quàm abſcindit breuiſsima ex pun-
              <lb/>
            cto p ad axim ducta. </s>
            <s xml:id="echoid-s2438" xml:space="preserve">Ducatur ex p recta linea p x perpendicularis ad axim,
              <lb/>
            eum ſecans in x, & </s>
            <s xml:id="echoid-s2439" xml:space="preserve">ſecans S M in r, & </s>
            <s xml:id="echoid-s2440" xml:space="preserve">hyperbolen V o in t, pariterque ramus
              <lb/>
            E p ſecet S M in z, & </s>
            <s xml:id="echoid-s2441" xml:space="preserve">A F in q, atque I C in f. </s>
            <s xml:id="echoid-s2442" xml:space="preserve">Quoniam hyperbole V o ſe-
              <lb/>
            cat coniſectionem A B in V, & </s>
            <s xml:id="echoid-s2443" xml:space="preserve">p ponitur ſupra V ad partes A; </s>
            <s xml:id="echoid-s2444" xml:space="preserve">ergo t cadit
              <lb/>
            extra ſectionem A B, & </s>
            <s xml:id="echoid-s2445" xml:space="preserve">propterea t r maior erit, quàm p r; </s>
            <s xml:id="echoid-s2446" xml:space="preserve">vnde rectangulum
              <lb/>
            p r M minus erit rectangulo t r M; </s>
            <s xml:id="echoid-s2447" xml:space="preserve">ſed propter aſymptotos S M, M F eſt rectan-
              <lb/>
              <note position="right" xlink:label="note-0091-03" xlink:href="note-0091-03a" xml:space="preserve">12. lib.2.</note>
            gulum t r M æquale rectangulo o G M, ſeu rectangulo E M, vt dictum eſt; </s>
            <s xml:id="echoid-s2448" xml:space="preserve">ergo
              <lb/>
            rectangulum p r M minus eſt rectangulo E K M, & </s>
            <s xml:id="echoid-s2449" xml:space="preserve">propterea E K ad p r, ſeu
              <lb/>
              <note position="right" xlink:label="note-0091-04" xlink:href="note-0091-04a" xml:space="preserve">Lem. 5.</note>
            K z ad z r (propter ſimilitudinem triangulorum) maiorem proportionem habet,
              <lb/>
            quàm r M ad M K, & </s>
            <s xml:id="echoid-s2450" xml:space="preserve">componendo, eadé K r ad r z maioré proportioné habet,
              <lb/>
            quàm ad M K; </s>
            <s xml:id="echoid-s2451" xml:space="preserve">ergo r z minor eſt, quàm M K; </s>
            <s xml:id="echoid-s2452" xml:space="preserve">ideoque E I ad r z, ſeu I f ad
              <lb/>
            r p (propter ſimilitudinem triangulorum E I ſ, & </s>
            <s xml:id="echoid-s2453" xml:space="preserve">r p z) maiorem proportionem
              <lb/>
            habet, quàm E I ad M K, ſeu I C ad C S, vel ad r x; </s>
            <s xml:id="echoid-s2454" xml:space="preserve">ergo comparando homo-
              <lb/>
              <note position="right" xlink:label="note-0091-05" xlink:href="note-0091-05a" xml:space="preserve">Lem. 4.</note>
            logorum ſummas in ellipſi, & </s>
            <s xml:id="echoid-s2455" xml:space="preserve">eorundem differentias in hyperbola C ſ ad x </s>
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