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-div567" type="section" level="1" n="185">
          <p style="it">
            <s xml:id="echoid-s5976" xml:space="preserve">
              <pb o="152" file="0190" n="190" rhead="Apollonij Pergæi"/>
            entes; </s>
            <s xml:id="echoid-s5977" xml:space="preserve">ideoque ſi vnus eorum, nempe Z T extrinſecùs tangit communem portio-
              <lb/>
            nem conicam B C, reliquus V X extrinſecùs quoque eam langet, ſed ex conſtru-
              <lb/>
            ctione intrinſecùs ſectionem tangebat, quod eſt abſurdum: </s>
            <s xml:id="echoid-s5978" xml:space="preserve">Non ergo duæ por-
              <lb/>
            tiones B C, & </s>
            <s xml:id="echoid-s5979" xml:space="preserve">E F non æquè à verticibus axium remotæ ſibi mutuo congruent-
              <lb/>
            Quod erat oſtendendum.</s>
            <s xml:id="echoid-s5980" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5981" xml:space="preserve">Si autem cadit in ellipſi axis A C tranſuerſus ſuper axim rectum illius;
              <lb/>
            </s>
            <s xml:id="echoid-s5982" xml:space="preserve">
              <note position="right" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">b</note>
            vtique excedit illam, & </s>
            <s xml:id="echoid-s5983" xml:space="preserve">non ſibi mutuò congruunt ſectiones, & </s>
            <s xml:id="echoid-s5984" xml:space="preserve">quædam
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            congruunt, &</s>
            <s xml:id="echoid-s5985" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5986" xml:space="preserve">Senſus eſt. </s>
            <s xml:id="echoid-s5987" xml:space="preserve">Si intelligantur duæ ellipſes, habentes axes tran-
              <lb/>
            ſuerſos A B, & </s>
            <s xml:id="echoid-s5988" xml:space="preserve">G H æquales inier ſe, pariterque
              <lb/>
              <figure xlink:label="fig-0190-01" xlink:href="fig-0190-01a" number="204">
                <image file="0190-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0190-01"/>
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            axes rectos C D, I K æquales: </s>
            <s xml:id="echoid-s5989" xml:space="preserve">& </s>
            <s xml:id="echoid-s5990" xml:space="preserve">axis A B tran-
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            ſuerſus vnius ponatur ſuper I K axim rectum al-
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            terius, ita vt centra ſibi mutuò congruant in E:
              <lb/>
            </s>
            <s xml:id="echoid-s5991" xml:space="preserve">tunc quidem, quia axes in ellipſi inæquales ſunt
              <lb/>
            (alias eſſet circulus) igitur extremitates axis tran-
              <lb/>
            ſuerſi A B non cadunt ſuper extremitaites axis re-
              <lb/>
            cti K I, neque G, H cadunt ſuper C, D; </s>
            <s xml:id="echoid-s5992" xml:space="preserve">& </s>
            <s xml:id="echoid-s5993" xml:space="preserve">ideo
              <lb/>
            circumferentiæ ellipſium ſe ſe mutuò ſecant qua-
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            tuor in locis, vt in libro 4. </s>
            <s xml:id="echoid-s5994" xml:space="preserve">oſtenſnm eſt.</s>
            <s xml:id="echoid-s5995" xml:space="preserve"/>
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        <div xml:id="echoid-div572" type="section" level="1" n="186">
          <head xml:id="echoid-head240" xml:space="preserve">SECTIO TERTIA
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          Continens Propoſit. V. & VIII.
            <lb/>
          PROPOSITIO V.</head>
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            <s xml:id="echoid-s5996" xml:space="preserve">SI per centrum E ellipſis A B, C D tranſeat linea recta A
              <lb/>
            C vſque ad ſectionem; </s>
            <s xml:id="echoid-s5997" xml:space="preserve">vtique bifariam diuidit ſuperſiciem
              <lb/>
            ſectionis, & </s>
            <s xml:id="echoid-s5998" xml:space="preserve">circumferentiam illius, ſcilicet erit ſuperſicies A B
              <lb/>
            C æqualis ſuperficiei A D C.</s>
            <s xml:id="echoid-s5999" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6000" xml:space="preserve">Nam ſi A C fuerit axis ſectio-
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                <image file="0190-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0190-02"/>
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            nis, vtique circumferentia A B C
              <lb/>
            congruet A D C, nam ſi non cõ-
              <lb/>
            gruit ſignemus locum B, quod al-
              <lb/>
            teri ſectioni nõ coincidat, & </s>
            <s xml:id="echoid-s6001" xml:space="preserve">pro-
              <lb/>
            ducamus ex illo perpendicularem
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            B F ſuper A C vſque ad D. </s>
            <s xml:id="echoid-s6002" xml:space="preserve">Er-
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            go B D ordinata eſt ad C A, & </s>
            <s xml:id="echoid-s6003" xml:space="preserve">
              <lb/>
            propterea B F ſuperpoſita cõgru-
              <lb/>
            et ipſi D F, & </s>
            <s xml:id="echoid-s6004" xml:space="preserve">cadet B ſuper D,
              <lb/>
            quia B F æqualis eſt D F (8. </s>
            <s xml:id="echoid-s6005" xml:space="preserve">ex
              <lb/>
            1.)</s>
            <s xml:id="echoid-s6006" xml:space="preserve">; </s>
            <s xml:id="echoid-s6007" xml:space="preserve">ſed non cadebat ſuper illum; </s>
            <s xml:id="echoid-s6008" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s6009" xml:space="preserve">Igitur </s>
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