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-div237" type="section" level="1" n="78">
          <head xml:id="echoid-head111" xml:space="preserve">SECTIO NONA
            <lb/>
          Continens Propoſ. LVIII. LIX. LX. LXI.
            <lb/>
          LXII. & LXIII.</head>
          <p>
            <s xml:id="echoid-s2684" xml:space="preserve">I Am ex puncto dato C extra, vel intra ſectionem A B (quod
              <lb/>
              <note position="right" xlink:label="note-0098-01" xlink:href="note-0098-01a" xml:space="preserve">a</note>
            in axi I A non ſit) poſſumus rectam lineam ducere, cuius
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            portio intercepta inter ſectionem, & </s>
            <s xml:id="echoid-s2685" xml:space="preserve">axim ſit linea breuiſſima.</s>
            <s xml:id="echoid-s2686" xml:space="preserve"/>
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        <div xml:id="echoid-div239" type="section" level="1" n="79">
          <head xml:id="echoid-head112" xml:space="preserve">PROPOSITIO LVIII.</head>
          <p>
            <s xml:id="echoid-s2687" xml:space="preserve">Sit ſectio parabole, & </s>
            <s xml:id="echoid-s2688" xml:space="preserve">producamus perpendicularem C E ſu-
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            per I E A, & </s>
            <s xml:id="echoid-s2689" xml:space="preserve">ponamus E F æqualem dimidio erecti, & </s>
            <s xml:id="echoid-s2690" xml:space="preserve">du-
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            camus G F parallelam ipſi C E, & </s>
            <s xml:id="echoid-s2691" xml:space="preserve">per C ducamus hyperbolen
              <lb/>
              <note position="left" xlink:label="note-0098-02" xlink:href="note-0098-02a" xml:space="preserve">4. lib. 2.</note>
              <note position="right" xlink:label="note-0098-03" xlink:href="note-0098-03a" xml:space="preserve">b</note>
            H C B circa duas continentes illam G F, I F, quæ occurat ſe-
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            ctioni A B in B, & </s>
            <s xml:id="echoid-s2692" xml:space="preserve">per B, C producatur linea occurrens con-
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            tinenti I A in I, & </s>
            <s xml:id="echoid-s2693" xml:space="preserve">continenti G F in G: </s>
            <s xml:id="echoid-s2694" xml:space="preserve">Dico, quod B I eſt
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            linea breuiſsima.</s>
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            <s xml:id="echoid-s2696" xml:space="preserve">Producatur perpendicularis B K. </s>
            <s xml:id="echoid-s2697" xml:space="preserve">Quoniam C I æqualis eſt B G (sexta
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              <note position="right" xlink:label="note-0098-04" xlink:href="note-0098-04a" xml:space="preserve">C</note>
            ex ſecundo) erit E I æqualis K F, & </s>
            <s xml:id="echoid-s2698" xml:space="preserve">E F, K I erunt æquales, atque ſup-
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              <note position="left" xlink:label="note-0098-05" xlink:href="note-0098-05a" xml:space="preserve">8. lib. 2.</note>
            poſita, eſt E F æqualis dimidio erecti; </s>
            <s xml:id="echoid-s2699" xml:space="preserve">ergo K I ita eſt pariter; </s>
            <s xml:id="echoid-s2700" xml:space="preserve">Quare
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            B I eſt breuiſsima, (octaua ex quinto) & </s>
            <s xml:id="echoid-s2701" xml:space="preserve">hoc erat probandum.</s>
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        <div xml:id="echoid-div242" type="section" level="1" n="80">
          <head xml:id="echoid-head113" xml:space="preserve">PROPOSITIO LIX. LXII. & LXIII.</head>
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            <s xml:id="echoid-s2703" xml:space="preserve">D Einde fit ſectio hyperbole, aut ellipſis, cuius centrum D, & </s>
            <s xml:id="echoid-s2704" xml:space="preserve">lineis,
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            atque ſignis in eodem ſtatu manentibus, ponamus D F ad F E, &</s>
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