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-div783" type="section" level="1" n="242">
          <p style="it">
            <s xml:id="echoid-s9248" xml:space="preserve">
              <pb o="247" file="0285" n="285" rhead="Conicor. Lib. VI."/>
            I S, vt F K ad K L: </s>
            <s xml:id="echoid-s9249" xml:space="preserve">ſed erat D B ad B E, vt F I ad I S; </s>
            <s xml:id="echoid-s9250" xml:space="preserve">igitur F K ad K L
              <lb/>
            eandem proportionem habebit: </s>
            <s xml:id="echoid-s9251" xml:space="preserve">quàm D B ad D E.</s>
            <s xml:id="echoid-s9252" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9253" xml:space="preserve">Et educamus in triangulo chordam M N parallelam K F, & </s>
            <s xml:id="echoid-s9254" xml:space="preserve">æqualem
              <lb/>
              <note position="left" xlink:label="note-0285-01" xlink:href="note-0285-01a" xml:space="preserve">b</note>
            D B, &</s>
            <s xml:id="echoid-s9255" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9256" xml:space="preserve">Non vna, ſed duplex recta linea M N duci poteſt parallela cuilibet
              <lb/>
            duarum F K, quæ interius ſubtendat angulum verticis F trianguli H F I per
              <lb/>
            axim ducti. </s>
            <s xml:id="echoid-s9257" xml:space="preserve">Et poteſt etiam effici M N æqualis ipſi D B, vt in expoſitione præ-
              <lb/>
            cedentis propoſitionis oſtenſum eſt.</s>
            <s xml:id="echoid-s9258" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9259" xml:space="preserve">Itaque planum, tranſiens per M N, producit in cono H F I ſectionem
              <lb/>
              <note position="left" xlink:label="note-0285-02" xlink:href="note-0285-02a" xml:space="preserve">c</note>
            ellipticam æqualem ſectioni A B; </s>
            <s xml:id="echoid-s9260" xml:space="preserve">quia, &</s>
            <s xml:id="echoid-s9261" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9262" xml:space="preserve">Addidi verba, quæ in textu
              <lb/>
            deſiderantur, vt ſenſus perfectus ſit.</s>
            <s xml:id="echoid-s9263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9264" xml:space="preserve">Ergo duæ illæ ſectiones ſunt æquales, &</s>
            <s xml:id="echoid-s9265" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9266" xml:space="preserve">Concipi debet ſectio N O M
              <lb/>
              <note position="left" xlink:label="note-0285-03" xlink:href="note-0285-03a" xml:space="preserve">d</note>
            P, duplex, quia nimirum duæ ſectiones ſub contrariæ, æquales ſunt, vt faci-
              <lb/>
            le cum Mydorgìo oſtendi poteſt.</s>
            <s xml:id="echoid-s9267" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9268" xml:space="preserve">Et dico, quod non reperiatur in cono H F I ſectio elliptica, habens
              <lb/>
              <note position="left" xlink:label="note-0285-04" xlink:href="note-0285-04a" xml:space="preserve">e</note>
            verticem ſuper F I; </s>
            <s xml:id="echoid-s9269" xml:space="preserve">quia ſi poſſibile eſſet, &</s>
            <s xml:id="echoid-s9270" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9271" xml:space="preserve">Textus valde corruptus ex-
              <lb/>
            poſito modo reſtitui debere conſtat ex progreſſu demonſtrationis.</s>
            <s xml:id="echoid-s9272" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9273" xml:space="preserve">Et diuidendo F R maior ad minorem R Q eſt vt F L minor ad maio-
              <lb/>
              <note position="left" xlink:label="note-0285-05" xlink:href="note-0285-05a" xml:space="preserve">f</note>
            rem K L, &</s>
            <s xml:id="echoid-s9274" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9275" xml:space="preserve">Supplendæ fuerunt particulæ aliquæ ad tollendam equiuocatio-
              <lb/>
            nem.</s>
            <s xml:id="echoid-s9276" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div790" type="section" level="1" n="243">
          <head xml:id="echoid-head304" xml:space="preserve">SECTIO VNDECIMA</head>
          <head xml:id="echoid-head305" xml:space="preserve">Continens Propoſit. XXIX. XXX.
            <lb/>
          & XXXI.</head>
          <head xml:id="echoid-head306" xml:space="preserve">PROPOSTIO XXIX.</head>
          <p>
            <s xml:id="echoid-s9277" xml:space="preserve">DAto cono recto A B C, conum exhibere ei ſimilem, qui
              <lb/>
            datam ſectionem D E F contineat, cuius axis E G, & </s>
            <s xml:id="echoid-s9278" xml:space="preserve">
              <lb/>
            erectus E H; </s>
            <s xml:id="echoid-s9279" xml:space="preserve">ſitque prius ſectio parabole.</s>
            <s xml:id="echoid-s9280" xml:space="preserve"/>
          </p>
          <figure number="333">
            <image file="0285-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0285-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s9281" xml:space="preserve">Super E G educatur planum ad ſectionem D
              <lb/>
            E F ad angulos rectos eleuatum, in quo duca-
              <lb/>
            tur E I K, quæ contineat cum E G angulum
              <lb/>
            æqualem ipſi angulo C: </s>
            <s xml:id="echoid-s9282" xml:space="preserve">& </s>
            <s xml:id="echoid-s9283" xml:space="preserve">ponamus E H ad E
              <lb/>
              <note position="left" xlink:label="note-0285-06" xlink:href="note-0285-06a" xml:space="preserve">a</note>
            K, vt A C ad C B, & </s>
            <s xml:id="echoid-s9284" xml:space="preserve">faciamus ſuper E K tri-
              <lb/>
            angulum E L K ſimile triangulo A B C, vt an-
              <lb/>
            gulus verticalis L æqualis ſit angulo B. </s>
            <s xml:id="echoid-s9285" xml:space="preserve">Facia-
              <lb/>
            mus etiam conum, cuius vertex ſit L, eiuſque
              <lb/>
            baſis circulus, cuius diameter ſit E K, qui ſit
              <lb/>
            eleuatus ſuper triangulum E L K ad angulos re-
              <lb/>
            ctos: </s>
            <s xml:id="echoid-s9286" xml:space="preserve">erit igitur angulus E K L æqualis ipſi </s>
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