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-div550" type="section" level="1" n="179">
          <pb o="148" file="0186" n="186" rhead="Apollonij Pergæi"/>
          <p>
            <s xml:id="echoid-s5810" xml:space="preserve">Sit coniſectio A B C, & </s>
            <s xml:id="echoid-s5811" xml:space="preserve">eius axis B D, & </s>
            <s xml:id="echoid-s5812" xml:space="preserve">ſu-
              <lb/>
              <figure xlink:label="fig-0186-01" xlink:href="fig-0186-01a" number="194">
                <image file="0186-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0186-01"/>
              </figure>
            mantur in ſectione puncta G, C, ab eis educã-
              <lb/>
            tur duæ ordinationes G H, C A occurrentes axi
              <lb/>
            in I, D. </s>
            <s xml:id="echoid-s5813" xml:space="preserve">Dico, quod B G congruit B H, & </s>
            <s xml:id="echoid-s5814" xml:space="preserve">G
              <lb/>
            C ipſi H A, & </s>
            <s xml:id="echoid-s5815" xml:space="preserve">ſuperſicies B D C ſuperficiei B
              <lb/>
            D A, & </s>
            <s xml:id="echoid-s5816" xml:space="preserve">ſegmentum B G C ſegmento B H A.
              <lb/>
            </s>
            <s xml:id="echoid-s5817" xml:space="preserve">Quoniam axis B D bifariam diuidit G H, A C
              <lb/>
            in I, D, vtique G I ipſi I H congruet, & </s>
            <s xml:id="echoid-s5818" xml:space="preserve">D C
              <lb/>
              <note position="right" xlink:label="note-0186-01" xlink:href="note-0186-01a" xml:space="preserve">b</note>
            ipſi D A, & </s>
            <s xml:id="echoid-s5819" xml:space="preserve">duo puncta G, C ſuper duobus
              <lb/>
            punctis H, A cadent, & </s>
            <s xml:id="echoid-s5820" xml:space="preserve">portio ſectionis conicæ
              <lb/>
            G C ſuper portionem H A, & </s>
            <s xml:id="echoid-s5821" xml:space="preserve">G B ſuper H B:
              <lb/>
            </s>
            <s xml:id="echoid-s5822" xml:space="preserve">
              <figure xlink:label="fig-0186-02" xlink:href="fig-0186-02a" number="195">
                <image file="0186-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0186-02"/>
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            Et dico, quod portio H A non congruit
              <lb/>
            alicui alteri portioni, quàm G C: </s>
            <s xml:id="echoid-s5823" xml:space="preserve">ſi enim
              <lb/>
            poſſibile eſt cõgruat portioni C K, & </s>
            <s xml:id="echoid-s5824" xml:space="preserve">por-
              <lb/>
            tio H B congruet portioni, quæ continua-
              <lb/>
            tur ipſi K C; </s>
            <s xml:id="echoid-s5825" xml:space="preserve">ergo cadet B ex H B non ſu-
              <lb/>
            per B ex C G B; </s>
            <s xml:id="echoid-s5826" xml:space="preserve">quia portio H B non eſt
              <lb/>
            æqualis portioni C B; </s>
            <s xml:id="echoid-s5827" xml:space="preserve">& </s>
            <s xml:id="echoid-s5828" xml:space="preserve">propterea incidet
              <lb/>
            axis B D in alium locum, eſſentque eidem
              <lb/>
            ſectioni plures axes: </s>
            <s xml:id="echoid-s5829" xml:space="preserve">quod eſt abſurdum;
              <lb/>
            </s>
            <s xml:id="echoid-s5830" xml:space="preserve">(51. </s>
            <s xml:id="echoid-s5831" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5832" xml:space="preserve">ex 2.) </s>
            <s xml:id="echoid-s5833" xml:space="preserve">igitur non cadit H A niſi
              <lb/>
              <note position="left" xlink:label="note-0186-02" xlink:href="note-0186-02a" xml:space="preserve">48. lib. 2.</note>
            ſuper C G. </s>
            <s xml:id="echoid-s5834" xml:space="preserve">Vt fuerat propoſitum.</s>
            <s xml:id="echoid-s5835" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div553" type="section" level="1" n="180">
          <head xml:id="echoid-head234" xml:space="preserve">PROPOSITIO IX.</head>
          <p>
            <s xml:id="echoid-s5836" xml:space="preserve">M Anifeſtum eſt ex demoſtratis, quod portiones ſectionum
              <lb/>
              <note position="right" xlink:label="note-0186-03" xlink:href="note-0186-03a" xml:space="preserve">a</note>
            æqualium non congruunt ſibi inuicem, niſi earum di-
              <lb/>
            ſtantiæ à verticibus ſint æquales.</s>
            <s xml:id="echoid-s5837" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5838" xml:space="preserve">Oſtenſum enim eſt ſibi non congruere, quarum diſtantiæ à verticibus
              <lb/>
            non ſunt æquales, quia portio H A, ſi caderet ſuper portionem C K, & </s>
            <s xml:id="echoid-s5839" xml:space="preserve">
              <lb/>
            earum diſtantiæ à B non eſſent æquales, conſequitur, quod in hyperbola
              <lb/>
            ſint duo axes, & </s>
            <s xml:id="echoid-s5840" xml:space="preserve">in ellipſi tres axes: </s>
            <s xml:id="echoid-s5841" xml:space="preserve">quod eſt abſurdum (51. </s>
            <s xml:id="echoid-s5842" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5843" xml:space="preserve">53.
              <lb/>
            </s>
            <s xml:id="echoid-s5844" xml:space="preserve">
              <note position="left" xlink:label="note-0186-04" xlink:href="note-0186-04a" xml:space="preserve">48. lib. 2</note>
            ex 2.)</s>
            <s xml:id="echoid-s5845" xml:space="preserve"/>
          </p>
          <figure number="196">
            <image file="0186-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0186-03"/>
          </figure>
          <p>
            <s xml:id="echoid-s5846" xml:space="preserve">Si autem in ellipſi cadit axis A E tranſuer-
              <lb/>
              <note position="right" xlink:label="note-0186-05" xlink:href="note-0186-05a" xml:space="preserve">b</note>
              <figure xlink:label="fig-0186-04" xlink:href="fig-0186-04a" number="197">
                <image file="0186-04" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0186-04"/>
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            ſus ſuper axim rectum illius, vtique differunt
              <lb/>
            inter ſe, & </s>
            <s xml:id="echoid-s5847" xml:space="preserve">non ſibi inuicem congruunt ſectio-
              <lb/>
            nes.</s>
            <s xml:id="echoid-s5848" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5849" xml:space="preserve">Conſtat etiam, quod in ſectionibus inæ-
              <lb/>
            qualibus, vt A B C, D E F portio vnius ea-
              <lb/>
            rum non congruit portioni alterius.</s>
            <s xml:id="echoid-s5850" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5851" xml:space="preserve">Alioqui congruet B A ipſi D E, & </s>
            <s xml:id="echoid-s5852" xml:space="preserve">congrue-
              <lb/>
            ret etiam E F ipſi B C (6. </s>
            <s xml:id="echoid-s5853" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s5854" xml:space="preserve">eſſetque ſe-
              <lb/>
            ctio C B A æqualis ſectioni F E D: </s>
            <s xml:id="echoid-s5855" xml:space="preserve">at ſuppo-
              <lb/>
            ſuimus, non eſſe æquales, quod eſt abſurdum:</s>
            <s xml:id="echoid-s5856" xml:space="preserve"/>
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