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

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            <s xml:id="echoid-s6305" xml:space="preserve">PROP. </s>
            <s xml:id="echoid-s6306" xml:space="preserve">II. </s>
            <s xml:id="echoid-s6307" xml:space="preserve">Datis poſitione quotlibet punctis; </s>
            <s xml:id="echoid-s6308" xml:space="preserve">ſive in eodem
              <lb/>
            plano fuerint, ſive non: </s>
            <s xml:id="echoid-s6309" xml:space="preserve">ſi à puncto quod eorum commune eſt
              <lb/>
            gravitatis centrum, ad unum quodque datorum fila extendan-
              <lb/>
            tur, eaque ſingula trahantur à potentiis quæ ſint inter ſe ut
              <lb/>
            filorum longitudines, fiet æquilibrium manente nodo commu-
              <lb/>
            ni in dicto gravitatis centro.</s>
            <s xml:id="echoid-s6310" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s6311" xml:space="preserve">Sint data puncta A, B, C, D, E, quæ vel in eodem
              <lb/>
              <note position="left" xlink:label="note-0374-01" xlink:href="note-0374-01a" xml:space="preserve">TAB. XXXIII.
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              Fig. 2.</note>
            plano vel aliter utcunque collocata intelligantur: </s>
            <s xml:id="echoid-s6312" xml:space="preserve">attributâ
              <lb/>
            autem ſingulis æquali gravitate, conſtat commune eorum
              <lb/>
            gravitatis centrum inveniri hoc modo.</s>
            <s xml:id="echoid-s6313" xml:space="preserve"/>
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            <s xml:id="echoid-s6314" xml:space="preserve">Jungantur nempe duo quælibet datorum punctorum rectâ
              <lb/>
            A B, quâ bifariam ſectâ in F, erit hoc centrum gravitatis
              <lb/>
            punctorum A, B. </s>
            <s xml:id="echoid-s6315" xml:space="preserve">Ducatur deinde ad punctum aliud C re-
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            cta F C quæ ſecetur in G, ut ſit C G dupla G F; </s>
            <s xml:id="echoid-s6316" xml:space="preserve">& </s>
            <s xml:id="echoid-s6317" xml:space="preserve">erit
              <lb/>
            G centrum gravitatis punctorum trium A, B, C. </s>
            <s xml:id="echoid-s6318" xml:space="preserve">Rurſus
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            ducatur ad aliud punctum recta G D, ſeceturque in H, ut
              <lb/>
            ſit D H tripla H G, & </s>
            <s xml:id="echoid-s6319" xml:space="preserve">fiet H centrum gravitatis punctorum
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            quatuor A, B, C, D.</s>
            <s xml:id="echoid-s6320" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6321" xml:space="preserve">Similiterque ductâ H E ad punctum quintum E, ſectâque
              <lb/>
            in K, ut K E ſit quadrupla K H, erit K centrum gravi-
              <lb/>
            tatis punctorum quinque A, B, C, D, E. </s>
            <s xml:id="echoid-s6322" xml:space="preserve">Ac ſimili ratione
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            quotcunque punctorum centrum gravitatis invenire licebit.</s>
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            <s xml:id="echoid-s6324" xml:space="preserve">Porro extentis filis à puncto K ad A, B, C, D, E,
              <lb/>
            quæ trahantur ſingula à potentiis quæ ſint inter ſe ut ipſæ
              <lb/>
            longitudines K A, K B, K C, K D, K E: </s>
            <s xml:id="echoid-s6325" xml:space="preserve">dico fieri æ-
              <lb/>
            quilibrium manente nodo communi in K. </s>
            <s xml:id="echoid-s6326" xml:space="preserve">Ducantur enim à
              <lb/>
            centris gravitatis inventis F, G, H, ad centrum gravitatis
              <lb/>
            omnium punctorum K, rectæ F K, G K, H K. </s>
            <s xml:id="echoid-s6327" xml:space="preserve">Itaque con-
              <lb/>
            ſtat filis A K, B K, punctum K trahentibus cum potentiis quæ
              <lb/>
            ſint ut longitudines eorum filorum, æquipollere filum F K,
              <lb/>
            tractum à potentia quæ ſit ut dupla longitudo F K. </s>
            <s xml:id="echoid-s6328" xml:space="preserve">Rurſus
              <lb/>
            verò duobus his, filo F K trahenti cum potentia quæ ſit ut
              <lb/>
            dupla F K, & </s>
            <s xml:id="echoid-s6329" xml:space="preserve">filo C K trahenti cum potentia quæ ſit ut
              <lb/>
            ſimplex longitudo C K, æquipollet filum G K tractum à
              <lb/>
            potentia quæ ſit ut tripla K G per præcedentem: </s>
            <s xml:id="echoid-s6330" xml:space="preserve">ergo
              <lb/>
            filum G K ita tractum æquipollet filis tribus K A, K </s>
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