Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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              <pb o="124" file="0182" n="199" rhead="CHRISTIANI HUGENII"/>
            cujus ſectio recta D F, inque ipſum à ſingulis ponderibus
              <lb/>
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                <emph style="sc">De centro</emph>
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                <emph style="sc">OSCILLA-</emph>
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                <emph style="sc">TIONIS.</emph>
              </note>
            ducantur perpendiculares A D, B E, C F. </s>
            <s xml:id="echoid-s2820" xml:space="preserve">Sit autem G
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            punctum centrum gravitatis ponderum omnium A, B, C,
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            à quo ducatur perpendicularis in idem planum G H. </s>
            <s xml:id="echoid-s2821" xml:space="preserve">Dico
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            ſummam productorum, quæ fiunt à ſingulis ponderibus in
              <lb/>
            ſuas perpendiculares, æquari producto ab recta G H in
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            omnia pondera A, B, C.</s>
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            <s xml:id="echoid-s2823" xml:space="preserve">Intelligantur enim perpendiculares, à ſingulis ponderibus
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            eductæ, continuari in alteram partem plani D F, ſintque
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            ſingulæ D K, E L, F M, ipſi H G æquales; </s>
            <s xml:id="echoid-s2824" xml:space="preserve">omnesque
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            lineæ, inflexiles virgas referant, ad horizontem parallelas;
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            </s>
            <s xml:id="echoid-s2825" xml:space="preserve">& </s>
            <s xml:id="echoid-s2826" xml:space="preserve">ponantur in K, L, M, gravitates ejusmodi, quæ ſingu-
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            læ cum ſibi oppoſitis A, B, C, æquilibrium faciant ad in-
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            terſectionem plani D E F. </s>
            <s xml:id="echoid-s2827" xml:space="preserve">Omnes igitur K, L, M, æqui-
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            ponderabunt omnibus A, B, C. </s>
            <s xml:id="echoid-s2828" xml:space="preserve">Erit autem, ſicut longitu-
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            do A D ad D K, ita pondus K ad pondus A, ac proinde
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            D A ducta in magnitudinem A, æquabitur D K, ſive G H,
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            ductæ in K. </s>
            <s xml:id="echoid-s2829" xml:space="preserve">Similiter E B in B æquabitur E L, ſive G H,
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            in L; </s>
            <s xml:id="echoid-s2830" xml:space="preserve">& </s>
            <s xml:id="echoid-s2831" xml:space="preserve">F C in C æquabitur F M, ſive G H, in M. </s>
            <s xml:id="echoid-s2832" xml:space="preserve">Er-
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            go ſumma productorum ex A D in A, B E in B, C F in
              <lb/>
            F, æquabitur ſummæ productorum ex G H in omnes
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            K, L, M. </s>
            <s xml:id="echoid-s2833" xml:space="preserve">Quum autem K, L, M, æquiponderent ipſis A,
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            B, C, etiam iisdem A, B, C, ex centro ipſorum gravita-
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            tis G ſuſpenſis, æquiponderabunt. </s>
            <s xml:id="echoid-s2834" xml:space="preserve">Unde, cum diſtantia
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            G H æqualis ſit ſingulis D K, E L, F M, neceſſe eſt ma-
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            gnitudines A, B, C, ſimul ſumptas, æquari ipſis
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            K, L, M. </s>
            <s xml:id="echoid-s2835" xml:space="preserve">Itaque & </s>
            <s xml:id="echoid-s2836" xml:space="preserve">ſumma productorum ex G H in omnes
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            A, B, C, æquabitur productis ex D A in A, E B in B, & </s>
            <s xml:id="echoid-s2837" xml:space="preserve">
              <lb/>
            F C in C. </s>
            <s xml:id="echoid-s2838" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s2839" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s2840" xml:space="preserve">Etſi vero in demonſtratione poſitæ fuerint rectæ A K, B L,
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            C M, horizonti parallelæ, & </s>
            <s xml:id="echoid-s2841" xml:space="preserve">planum ad horizontem ere-
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            ctum; </s>
            <s xml:id="echoid-s2842" xml:space="preserve">patet, ſi omnia ſimul in alium quemlibet ſitum trans-
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            ponantur, eandem manere productorum æqualitatem, cum
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            rectæ omnes ſint eædem quæ prius. </s>
            <s xml:id="echoid-s2843" xml:space="preserve">Quare conſtat propo-
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            ſitum.</s>
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