Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

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          <p>
            <s xml:id="echoid-s2853" xml:space="preserve">
              <pb o="418" file="0136" n="145" rhead="VERA CIRCULI"/>
            proportionalia, & </s>
            <s xml:id="echoid-s2854" xml:space="preserve">ex prædictis ſatis facile colligi poteſt
              <lb/>
            trapezium A I L P eſſe dimidium polygoni A B D L P & </s>
            <s xml:id="echoid-s2855" xml:space="preserve">
              <lb/>
            trapezium A I O P eſſe dimidium polygoni A B E I O P
              <lb/>
            & </s>
            <s xml:id="echoid-s2856" xml:space="preserve">triangulum A I P eſſe dimidium trapezii A B I P: </s>
            <s xml:id="echoid-s2857" xml:space="preserve">& </s>
            <s xml:id="echoid-s2858" xml:space="preserve">
              <lb/>
            proinde terminos duplicando, polygonum A B D L P, po-
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            lygonum A B E I O P & </s>
            <s xml:id="echoid-s2859" xml:space="preserve">trapezium A B I P ſunt continuè
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            proportionalia, quod demonſtrare oportuit.</s>
            <s xml:id="echoid-s2860" xml:space="preserve"/>
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            <s xml:id="echoid-s2861" xml:space="preserve">Ducantur rectæ C G, K N, ſegmentum tangentes in
              <lb/>
            punctis E, O, & </s>
            <s xml:id="echoid-s2862" xml:space="preserve">rectis D L, D B, L P, occurrentes in
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            punctis C, G, K, N, ut compleatur polygonum
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            A B C G K N P.</s>
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        <div xml:id="echoid-div152" type="section" level="1" n="69">
          <head xml:id="echoid-head104" xml:space="preserve">PROP. V. THEOREMA.</head>
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            <s xml:id="echoid-s2864" xml:space="preserve">Dico trapezium A B I P & </s>
            <s xml:id="echoid-s2865" xml:space="preserve">polygonum A B E I O P
              <lb/>
              <note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">TAB. XLIII.
                <lb/>
              Fig. 1. 2. 3.</note>
            ſimul, eße ad polygonum A B E I O P, ut
              <lb/>
            duplum polygoni A B E I O P ad poly-
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            gonum A B C G K N P.</s>
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            <s xml:id="echoid-s2867" xml:space="preserve">Ex hujus tertia manifeſtum eſt triangulum A B I & </s>
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            pezium A B E I ſimul, eſſe ad trapezium A B E I,
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            ut duplum trapezii A B E Iad polygonum A B C G I: </s>
            <s xml:id="echoid-s2869" xml:space="preserve">& </s>
            <s xml:id="echoid-s2870" xml:space="preserve">
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            ex prædictis facile concludi poteſt triangulum A B I eſſe di-
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            midium trapezii A B I P, & </s>
            <s xml:id="echoid-s2871" xml:space="preserve">trapezium A B E I eſſe dimi-
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            dium polygoni A B E I O P, & </s>
            <s xml:id="echoid-s2872" xml:space="preserve">polygonum A B C G I
              <lb/>
            eſſe dimidium polygoni A B C G K N P; </s>
            <s xml:id="echoid-s2873" xml:space="preserve">& </s>
            <s xml:id="echoid-s2874" xml:space="preserve">proinde termi-
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            nos duplicando, trapezium A B I P & </s>
            <s xml:id="echoid-s2875" xml:space="preserve">polygonum A B E I O P
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            ſimul, erunt ad polygonum A B E I O P ut duplum polygo-
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            ni A B E I O P ad polygonum A B C G K N P, quod
              <lb/>
            demonſtrandum erat.</s>
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          <p>
            <s xml:id="echoid-s2877" xml:space="preserve">Hinc facile colligi poteſt polygonum A B C G K N P
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            eſſe medium harmonicum inter polygona A B E I O P,
              <lb/>
            A B D L P, quod hic admonuiſſe ſufficiat, in ſequentibus
              <lb/>
            enim demonſtrabitur.</s>
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