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-div50" type="section" level="1" n="40">
          <head xml:id="echoid-head65" xml:space="preserve">Notæ in propoſitionem quintam.</head>
          <p style="it">
            <s xml:id="echoid-s971" xml:space="preserve">ERit I M æqualis M O, &</s>
            <s xml:id="echoid-s972" xml:space="preserve">c. </s>
            <s xml:id="echoid-s973" xml:space="preserve">Propter parallelas M O, C H, & </s>
            <s xml:id="echoid-s974" xml:space="preserve">ſimilitudi-
              <lb/>
              <note position="right" xlink:label="note-0048-01" xlink:href="note-0048-01a" xml:space="preserve">a</note>
            nem triangulorum I M O, & </s>
            <s xml:id="echoid-s975" xml:space="preserve">I C H.</s>
            <s xml:id="echoid-s976" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s977" xml:space="preserve">Ergo quadratum
              <lb/>
              <figure xlink:label="fig-0048-01" xlink:href="fig-0048-01a" number="16">
                <image file="0048-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0048-01"/>
              </figure>
              <note position="right" xlink:label="note-0048-02" xlink:href="note-0048-02a" xml:space="preserve">b</note>
            I L duplum eſt triã-
              <lb/>
            guli I C H, &</s>
            <s xml:id="echoid-s978" xml:space="preserve">c. </s>
            <s xml:id="echoid-s979" xml:space="preserve">Eo
              <lb/>
            quod quadratum I L
              <lb/>
            æquale eſt duobus qua-
              <lb/>
            dratis I M, M L in
              <lb/>
            rectangulo triangulo I
              <lb/>
            M L; </s>
            <s xml:id="echoid-s980" xml:space="preserve">Quadratis au-
              <lb/>
            tẽ I M, & </s>
            <s xml:id="echoid-s981" xml:space="preserve">L M æqua-
              <lb/>
            lia ſunt triangulum
              <lb/>
            I M O bis ſumptum
              <lb/>
            cum trapezio C M Q
              <lb/>
            H bis ſumpto; </s>
            <s xml:id="echoid-s982" xml:space="preserve">& </s>
            <s xml:id="echoid-s983" xml:space="preserve">quia
              <lb/>
              <note position="left" xlink:label="note-0048-03" xlink:href="note-0048-03a" xml:space="preserve">1. huius.</note>
            trapezium C M Q H
              <lb/>
            æquale eſt trapezio C
              <lb/>
            M O H, cum triangu-
              <lb/>
            lo H O Q; </s>
            <s xml:id="echoid-s984" xml:space="preserve">at triangulo I M O,
              <lb/>
            & </s>
            <s xml:id="echoid-s985" xml:space="preserve">trapezio C M Q H ſimul ſum-
              <lb/>
            ptis æqualia ſunt triangulum
              <lb/>
            I C H, cum triangulo H O Q.
              <lb/>
            </s>
            <s xml:id="echoid-s986" xml:space="preserve">Ergo quadratum L I æquale erit
              <lb/>
            duplo trianguli I C H cum duplo
              <lb/>
            trianguli H O Q.</s>
            <s xml:id="echoid-s987" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s988" xml:space="preserve">Deindè ponamus in ellipſi
              <lb/>
              <note position="right" xlink:label="note-0048-04" xlink:href="note-0048-04a" xml:space="preserve">c</note>
            Y F æqualem D C, & </s>
            <s xml:id="echoid-s989" xml:space="preserve">in hy-
              <lb/>
            perbola, &</s>
            <s xml:id="echoid-s990" xml:space="preserve">c. </s>
            <s xml:id="echoid-s991" xml:space="preserve">Textus videtur
              <lb/>
            corruptus, quem ſic corrigendum
              <lb/>
            puto. </s>
            <s xml:id="echoid-s992" xml:space="preserve">Ponamus γ F in ellipſi æ-
              <lb/>
            qualem differentiæ, & </s>
            <s xml:id="echoid-s993" xml:space="preserve">in hyper-
              <lb/>
            bola æqualem aggregato D C, & </s>
            <s xml:id="echoid-s994" xml:space="preserve">C F.</s>
            <s xml:id="echoid-s995" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s996" xml:space="preserve">Propter ſimilitudinem triangulorum, &</s>
            <s xml:id="echoid-s997" xml:space="preserve">c. </s>
            <s xml:id="echoid-s998" xml:space="preserve">Sunt enim duæ rectæ lineæ C G,
              <lb/>
              <note position="right" xlink:label="note-0048-05" xlink:href="note-0048-05a" xml:space="preserve">d</note>
            & </s>
            <s xml:id="echoid-s999" xml:space="preserve">V H æquidiſtantes, quæ ſecant rectas lineas conuenientes in Q, & </s>
            <s xml:id="echoid-s1000" xml:space="preserve">O.</s>
            <s xml:id="echoid-s1001" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1002" xml:space="preserve">Erit H V æqualis V O, &</s>
            <s xml:id="echoid-s1003" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1004" xml:space="preserve">Eo quòd M I oſtenſa eſt æqualis M O, eſtque
              <lb/>
              <note position="right" xlink:label="note-0048-06" xlink:href="note-0048-06a" xml:space="preserve">e</note>
            H V ad V O in eadem proportione æqualitatis propter iam dictam ſimilitudinem
              <lb/>
            triangulorum.</s>
            <s xml:id="echoid-s1005" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1006" xml:space="preserve">Igitur V O ad V Q eſt, vt D C ad C F, & </s>
            <s xml:id="echoid-s1007" xml:space="preserve">conuerſa proportione dein-
              <lb/>
              <note position="right" xlink:label="note-0048-07" xlink:href="note-0048-07a" xml:space="preserve">f</note>
            dè componendo in hyperbola, & </s>
            <s xml:id="echoid-s1008" xml:space="preserve">inuertendo in ellipſi fiet in hyperbola
              <lb/>
            Q O ad O V, &</s>
            <s xml:id="echoid-s1009" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1010" xml:space="preserve">Textum corruptum, atque confuſum clariùs exponi poſſe
              <lb/>
            cenſeo per Lemma inferius appoſitum hac ratione. </s>
            <s xml:id="echoid-s1011" xml:space="preserve">Et comparando ſummas in
              <lb/>
            hyperbola, & </s>
            <s xml:id="echoid-s1012" xml:space="preserve">differentias terminorum in ellipſi ad antecedentes.</s>
            <s xml:id="echoid-s1013" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1014" xml:space="preserve">Vt Y F ad Y C, & </s>
            <s xml:id="echoid-s1015" xml:space="preserve">in ellipſi, vt F C ad C F, & </s>
            <s xml:id="echoid-s1016" xml:space="preserve">Y F in ellipſi æqualis
              <lb/>
              <note position="right" xlink:label="note-0048-08" xlink:href="note-0048-08a" xml:space="preserve">g</note>
            </s>
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