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-div767" type="section" level="1" n="238">
          <p>
            <s xml:id="echoid-s9017" xml:space="preserve">
              <pb o="241" file="0279" n="279" rhead="Conicor. Lib. VI."/>
            bamus circulum, & </s>
            <s xml:id="echoid-s9018" xml:space="preserve">ex F ducamus lineam ad H I, occurrentem
              <lb/>
            ipſi extra circulum in K, & </s>
            <s xml:id="echoid-s9019" xml:space="preserve">occurrat circulo in L, itaut ſit F K
              <lb/>
            ad K L, vt D B ad B E (& </s>
            <s xml:id="echoid-s9020" xml:space="preserve">hoc eſt facile, vti demonſtraui-
              <lb/>
            mus in 59. </s>
            <s xml:id="echoid-s9021" xml:space="preserve">ex 1.)</s>
            <s xml:id="echoid-s9022" xml:space="preserve">, & </s>
            <s xml:id="echoid-s9023" xml:space="preserve">educamus in triangulo chordam M N
              <lb/>
              <note position="left" xlink:label="note-0279-01" xlink:href="note-0279-01a" xml:space="preserve">b</note>
            parallelam F K, & </s>
            <s xml:id="echoid-s9024" xml:space="preserve">æqualem D B; </s>
            <s xml:id="echoid-s9025" xml:space="preserve">Aio quod planum tranſiens
              <lb/>
              <note position="left" xlink:label="note-0279-02" xlink:href="note-0279-02a" xml:space="preserve">c</note>
            per M N erectum ſuper triangulum coni producit in cono H F I
              <lb/>
            ſectionem ellipticam, æqualem ſectioni A B.</s>
            <s xml:id="echoid-s9026" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9027" xml:space="preserve">Quia D B tranſuerſus ad eius erectum B E eandem proportionem habe-
              <lb/>
            bat, quàm F K ad K L, nempe quàm quadratum F K habet ad F K in-
              <lb/>
            K L, quod eſt æquale ipſi I K in K H; </s>
            <s xml:id="echoid-s9028" xml:space="preserve">eſtque vt M N parallela ipſi F K
              <lb/>
              <note position="right" xlink:label="note-0279-03" xlink:href="note-0279-03a" xml:space="preserve">13. lib. 1.</note>
            ad illius erectum; </s>
            <s xml:id="echoid-s9029" xml:space="preserve">quare D B ad B E eandem proportionem habet, quàm
              <lb/>
            M N ad illius erectum; </s>
            <s xml:id="echoid-s9030" xml:space="preserve">& </s>
            <s xml:id="echoid-s9031" xml:space="preserve">M N æqualis eſt D B; </s>
            <s xml:id="echoid-s9032" xml:space="preserve">igitur figuræ dua-
              <lb/>
              <note position="left" xlink:label="note-0279-04" xlink:href="note-0279-04a" xml:space="preserve">d</note>
            rum ſectionum A B D, M O N P ſunt æquales, & </s>
            <s xml:id="echoid-s9033" xml:space="preserve">ſimiles, & </s>
            <s xml:id="echoid-s9034" xml:space="preserve">ideo
              <lb/>
              <note position="right" xlink:label="note-0279-05" xlink:href="note-0279-05a" xml:space="preserve">2. huius.</note>
            duæ illæ ſectiones ſunt æquales. </s>
            <s xml:id="echoid-s9035" xml:space="preserve">Dico inſuper, quod non reperitur in.
              <lb/>
            </s>
            <s xml:id="echoid-s9036" xml:space="preserve">
              <note position="left" xlink:label="note-0279-06" xlink:href="note-0279-06a" xml:space="preserve">e</note>
            cono H F I vlla alia ſectio elliptica, habens verticem ſuper F I, cuius
              <lb/>
            axis non æquidiſter alicui duarum F L K, quæ æqualis ſit eidem B A D.
