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-div586" type="section" level="1" n="192">
          <p>
            <s xml:id="echoid-s6131" xml:space="preserve">
              <pb o="157" file="0195" n="195" rhead="Conicor. Lib. VI."/>
            lis alicui earum (ſi poſ-
              <lb/>
              <note position="left" xlink:label="note-0195-01" xlink:href="note-0195-01a" xml:space="preserve">b</note>
            ſibile eſt) ergo poſſu-
              <lb/>
              <figure xlink:label="fig-0195-01" xlink:href="fig-0195-01a" number="212">
                <image file="0195-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0195-01"/>
              </figure>
            mus educere in ſingulis
              <lb/>
            ſectionibus potentes,
              <lb/>
            quæ habeant ad ſua ab-
              <lb/>
            ſciſſa axium eaſdẽ pro-
              <lb/>
            portiones, & </s>
            <s xml:id="echoid-s6132" xml:space="preserve">abſciſſæ in
              <lb/>
            ter ſe ſint proportiona-
              <lb/>
            les; </s>
            <s xml:id="echoid-s6133" xml:space="preserve">ſintque illæ V M,
              <lb/>
            Y N, P K, R L. </s>
            <s xml:id="echoid-s6134" xml:space="preserve">Quia
              <lb/>
            Y N ad N F poſita fuit,
              <lb/>
            vt R L ad L B, & </s>
            <s xml:id="echoid-s6135" xml:space="preserve">N F
              <lb/>
            ad F M, vt L B ad BK,
              <lb/>
            & </s>
            <s xml:id="echoid-s6136" xml:space="preserve">F M ad M V, vt B
              <lb/>
            K ad K P; </s>
            <s xml:id="echoid-s6137" xml:space="preserve">ergo Y N ad
              <lb/>
            M V in potentia, nem-
              <lb/>
            pe N F ad M F (cum
              <lb/>
            ſectio ſit parabola 19.
              <lb/>
            </s>
            <s xml:id="echoid-s6138" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6139" xml:space="preserve">nempe L B ad B K ex contructione erit, vt R L ad K P potentia,
              <lb/>
              <note position="right" xlink:label="note-0195-02" xlink:href="note-0195-02a" xml:space="preserve">20. lib. 1.</note>
            quæ eandem proportionem habent, quàm a L in L B ad a K in K B;
              <lb/>
            </s>
            <s xml:id="echoid-s6140" xml:space="preserve">
              <note position="right" xlink:label="note-0195-03" xlink:href="note-0195-03a" xml:space="preserve">21. lib. 1.</note>
            quia ſectio eſt hyperbolæ, aut ellipſis (20. </s>
            <s xml:id="echoid-s6141" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s6142" xml:space="preserve">quare a L in L B ad a
              <lb/>
            K in K B eſt, vt L B ad B K; </s>
            <s xml:id="echoid-s6143" xml:space="preserve">quare a L eſt æqualis a K: </s>
            <s xml:id="echoid-s6144" xml:space="preserve">quod eſt abſur-
              <lb/>
            dum. </s>
            <s xml:id="echoid-s6145" xml:space="preserve">Igitur parabole non eſt ſimilis vlli reliquarum ſectionum. </s>
            <s xml:id="echoid-s6146" xml:space="preserve">Et hoc
              <lb/>
            erat probandum.</s>
            <s xml:id="echoid-s6147" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div588" type="section" level="1" n="193">
          <head xml:id="echoid-head247" xml:space="preserve">PROPOSITIO XIV.</head>
          <p>
            <s xml:id="echoid-s6148" xml:space="preserve">ET ſic oſtendetur, quod hyperbolæ non eſt ſimilis ellipſi.</s>
            <s xml:id="echoid-s6149" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6150" xml:space="preserve">Alioquin ſequitur, quod quadratum
              <lb/>
              <figure xlink:label="fig-0195-02" xlink:href="fig-0195-02a" number="213">
                <image file="0195-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0195-02"/>
              </figure>
              <note position="left" xlink:label="note-0195-04" xlink:href="note-0195-04a" xml:space="preserve">a</note>
            R L ad quadratum K P, nempe a L in
              <lb/>
            L B ad a K in K B in hyperbola eſt, vt
              <lb/>
            quadratum Y N ad quadratum M V,
              <lb/>
            ſeu vt b N in N F ad b M in M F in el-
              <lb/>
            lipſi. </s>
            <s xml:id="echoid-s6151" xml:space="preserve">His poſitis: </s>
            <s xml:id="echoid-s6152" xml:space="preserve">quia L B ad B K po-
              <lb/>
              <note position="right" xlink:label="note-0195-05" xlink:href="note-0195-05a" xml:space="preserve">21. lib. 1.</note>
            ſita fuit, vt N F ad M F; </s>
            <s xml:id="echoid-s6153" xml:space="preserve">ergo a L ad
              <lb/>
            a K eandem proportionem habet, quàm
              <lb/>
            b N ad b M: </s>
            <s xml:id="echoid-s6154" xml:space="preserve">& </s>
            <s xml:id="echoid-s6155" xml:space="preserve">hoc eſt abſurdum. </s>
            <s xml:id="echoid-s6156" xml:space="preserve">Qua-
              <lb/>
            re ſectio A B non eſt ſimilis E F; </s>
            <s xml:id="echoid-s6157" xml:space="preserve">vt fue-
              <lb/>
            rat propoſitum.</s>
            <s xml:id="echoid-s6158" xml:space="preserve"/>
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