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-div588" type="section" level="1" n="193">
          <pb o="158" file="0196" n="196" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div590" type="section" level="1" n="194">
          <head xml:id="echoid-head248" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s6159" xml:space="preserve">IN principio huius libri monuimus, definitionem ſimilium conicarum
              <lb/>
            ſectionum, quæ circunfertur, vitioſam eſſe; </s>
            <s xml:id="echoid-s6160" xml:space="preserve">quod hic oſtendendum
              <lb/>
            ſuſcepimus: </s>
            <s xml:id="echoid-s6161" xml:space="preserve">ſed prius hæc demonſtranda ſunt.</s>
            <s xml:id="echoid-s6162" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div591" type="section" level="1" n="195">
          <head xml:id="echoid-head249" xml:space="preserve">LEMMA II.</head>
          <p style="it">
            <s xml:id="echoid-s6163" xml:space="preserve">IN duabus coniſectionibus A B, E F eiuſdem nominis ſint axium
              <lb/>
            figuræ G B D, K F I ſimiles inter ſe, ideſt tranſuerſa latera G B,
              <lb/>
            K F proportionalia ſint lateribus rectis B D, F I : </s>
            <s xml:id="echoid-s6164" xml:space="preserve">duci debent in ſingu-
              <lb/>
            lis ſectionibus ſeries applicatarum ad axes, ita vt axium abſciſſæ (quæ
              <lb/>
            proportionales ſunt inter ſe) ad conterminas potentiales non ſint in ijſdem
              <lb/>
            rationibus.</s>
            <s xml:id="echoid-s6165" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6166" xml:space="preserve">Sumantur duæ abſciſſæ B C, F H, quarum C B ad B D habeat maiorem pro-
              <lb/>
            portionem, quàm habet H F ad F I, & </s>
            <s xml:id="echoid-s6167" xml:space="preserve">C B, H F ſecentur proportionaliter in
              <lb/>
            R, V.</s>
            <s xml:id="echoid-s6168" xml:space="preserve">, & </s>
            <s xml:id="echoid-s6169" xml:space="preserve">per ea puncta ducantur ad axes ordinatim applicatæ A C, E H, Q
              <lb/>
            R, T V. </s>
            <s xml:id="echoid-s6170" xml:space="preserve">Quoniam quadratum A C ad rectangulum G C B eandem proportio-
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              <figure xlink:label="fig-0196-01" xlink:href="fig-0196-01a" number="214">
                <image file="0196-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0196-01"/>
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            nem babet, quàm latus rectum D B ad tranſuerſum G B, pariterq; </s>
            <s xml:id="echoid-s6171" xml:space="preserve">quadratum
              <lb/>
              <note position="left" xlink:label="note-0196-01" xlink:href="note-0196-01a" xml:space="preserve">21. lib. 5.</note>
            E H ad rectangulum K H F eſt vt I F ad F K; </s>
            <s xml:id="echoid-s6172" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s6173" xml:space="preserve">D B ad B G ex hypotheſi,
              <lb/>
            eſt vt I F ad F K; </s>
            <s xml:id="echoid-s6174" xml:space="preserve">ergo quadratum A C ad rectangulum G C B eandem pro-
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            portionem habet quàm quadratum E H ad rectangulum K H F : </s>
            <s xml:id="echoid-s6175" xml:space="preserve">& </s>
            <s xml:id="echoid-s6176" xml:space="preserve">quia G B
              <lb/>
            ad B D eſt vt K F ad F I, & </s>
            <s xml:id="echoid-s6177" xml:space="preserve">D B ad B C minorem proportionẽ habet quàm
              <lb/>
            I F ad F H, ergo ex æquali G B ad B C, minorem proportionem habet quàm
              <lb/>
            K F ad F H, & </s>
            <s xml:id="echoid-s6178" xml:space="preserve">componendo in hyperbola, & </s>
            <s xml:id="echoid-s6179" xml:space="preserve">diuidendo in ellipſi G C ad C B
              <lb/>
            ſeu rectangulum G C B ad quadratum B C minorem proportionẽ habebit quàm
              <lb/>
            K H ad H F, ſeu quàm rectangulum K H F ad quadratum F H : </s>
            <s xml:id="echoid-s6180" xml:space="preserve">erat autem
              <lb/>
            quadratum A C ad rectangulum G C B vt quadratum E H ad rectangulum K
              <lb/>
            H F ; </s>
            <s xml:id="echoid-s6181" xml:space="preserve">igitur ex æquali, quadratum A C, ad quadratum C B minorem propor-
              <lb/>
            tionem habet quàm quaàratum E H ad quadratum H F, & </s>
            <s xml:id="echoid-s6182" xml:space="preserve">ideo A C ad C </s>
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