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-div252" type="section" level="1" n="84">
          <head xml:id="echoid-head117" xml:space="preserve">Notæ in Propoſit. LIX. LXII. & LXIII.</head>
          <p style="it">
            <s xml:id="echoid-s2796" xml:space="preserve">E T lineis, atque ſignis eodem ſtatu manentibus, &</s>
            <s xml:id="echoid-s2797" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2798" xml:space="preserve">Ideſt punctum
              <lb/>
              <note position="right" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">a</note>
            C extra, aut intra ſectionem ponatur, dummodo non ſit in axi, ducaturq;
              <lb/>
            </s>
            <s xml:id="echoid-s2799" xml:space="preserve">C E perpendicularis ad axim, ſecans eum in E, & </s>
            <s xml:id="echoid-s2800" xml:space="preserve">vt latus tranſuerſum ad re-
              <lb/>
            ctum, ita ſiat D F ad F E, atque C L ad L E, & </s>
            <s xml:id="echoid-s2801" xml:space="preserve">per L producatur O L M pa-
              <lb/>
            rallela A I, & </s>
            <s xml:id="echoid-s2802" xml:space="preserve">per F ducatur F M G parallela C E, quæ ſecet O M in M, & </s>
            <s xml:id="echoid-s2803" xml:space="preserve">per
              <lb/>
            C deſcribatur hyperbole H C B circa aſymptotos G M O, quæ in ellipſi per eius
              <lb/>
              <note position="left" xlink:label="note-0102-02" xlink:href="note-0102-02a" xml:space="preserve">4. lib. 2.</note>
            centrum D tranſibit, & </s>
            <s xml:id="echoid-s2804" xml:space="preserve">ideo eam ſecabit ſicuti oſtenſum eſt in 56. </s>
            <s xml:id="echoid-s2805" xml:space="preserve">huius.</s>
            <s xml:id="echoid-s2806" xml:space="preserve"/>
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            <s xml:id="echoid-s2807" xml:space="preserve">Eo quod O M parallela axi D A inclinato ſubtendit, &</s>
            <s xml:id="echoid-s2808" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2809" xml:space="preserve">Quoniam
              <lb/>
              <note position="right" xlink:label="note-0102-03" xlink:href="note-0102-03a" xml:space="preserve">b</note>
            in hyperbola O M parallela axi ſecat vtrãque linearum continentium angulum,
              <lb/>
            qui deinceps eſt ei, qui hyperbolen continet ſectioni occurret, & </s>
            <s xml:id="echoid-s2810" xml:space="preserve">producta ſectio-
              <lb/>
              <note position="left" xlink:label="note-0102-04" xlink:href="note-0102-04a" xml:space="preserve">11. lib. 2.</note>
            nem A B ſecabit, & </s>
            <s xml:id="echoid-s2811" xml:space="preserve">ideo O M cadit intra ſectionem A B, atque hyperbole A B
              <lb/>
            producta ſemper magis, ac magis recedit tum ab M O parallela axi, cum ab M
              <lb/>
            G parallela tangenti verticali, & </s>
            <s xml:id="echoid-s2812" xml:space="preserve">ſectio H C B, & </s>
            <s xml:id="echoid-s2813" xml:space="preserve">asymptoti O M G ad ſe ip-
              <lb/>
              <note position="left" xlink:label="note-0102-05" xlink:href="note-0102-05a" xml:space="preserve">14. lib. 2.</note>
            ſas jemper propius accedunt, igitur ſectiones A B, B C conueniunt; </s>
            <s xml:id="echoid-s2814" xml:space="preserve">ſecent ſe
              <lb/>
            ſe in B, & </s>
            <s xml:id="echoid-s2815" xml:space="preserve">ducamus per B, C lineam occurrentem axi in I, ipſi M O in O, & </s>
            <s xml:id="echoid-s2816" xml:space="preserve">
              <lb/>
            M G in G.</s>
            <s xml:id="echoid-s2817" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s2818" xml:space="preserve">Et quia B O æqualis eſt ipſi C G, &</s>
            <s xml:id="echoid-s2819" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2820" xml:space="preserve">Cum lineæ rectæ O M, O G ſe ſe-
              <lb/>
              <note position="right" xlink:label="note-0102-06" xlink:href="note-0102-06a" xml:space="preserve">c</note>
            cantes in O, ſecentur à parallelis E C, K B, F G proportionaliter, erit O N
              <lb/>
            æqualis M L, ſicuti O B æqualis erat C G, & </s>
            <s xml:id="echoid-s2821" xml:space="preserve">O L, æqualis erit N M, ſicuti
              <lb/>
            O C æqualis erat B G, cumque triangula O C L, & </s>
            <s xml:id="echoid-s2822" xml:space="preserve">I C E ſint ſimilia propter
              <lb/>
              <note position="left" xlink:label="note-0102-07" xlink:href="note-0102-07a" xml:space="preserve">8. lib. 2.</note>
            parallelas O L, I E, erit O L ad E I, vt L C ad C E; </s>
            <s xml:id="echoid-s2823" xml:space="preserve">eſt vero M N, ſeu F
              <lb/>
            K æqualis ipſi L O, igitur F K ad E I eſt, vt L C ad E C, ſed ex conſtru-
              <lb/>
            ctione erat D F ad F E, vt C L ad L E, ſciluet vt latus tranſuerſum ad
              <lb/>
            rectum; </s>
            <s xml:id="echoid-s2824" xml:space="preserve">ergo antecedentes ad ſummas terminorum in hyperbola, & </s>
            <s xml:id="echoid-s2825" xml:space="preserve">ad
              <lb/>
              <note position="left" xlink:label="note-0102-08" xlink:href="note-0102-08a" xml:space="preserve">Lem. 1.</note>
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