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

Table of Notes

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            fieri poſſit) generalis methodus inveniendi omnium ſerierum
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            convergentium terminationes.</s>
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          <head xml:id="echoid-head106" xml:space="preserve">PROP. VI. THEOREMATA.</head>
          <p style="it">
            <s xml:id="echoid-s2902" xml:space="preserve">Dico differentiam inter triangulum A B P & </s>
            <s xml:id="echoid-s2903" xml:space="preserve">trape-
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              <note position="left" xlink:label="note-0138-01" xlink:href="note-0138-01a" xml:space="preserve">TAB. XLIII.
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              Fig. 1. 2. 3.</note>
            zium A B F P majorem eſſe duplo differentiæ inter
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            trapezium A B I P & </s>
            <s xml:id="echoid-s2904" xml:space="preserve">polygonum A B D L P.</s>
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            <s xml:id="echoid-s2906" xml:space="preserve">Sit triangulum A B P, A; </s>
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            <s xml:id="echoid-s2908" xml:space="preserve">tra-
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            pezium A B I P, C, & </s>
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            <s xml:id="echoid-s2910" xml:space="preserve">quo-
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            niam A eſt ad C ut C ad B, igitur ut differentia inter A
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            & </s>
            <s xml:id="echoid-s2911" xml:space="preserve">C ad A, ita differentia inter C & </s>
            <s xml:id="echoid-s2912" xml:space="preserve">B ad C; </s>
            <s xml:id="echoid-s2913" xml:space="preserve">& </s>
            <s xml:id="echoid-s2914" xml:space="preserve">permutan-
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            do, ut differentia inter A & </s>
            <s xml:id="echoid-s2915" xml:space="preserve">C ad differentiam inter C & </s>
            <s xml:id="echoid-s2916" xml:space="preserve">B
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            ita A ad C; </s>
            <s xml:id="echoid-s2917" xml:space="preserve">& </s>
            <s xml:id="echoid-s2918" xml:space="preserve">componendo, ut differentia inter A & </s>
            <s xml:id="echoid-s2919" xml:space="preserve">C & </s>
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            differentia inter C & </s>
            <s xml:id="echoid-s2921" xml:space="preserve">B ſimul, hoc eſt differentia inter A & </s>
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            B, ad differentiam inter C & </s>
            <s xml:id="echoid-s2923" xml:space="preserve">B, ita A + C ad C; </s>
            <s xml:id="echoid-s2924" xml:space="preserve">ſed ut
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            A + C ad C ita 2 C ad D, & </s>
            <s xml:id="echoid-s2925" xml:space="preserve">ideo differentia inter A & </s>
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            B eſt ad differentiam inter C & </s>
            <s xml:id="echoid-s2927" xml:space="preserve">B ut 2 C ad D. </s>
            <s xml:id="echoid-s2928" xml:space="preserve">quoniam
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            A + C eſt ad C ut 2 C ad D, erit permutando ut A + C
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            ad 2 C ita C ad D; </s>
            <s xml:id="echoid-s2929" xml:space="preserve">& </s>
            <s xml:id="echoid-s2930" xml:space="preserve">dividendo, ut differentia inter A & </s>
            <s xml:id="echoid-s2931" xml:space="preserve">
              <lb/>
            C ad 2 C ita differentia inter C & </s>
            <s xml:id="echoid-s2932" xml:space="preserve">D ad D; </s>
            <s xml:id="echoid-s2933" xml:space="preserve">& </s>
            <s xml:id="echoid-s2934" xml:space="preserve">permutan-
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            do, differentia inter A & </s>
            <s xml:id="echoid-s2935" xml:space="preserve">C eſt ad differentiam inter C & </s>
            <s xml:id="echoid-s2936" xml:space="preserve">D
              <lb/>
            ut 2 C ad D; </s>
            <s xml:id="echoid-s2937" xml:space="preserve">ſed demonſtratum eſt differentiam inter A & </s>
            <s xml:id="echoid-s2938" xml:space="preserve">
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            B eſſe ad differentiam inter C & </s>
            <s xml:id="echoid-s2939" xml:space="preserve">B ut 2 C ad D; </s>
            <s xml:id="echoid-s2940" xml:space="preserve">& </s>
            <s xml:id="echoid-s2941" xml:space="preserve">proin-
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            de differentia inter A & </s>
            <s xml:id="echoid-s2942" xml:space="preserve">B eſt ad differentiam inter C & </s>
            <s xml:id="echoid-s2943" xml:space="preserve">B,
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            ut differentia inter A & </s>
            <s xml:id="echoid-s2944" xml:space="preserve">C ad differentiam inter C & </s>
            <s xml:id="echoid-s2945" xml:space="preserve">D; </s>
            <s xml:id="echoid-s2946" xml:space="preserve">ſed
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            differentia inter A & </s>
            <s xml:id="echoid-s2947" xml:space="preserve">B eſt major differentia inter C & </s>
            <s xml:id="echoid-s2948" xml:space="preserve">B,
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            & </s>
            <s xml:id="echoid-s2949" xml:space="preserve">ideo differentia inter A & </s>
            <s xml:id="echoid-s2950" xml:space="preserve">C eſt major differentia inter C
              <lb/>
            & </s>
            <s xml:id="echoid-s2951" xml:space="preserve">D: </s>
            <s xml:id="echoid-s2952" xml:space="preserve">& </s>
            <s xml:id="echoid-s2953" xml:space="preserve">prædictam analogiam permutando, differentia in-
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            ter A & </s>
            <s xml:id="echoid-s2954" xml:space="preserve">B eſt ad differentiam inter A & </s>
            <s xml:id="echoid-s2955" xml:space="preserve">C, ut differentia
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            inter C & </s>
            <s xml:id="echoid-s2956" xml:space="preserve">B ad differentiam inter C & </s>
            <s xml:id="echoid-s2957" xml:space="preserve">D; </s>
            <s xml:id="echoid-s2958" xml:space="preserve">at differentia in-
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            ter A & </s>
            <s xml:id="echoid-s2959" xml:space="preserve">B eſt major differentia inter A & </s>
            <s xml:id="echoid-s2960" xml:space="preserve">C, & </s>
            <s xml:id="echoid-s2961" xml:space="preserve">ideo diffe-
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            rentia inter C & </s>
            <s xml:id="echoid-s2962" xml:space="preserve">B eſt major differentia inter C & </s>
            <s xml:id="echoid-s2963" xml:space="preserve">D; </s>
            <s xml:id="echoid-s2964" xml:space="preserve">atque
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            differentia inter A & </s>
            <s xml:id="echoid-s2965" xml:space="preserve">B æqualis eſt differentiis, inter A & </s>
            <s xml:id="echoid-s2966" xml:space="preserve">C,
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            inter C & </s>
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            <s xml:id="echoid-s2968" xml:space="preserve">cumque earum utravis ſit major differentia </s>
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