              <lb/>
            </s>
            <s xml:id="echoid-s9037" xml:space="preserve">Quia ſi poſſibile eſſet, oſtenderetur axis eius cadere in planum trianguli
              <lb/>
            H F I, quia ſectio eſt elliptica, & </s>
            <s xml:id="echoid-s9038" xml:space="preserve">æqualis ſectioni A B, vtiq; </s>
            <s xml:id="echoid-s9039" xml:space="preserve">eius axis
              <lb/>
            occurret F I, F H, & </s>
            <s xml:id="echoid-s9040" xml:space="preserve">æqualis eſt D B; </s>
            <s xml:id="echoid-s9041" xml:space="preserve">cumque vertex illius ſit ſuper F
              <lb/>
            I, non cadet axis eius ſuper M N, nec ipſi erit parallelus; </s>
            <s xml:id="echoid-s9042" xml:space="preserve">& </s>
            <s xml:id="echoid-s9043" xml:space="preserve">ideo edu-
              <lb/>
            cta F Q parallela axi eius non cadet F Q ſuper F K, & </s>
            <s xml:id="echoid-s9044" xml:space="preserve">ſecabit arcum
              <lb/>
            F H in R; </s>
            <s xml:id="echoid-s9045" xml:space="preserve">eritque proportio axis illius ſectionis ad eius erectum, nempe
              <lb/>
              <note position="right" xlink:label="note-0279-07" xlink:href="note-0279-07a" xml:space="preserve">13. lib. 1.</note>
            quadratum F Q ad I Q in Q H, quod eſt æquale ipſi Q F in Q R, nẽ-
              <lb/>
            pe vt F Q ad Q R, ita erit D B ad B E, quæ eandem proportionem ha-
              <lb/>
            bet quàm F K ad K L, & </s>
            <s xml:id="echoid-s9046" xml:space="preserve">diuidendo permutandoq; </s>
            <s xml:id="echoid-s9047" xml:space="preserve">F R maior ſubtenſa
              <lb/>
              <note position="left" xlink:label="note-0279-08" xlink:href="note-0279-08a" xml:space="preserve">f</note>
            ad minorem F L eandem proportionem habebit, quàm R Q minor in-
              <lb/>
            tercepta ad maiorem K L; </s>
            <s xml:id="echoid-s9048" xml:space="preserve">quod eſt abſurdum: </s>
            <s xml:id="echoid-s9049" xml:space="preserve">non ergo reperitur in co-
              <lb/>
            no H F I ſectio elliptica, verticem habens in F I, quæ ſit æqualis ſe-
              <lb/>
            ctioni A B, præter ſuperius expoſitam. </s>
            <s xml:id="echoid-s9050" xml:space="preserve">Et hoc erat propoſitum.</s>
            <s xml:id="echoid-s9051" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div770" type="section" level="1" n="239">
          <head xml:id="echoid-head300" xml:space="preserve">Notæ in Propoſit. XXVI.</head>
          <p style="it">
            <s xml:id="echoid-s9052" xml:space="preserve">ERgo potentes egredientes ex ſe-
              <lb/>
              <note position="left" xlink:label="note-0279-09" xlink:href="note-0279-09a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0279-01" xlink:href="fig-0279-01a" number="325">
                <image file="0279-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0279-01"/>
              </figure>
            ctione L H K ad axim H I pote-
              <lb/>
            runt applicatum, quod continet ab-
              <lb/>
            ſciſſum illius potentis cum G E; </s>
            <s xml:id="echoid-s9053" xml:space="preserve">ergo
              <lb/>
            G E eſt erectus ſectionis L H; </s>
            <s xml:id="echoid-s9054" xml:space="preserve">& </s>
            <s xml:id="echoid-s9055" xml:space="preserve">eſt
              <lb/>
            etiã erectus ſectionis D E; </s>
            <s xml:id="echoid-s9056" xml:space="preserve">igitur duo
              <lb/>
            applicata duarum ſectionũ ſunt æqua-
              <lb/>
            lia, & </s>
            <s xml:id="echoid-s9057" xml:space="preserve">ideo ſectio D E congruit ſe-
              <lb/>
            ctioni K H L, & </s>
            <s xml:id="echoid-s9058" xml:space="preserve">propterea æquales
              <lb/>
            ſunt, &</s>
            <s xml:id="echoid-s9059" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9060" xml:space="preserve">Ex eo quod quadratum A C
              <lb/>
            baſis trianguli per axim coni recti ad
              <lb/>
            rectangulum C B A, ſub eius </s>
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