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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        <div xml:id="echoid-div187" type="section" level="1" n="72">
          <p style="it">
            <s xml:id="echoid-s2233" xml:space="preserve">
              <pb o="47" file="0085" n="85" rhead="Conicor. Lib. V."/>
            figuræ compoſitæ, vel diuiſæ, &</s>
            <s xml:id="echoid-s2234" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2235" xml:space="preserve">Quia E K ad K D, atque C F ad F D eandem
              <lb/>
            proportionem habebant, quàm latus tranſuerſum ad rectum; </s>
            <s xml:id="echoid-s2236" xml:space="preserve">ergo componendo in
              <lb/>
            hyperbola, & </s>
            <s xml:id="echoid-s2237" xml:space="preserve">diuidendo in ellipſi erit E D ad D K, vt C D ad D F.</s>
            <s xml:id="echoid-s2238" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2239" xml:space="preserve">Et ponamus re-
              <lb/>
              <note position="left" xlink:label="note-0085-01" xlink:href="note-0085-01a" xml:space="preserve">h</note>
              <figure xlink:label="fig-0085-01" xlink:href="fig-0085-01a" number="62">
                <image file="0085-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0085-01"/>
              </figure>
            ctangulum F G cõ-
              <lb/>
            mune, &</s>
            <s xml:id="echoid-s2240" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2241" xml:space="preserve">Scilicet
              <lb/>
            rectangulũ F G ad-
              <lb/>
            datur in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s2242" xml:space="preserve">auferatur cõmu-
              <lb/>
            niter in ellipſi.</s>
            <s xml:id="echoid-s2243" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2244" xml:space="preserve">Et propterea E
              <lb/>
              <note position="left" xlink:label="note-0085-02" xlink:href="note-0085-02a" xml:space="preserve">i</note>
            K ad B G, nempe
              <lb/>
            K R ad R G, &</s>
            <s xml:id="echoid-s2245" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s2246" xml:space="preserve">Quia propter ſimili-
              <lb/>
            tudinem triangulo-
              <lb/>
            rum E K R, & </s>
            <s xml:id="echoid-s2247" xml:space="preserve">B G
              <lb/>
            R erit E K ad B G,
              <lb/>
            vt K R ad R G; </s>
            <s xml:id="echoid-s2248" xml:space="preserve">qua-
              <lb/>
            re K R ad R G maio-
              <lb/>
            rem proportionẽ ha-
              <lb/>
            bet, quàm G M ad
              <lb/>
            M K; </s>
            <s xml:id="echoid-s2249" xml:space="preserve">& </s>
            <s xml:id="echoid-s2250" xml:space="preserve">componen-
              <lb/>
            do K G ad G R ma-
              <lb/>
            iorem rationem ha-
              <lb/>
            bet, quam eadem G
              <lb/>
            K ad K M, quare
              <lb/>
            K M, nẽpe e i æqua-
              <lb/>
            lis D F maior eſt,
              <lb/>
            quàm G R.</s>
            <s xml:id="echoid-s2251" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2252" xml:space="preserve">Et auferẽdo ho-
              <lb/>
              <note position="left" xlink:label="note-0085-03" xlink:href="note-0085-03a" xml:space="preserve">k</note>
            mologũ ab homo-
              <lb/>
            logo in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s2253" xml:space="preserve">coniungendo e
              <lb/>
            a in ellipſi, habebit, &</s>
            <s xml:id="echoid-s2254" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2255" xml:space="preserve">Scilicet comparando homologorum differentias in hy-
              <lb/>
              <note position="right" xlink:label="note-0085-04" xlink:href="note-0085-04a" xml:space="preserve">Lem. 4.
                <lb/>
              præmiſ.</note>
            perbola, eorundem ſummas in ellipſi, ideſt C T ad B O, nempe C H ad H O (pro-
              <lb/>
            pter ſimilitudinem triangulorum C H T, & </s>
            <s xml:id="echoid-s2256" xml:space="preserve">O H B) habebit maiorem proportionem,
              <lb/>
            quàm I C ad C S, nempe C D ad D F.</s>
            <s xml:id="echoid-s2257" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2258" xml:space="preserve">Poſtea educamus ex E lineam occurrentem ſectioni in V, &</s>
            <s xml:id="echoid-s2259" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2260" xml:space="preserve">Educamus
              <lb/>
              <note position="left" xlink:label="note-0085-05" xlink:href="note-0085-05a" xml:space="preserve">l</note>
            ex E lineam occurrentem ſectioni in V, quæ ſecet axim in Z, & </s>
            <s xml:id="echoid-s2261" xml:space="preserve">S M in Y.</s>
            <s xml:id="echoid-s2262" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2263" xml:space="preserve">Et per f producamus f g h parallelam axi A D, &</s>
            <s xml:id="echoid-s2264" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2265" xml:space="preserve">Et per f ducamus f g pa-
              <lb/>
              <note position="left" xlink:label="note-0085-06" xlink:href="note-0085-06a" xml:space="preserve">m</note>
            rallelam axi A D, quæ ſecet tangentem B a in h, & </s>
            <s xml:id="echoid-s2266" xml:space="preserve">L F in g, atque V c ſecet illam in
              <lb/>
            i, & </s>
            <s xml:id="echoid-s2267" xml:space="preserve">S M in e.</s>
            <s xml:id="echoid-s2268" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2269" xml:space="preserve">Et ponamus rectangulum F f communiter, &</s>
            <s xml:id="echoid-s2270" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2271" xml:space="preserve">Et communiter addamus in
              <lb/>
              <note position="left" xlink:label="note-0085-07" xlink:href="note-0085-07a" xml:space="preserve">n</note>
            hyperbola, & </s>
            <s xml:id="echoid-s2272" xml:space="preserve">auferamus in ellipſi rectangulum F f, fiet rectangulum B fg æquale
              <lb/>
            rectangulo g F C. </s>
            <s xml:id="echoid-s2273" xml:space="preserve">Nomina Inuerſi, & </s>
            <s xml:id="echoid-s2274" xml:space="preserve">Trutinatæ definita fuerunt in primo libro ab
              <lb/>
            interprete Arabico.</s>
            <s xml:id="echoid-s2275" xml:space="preserve"/>
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