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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            <s xml:id="echoid-s6182" xml:space="preserve">
              <pb o="159" file="0197" n="197" rhead="Conicor. Lib. VI."/>
            minorem proportionem habebit, quàm E H ad H F. </s>
            <s xml:id="echoid-s6183" xml:space="preserve">Poſtea quia C B ad B R
              <lb/>
            erat vt H F ad F V, & </s>
            <s xml:id="echoid-s6184" xml:space="preserve">prius G B ad B C minorẽ proportionem habebat, quàm
              <lb/>
            K F ad F H, ergo ex æquali G B ad B R minorem proportionem habet, quàm
              <lb/>
            K F ad F V, & </s>
            <s xml:id="echoid-s6185" xml:space="preserve">componendo in hyperbola, & </s>
            <s xml:id="echoid-s6186" xml:space="preserve">diuidenào in ellipſi G R ad R B,
              <lb/>
            ſeu rectangulum G R B ad quadratum B R minorem proportionem habet, quàm
              <lb/>
            K V ad V F, ſeu rectangulum K V F ad quadratum V F ; </s>
            <s xml:id="echoid-s6187" xml:space="preserve">ſed propter ſimili-
              <lb/>
            tudinem figurarum, vt prius quadratum Q R ad rectangulum G R B eſt vt qua-
              <lb/>
            dratũ T V ad rectangulum K V F; </s>
            <s xml:id="echoid-s6188" xml:space="preserve">ergo ex æquali quadratum Q R ad quadra-
              <lb/>
            tum R B minorem proportionem habet, quàm quadratum T V ad quadratum
              <lb/>
            V F, & </s>
            <s xml:id="echoid-s6189" xml:space="preserve">Q R ad R B minorem proportionem habebit, quàm T V ad V F. </s>
            <s xml:id="echoid-s6190" xml:space="preserve">Et
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            ſic reliquæ omnes abſciſſæ : </s>
            <s xml:id="echoid-s6191" xml:space="preserve">quapropter patet propoſitum.</s>
            <s xml:id="echoid-s6192" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div593" type="section" level="1" n="196">
          <head xml:id="echoid-head250" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s6193" xml:space="preserve">HInc conſtat in duabus ſimilibus coniſectionibus duci poſſe duas ſeries appli-
              <lb/>
            catarum ad axes, itaut abſciſſæ axium, quæ inter ſe proportionales ſunt,
              <lb/>
            ad ſuas potentiales nonſint in ijſdem rationibus. </s>
            <s xml:id="echoid-s6194" xml:space="preserve">Quandoquidẽ ex prima parte
              <lb/>
            propoſitionis 12. </s>
            <s xml:id="echoid-s6195" xml:space="preserve">quotieſcunque axium figuræ ſimiles ſunt etiam ſectiones ipſæ
              <lb/>
            ſunt ſimiles.</s>
            <s xml:id="echoid-s6196" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div594" type="section" level="1" n="197">
          <head xml:id="echoid-head251" xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:id="echoid-s6197" xml:space="preserve">IN ijſdem figuris habeat G B ad B D maiorem proportionem, quàm
              <lb/>
            K F ad F I duci debent duæ ordinatim ad axes applicatæ, quæ ad
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            conterminas abſciſſas eandem proportionem habeant.</s>
            <s xml:id="echoid-s6198" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6199" xml:space="preserve">Ducatur quælibet ordinata E H, producanturq; </s>
            <s xml:id="echoid-s6200" xml:space="preserve">vt ſecet coniunctam K I in
              <lb/>
            L, & </s>
            <s xml:id="echoid-s6201" xml:space="preserve">vt D B ad B G ita fiat L H ad H N, atq; </s>
            <s xml:id="echoid-s6202" xml:space="preserve">fiat G C ad B C, vt N H ad
              <lb/>
            H F, ducaturque ordinata A C; </s>
            <s xml:id="echoid-s6203" xml:space="preserve">quæ producta ſecet coniunctam G D in P. </s>
            <s xml:id="echoid-s6204" xml:space="preserve">Di-
              <lb/>
            co A C, & </s>
            <s xml:id="echoid-s6205" xml:space="preserve">E H eße quæſitas. </s>
            <s xml:id="echoid-s6206" xml:space="preserve">Quoniam quadratum A C ad rectangulum G C
              <lb/>
              <note position="right" xlink:label="note-0197-01" xlink:href="note-0197-01a" xml:space="preserve">21. lib. 1.</note>
            B eandem proportionem habet, quàm D B ad B G, ſeu L H ad H N, & </s>
            <s xml:id="echoid-s6207" xml:space="preserve">rectã.
              <lb/>
            </s>
            <s xml:id="echoid-s6208" xml:space="preserve">gulum G C B ad quadratum B C eſt
              <lb/>
              <figure xlink:label="fig-0197-01" xlink:href="fig-0197-01a" number="215">
                <image file="0197-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0197-01"/>
              </figure>
            vt G C ad C B, ſeu vt N H ad H
              <lb/>
            F, ergo ex æqualitate quadratum
              <lb/>
            A C ad quadratum C B eſt vt L H
              <lb/>
            ad H F, ſeu vt rectangnlum L H
              <lb/>
            F ad quadratum H F; </s>
            <s xml:id="echoid-s6209" xml:space="preserve">vel potius
              <lb/>
            vt quadratum E H ad quadratum
              <lb/>
              <note position="right" xlink:label="note-0197-02" xlink:href="note-0197-02a" xml:space="preserve">12. 13.
                <lb/>
              lib. 1.</note>
            H F; </s>
            <s xml:id="echoid-s6210" xml:space="preserve">ideoque A C ad C B erit vt
              <lb/>
            E H ad H F. </s>
            <s xml:id="echoid-s6211" xml:space="preserve">Quod erat propoſi-
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            tum.</s>
            <s xml:id="echoid-s6212" xml:space="preserve"/>
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