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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              <pb o="251" file="0289" n="289" rhead="Conicor. Lib. VI."/>
            Inde demonſtrabitur, quod H E ad E I habebit neceſſario eandem pro-
              <lb/>
            portionem, quàm O e ad e Z; </s>
            <s xml:id="echoid-s9391" xml:space="preserve">quod eſt abſurdum, quia haberet eandem
              <lb/>
            proportionem, quàm O N ad N X. </s>
            <s xml:id="echoid-s9392" xml:space="preserve">Quapropter non continet illam ter-
              <lb/>
            tius alius conus ſimilis cono A B C.</s>
            <s xml:id="echoid-s9393" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9394" xml:space="preserve">Supponamus iam, quadratum B Q ad quadratum Q A maiorem pro-
              <lb/>
            portionem habere, quàm H E ad E I. </s>
            <s xml:id="echoid-s9395" xml:space="preserve">Dico, exhiberi non poſſe conum
              <lb/>
              <note position="left" xlink:label="note-0289-01" xlink:href="note-0289-01a" xml:space="preserve">i</note>
            ſimilem cono A B C, qui contineat ſectionem D E F. </s>
            <s xml:id="echoid-s9396" xml:space="preserve">Alioquin conti-
              <lb/>
            neat illam conus, cuius vertex eſt R, & </s>
            <s xml:id="echoid-s9397" xml:space="preserve">demonſtrabitur, quod O V ad
              <lb/>
            V R ſit, vt H E ad E I, quæ habet minorem proportionem, quàm qua-
              <lb/>
            dratum B Q ad quadratum Q A, quæ oſtenſa eſt eadem, quàm O N ad
              <lb/>
            N L; </s>
            <s xml:id="echoid-s9398" xml:space="preserve">ergo O V ad V R; </s>
            <s xml:id="echoid-s9399" xml:space="preserve">nempe O N ad N X minorem, proportionem
              <lb/>
            habet, quàm eadẽ O N ad N L, quod eſt abſurdum. </s>
            <s xml:id="echoid-s9400" xml:space="preserve">Non igitur conti-
              <lb/>
            nebit ſectionem D E F conus ſimilis cono A B C. </s>
            <s xml:id="echoid-s9401" xml:space="preserve">Vt propoſitũ fuerat.</s>
            <s xml:id="echoid-s9402" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div796" type="section" level="1" n="245">
          <head xml:id="echoid-head308" xml:space="preserve">PROPOSITIO XXXI.</head>
          <p>
            <s xml:id="echoid-s9403" xml:space="preserve">SIt tandem ſectio elliptica A B C, eiuſque tranſuerſus axis A C, & </s>
            <s xml:id="echoid-s9404" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0289-02" xlink:href="note-0289-02a" xml:space="preserve">a</note>
            erectus A D, & </s>
            <s xml:id="echoid-s9405" xml:space="preserve">in plano perpendiculariter erecto ad ſectionis pla-
              <lb/>
            num A B C, fiat ſuper A C ſegmentum circuli, quod capiat angulum.
              <lb/>
            </s>
            <s xml:id="echoid-s9406" xml:space="preserve">
              <figure xlink:label="fig-0289-01" xlink:href="fig-0289-01a" number="337">
                <image file="0289-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0289-01"/>
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            æqualem angulo F, eumque bifariam diuidamus in H, & </s>
            <s xml:id="echoid-s9407" xml:space="preserve">iungamus A H,
              <lb/>
            C H, & </s>
            <s xml:id="echoid-s9408" xml:space="preserve">ex H educamus H I, quæ ſecet circulum in K, & </s>
            <s xml:id="echoid-s9409" xml:space="preserve">occurrat ſub-
              <lb/>
              <note position="right" xlink:label="note-0289-03" xlink:href="note-0289-03a" xml:space="preserve">Lem. 10.
                <lb/>
              huius.</note>
            tenſæ extra circulum in I; </s>
            <s xml:id="echoid-s9410" xml:space="preserve">ſitque H I ad I K, vt A C ad A D: </s>
            <s xml:id="echoid-s9411" xml:space="preserve">& </s>
            <s xml:id="echoid-s9412" xml:space="preserve">e-
              <lb/>
            ducamus H L M eaſdem conditiones habens; </s>
            <s xml:id="echoid-s9413" xml:space="preserve">& </s>
            <s xml:id="echoid-s9414" xml:space="preserve">iungamus C K, A K,
              <lb/>
            ducaturque K N parallela A C, & </s>
            <s xml:id="echoid-s9415" xml:space="preserve">A N parallela H I, quæ ſecet K C
              <lb/>
              <note position="left" xlink:label="note-0289-04" xlink:href="note-0289-04a" xml:space="preserve">b</note>
            in O. </s>
            <s xml:id="echoid-s9416" xml:space="preserve">Quia H I in I K (quod eſt æquale ipſi C I in A I ad quadratum
              <lb/>
            I K) eſt vt A C ed A D; </s>
            <s xml:id="echoid-s9417" xml:space="preserve">& </s>
            <s xml:id="echoid-s9418" xml:space="preserve">proportio C I in A I ad quadratum I K
              <lb/>
            componitur ex ratione C I ad I K, nempe K N ad N O (propter </s>
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