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-div246" type="section" level="1" n="82">
          <pb o="63" file="0101" n="101" rhead="Conicor. Lib. V."/>
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        <div xml:id="echoid-div248" type="section" level="1" n="83">
          <head xml:id="echoid-head116" xml:space="preserve">Notæ in Propoſit. LVIII.</head>
          <p>
            <s xml:id="echoid-s2759" xml:space="preserve">I Am poſſumus producere ex puncto aſſignato C extra datam ſectionem
              <lb/>
              <note position="left" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">a</note>
            A B, aut intra (ſi punctum non fuerit ad axim I A) lineam diuiden-
              <lb/>
            tem ex illo inter ſectionem, & </s>
            <s xml:id="echoid-s2760" xml:space="preserve">axim lineam breuiſſimam, &</s>
            <s xml:id="echoid-s2761" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2762" xml:space="preserve">Sic legen-
              <lb/>
            dum puto. </s>
            <s xml:id="echoid-s2763" xml:space="preserve">Ex punto dato C extra, vel intra ſectionem A B, quod in axi non
              <lb/>
            ſit, lineam rectam ducere, cuius portio incercepta inter ſectionem, & </s>
            <s xml:id="echoid-s2764" xml:space="preserve">axim ſit
              <lb/>
            linea breuiſsima.</s>
            <s xml:id="echoid-s2765" xml:space="preserve"/>
          </p>
          <figure number="80">
            <image file="0101-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0101-01"/>
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            <s xml:id="echoid-s2766" xml:space="preserve">Et per C ducamus ſectionem H C B circa duas continentes illam G F,
              <lb/>
              <note position="left" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">b</note>
            I F, quæ occurrat ſectioni A B (16. </s>
            <s xml:id="echoid-s2767" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s2768" xml:space="preserve">in B, &</s>
            <s xml:id="echoid-s2769" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2770" xml:space="preserve">Scilicet ducamus per
              <lb/>
            C hyperbolen H C B circa aſymptots G F, F I, & </s>
            <s xml:id="echoid-s2771" xml:space="preserve">quia aſymptoti, & </s>
            <s xml:id="echoid-s2772" xml:space="preserve">hyperbo-
              <lb/>
              <note position="right" xlink:label="note-0101-03" xlink:href="note-0101-03a" xml:space="preserve">4. lib. 2.</note>
            le H C B productæ ad ſe ipſas ſemper proprius accedunt, atque parabole A B
              <lb/>
              <note position="right" xlink:label="note-0101-04" xlink:href="note-0101-04a" xml:space="preserve">14. 2.
                <lb/>
              Ex 8. 1.</note>
            producta ſemper magis ab axi A I remouetur; </s>
            <s xml:id="echoid-s2773" xml:space="preserve">igitur hyperbole H C B, & </s>
            <s xml:id="echoid-s2774" xml:space="preserve">para-
              <lb/>
            bola A B ſe mutuo ſecabunt; </s>
            <s xml:id="echoid-s2775" xml:space="preserve">ſecent ſe ſe in puncto B. </s>
            <s xml:id="echoid-s2776" xml:space="preserve">Animaduertendum eſt,
              <lb/>
            quod in textu Arabico aſſumitur hæc concluſio, vt demonſtrata in propoſitione
              <lb/>
            16. </s>
            <s xml:id="echoid-s2777" xml:space="preserve">huius quinti libri; </s>
            <s xml:id="echoid-s2778" xml:space="preserve">& </s>
            <s xml:id="echoid-s2779" xml:space="preserve">ſiquidem numeri huius citationis mendoſi non ſunt,
              <lb/>
            hæc propoſitio ſexta decima deſideratur in hoc libro.</s>
            <s xml:id="echoid-s2780" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2781" xml:space="preserve">Producatur perpendicularis B K. </s>
            <s xml:id="echoid-s2782" xml:space="preserve">Quoniam C I, &</s>
            <s xml:id="echoid-s2783" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2784" xml:space="preserve">Ex puncto B ad
              <lb/>
              <note position="left" xlink:label="note-0101-05" xlink:href="note-0101-05a" xml:space="preserve">c</note>
            axim ducatur perpendicularis B K, ſecans eum in K; </s>
            <s xml:id="echoid-s2785" xml:space="preserve">quoniam quando punctum
              <lb/>
            C ponitur intra parabolen, tunc B G æqualis eſt I C; </s>
            <s xml:id="echoid-s2786" xml:space="preserve">quando vero cadit extra,
              <lb/>
              <note position="right" xlink:label="note-0101-06" xlink:href="note-0101-06a" xml:space="preserve">8. lib. 2.</note>
            tunc C G eſt æqualis B I, & </s>
            <s xml:id="echoid-s2787" xml:space="preserve">addita communi B C erit I C æqualis B G, cumq;
              <lb/>
            </s>
            <s xml:id="echoid-s2788" xml:space="preserve">duæ rectæ lineæ I G, I F conuenientes in I ſecentur à rectis lineis K B, E C,
              <lb/>
            F G inter ſe parallelis, eo quod ſunt perpendiculares ad eundem axim; </s>
            <s xml:id="echoid-s2789" xml:space="preserve">ergo I G,
              <lb/>
            & </s>
            <s xml:id="echoid-s2790" xml:space="preserve">I F ſecantur in ijſdem rationibus, & </s>
            <s xml:id="echoid-s2791" xml:space="preserve">propterea E I æqualis erit K F; </s>
            <s xml:id="echoid-s2792" xml:space="preserve">ſicuti
              <lb/>
            I C æqualis erat B g, pariterque I K æqualis erit E F, ſicuti I B æqualis erat
              <lb/>
            C G; </s>
            <s xml:id="echoid-s2793" xml:space="preserve">poſita autem fuit E F æqualis ſemierecto; </s>
            <s xml:id="echoid-s2794" xml:space="preserve">igitur K I ſemiſsi lateris recti
              <lb/>
            pariter æqualis erit.</s>
            <s xml:id="echoid-s2795" xml:space="preserve"/>
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