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

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        <div xml:id="echoid-div148" type="section" level="1" n="65">
          <pb o="416" file="0134" n="143" rhead="VERA CIRCULI"/>
          <p>
            <s xml:id="echoid-s2803" xml:space="preserve">Ducatur recta D L ſegmentum tangens in puncto I, & </s>
            <s xml:id="echoid-s2804" xml:space="preserve">
              <lb/>
            rectis B F, F P, occurrens in punctis D, L, ita ut com-
              <lb/>
            pleatur polygonum A B D L P.</s>
            <s xml:id="echoid-s2805" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div149" type="section" level="1" n="66">
          <head xml:id="echoid-head98" xml:space="preserve">PROP. II. THEOREMA.</head>
          <head xml:id="echoid-head99" style="it" xml:space="preserve">Dico trapezia A B F P, A B I P ſimul, eſſe ad du-
            <lb/>
          plum trapezii A B I P, ſicut trapezium A B F P ad polygonum A B D L P.</head>
          <note position="left" xml:space="preserve">TAB. XLIII.
            <lb/>
          Fig. 1. 2. 3.</note>
          <p>
            <s xml:id="echoid-s2806" xml:space="preserve">Quoniam recta A F, ducta per contactum rectæ D L cum
              <lb/>
            ſegmento, ducitur etiam per concurſum duarum recta-
              <lb/>
            rum F B, F P, rectam D L terminantium & </s>
            <s xml:id="echoid-s2807" xml:space="preserve">ſegmen-
              <lb/>
            tum in duobus punctis tangentium; </s>
            <s xml:id="echoid-s2808" xml:space="preserve">igitur recta D L bifa-
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            riam ſecatur in puncto I; </s>
            <s xml:id="echoid-s2809" xml:space="preserve">& </s>
            <s xml:id="echoid-s2810" xml:space="preserve">proinde triangulum F D I æ-
              <lb/>
            quale eſt triangulo F I L, at triangulum A B F æquale eſt
              <lb/>
            triangulo A P F; </s>
            <s xml:id="echoid-s2811" xml:space="preserve">& </s>
            <s xml:id="echoid-s2812" xml:space="preserve">igitur trapezium A B D I æquale eſt
              <lb/>
            trapezio A P L I; </s>
            <s xml:id="echoid-s2813" xml:space="preserve">trapezium ergo A P L I dimidium eſt
              <lb/>
            polygoni A B D L P. </s>
            <s xml:id="echoid-s2814" xml:space="preserve">ducatur recta A L: </s>
            <s xml:id="echoid-s2815" xml:space="preserve">manifeſtum eſt
              <lb/>
            ex præcedentis demonſtratione triangulum A I L eſſe æqua-
              <lb/>
            le triangulo A L P; </s>
            <s xml:id="echoid-s2816" xml:space="preserve">ſed ut triangulum A L F ad triangu-
              <lb/>
            lum A L I ita F A ad A I, & </s>
            <s xml:id="echoid-s2817" xml:space="preserve">ut F A ad A I ita trapezium
              <lb/>
            A B F P ad trapezium A B I P; </s>
            <s xml:id="echoid-s2818" xml:space="preserve">& </s>
            <s xml:id="echoid-s2819" xml:space="preserve">igitur ut trapezium
              <lb/>
            A B F P ad trapezium A B I P; </s>
            <s xml:id="echoid-s2820" xml:space="preserve">ita triangulum A L F ad
              <lb/>
            triangulum A L I; </s>
            <s xml:id="echoid-s2821" xml:space="preserve">& </s>
            <s xml:id="echoid-s2822" xml:space="preserve">componendo, ut trapezia A B F P,
              <lb/>
            A B I P ſimul, ad trapezium A B I P, ita triangulum A F L
              <lb/>
            & </s>
            <s xml:id="echoid-s2823" xml:space="preserve">triangulum A I L ſimul, hoc eſt triangulum A F P, ad
              <lb/>
            triangulum A I L: </s>
            <s xml:id="echoid-s2824" xml:space="preserve">& </s>
            <s xml:id="echoid-s2825" xml:space="preserve">conſequentes duplicando, ut trape-
              <lb/>
            zia A B F P, A B I P ſimul, ad duplum trapezii A B I P,
              <lb/>
            ita triangulum A F P, ad trapezium A I L P: </s>
            <s xml:id="echoid-s2826" xml:space="preserve">at triangu-
              <lb/>
            lum A F P eſt dimidium trapezii A B F P, & </s>
            <s xml:id="echoid-s2827" xml:space="preserve">trapezium
              <lb/>
            A I L P eſt dimidium polygoni A B D L P; </s>
            <s xml:id="echoid-s2828" xml:space="preserve">& </s>
            <s xml:id="echoid-s2829" xml:space="preserve">igitur ut
              <lb/>
            trapezia A B F P, A B I P ſimul, ad duplum trapezii
              <lb/>
            A B I P, ita trapezium A B F P ad polygonum A B D L P,
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            quod demonſtrare oportuit.</s>
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