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

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              <pb o="236" file="0314" n="341" rhead="DE CENTRO OSCILL."/>
            ſuſpenſis, a quo pondus unum quater magis quam alterum
              <lb/>
            diſtat; </s>
            <s xml:id="echoid-s5174" xml:space="preserve">ita ut altitudines perpendiculares, unde deſcendunt
              <lb/>
            ſint ut 1 ad 4.</s>
            <s xml:id="echoid-s5175" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5176" xml:space="preserve">Convenit inter nos de proportione inter has altitudines, & </s>
            <s xml:id="echoid-s5177" xml:space="preserve">
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            de ſumma velocitatum, quas illa pondera acquirerent, ſi ſe-
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            paratim ab iis altitudinibus caderent; </s>
            <s xml:id="echoid-s5178" xml:space="preserve">ſed contendimus de
              <lb/>
            exprimendis his altitudinibus reſpectu ſpatii, quod ſit com-
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            munis earum menſura, & </s>
            <s xml:id="echoid-s5179" xml:space="preserve">pro unitate habeatur. </s>
            <s xml:id="echoid-s5180" xml:space="preserve">Cum omni-
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            bus, qui ante me de ſimilibus quæſtionibus ſcripſerunt, po-
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            no veros numeros, quibus exprimuntur altitudines, eſſe qua-
              <lb/>
            drata ipſorum numerorum qui velocitates deſignant, in illis
              <lb/>
            caſibus, in quibus inter altitudines & </s>
            <s xml:id="echoid-s5181" xml:space="preserve">inter velocitates non
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            alia datur ratio, præter generalem experientiâ detectam.</s>
            <s xml:id="echoid-s5182" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s5183" xml:space="preserve">Patet autem ex numeris quos in computatione mea detexi,
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            (cum 9 & </s>
            <s xml:id="echoid-s5184" xml:space="preserve">144 ducta in {1/25} pedis, id eſt 6 pedes cum 1 digito
              <lb/>
            5 lineis & </s>
            <s xml:id="echoid-s5185" xml:space="preserve">quod excedit, differant cum 1 pede & </s>
            <s xml:id="echoid-s5186" xml:space="preserve">4 pedibus,
              <lb/>
            aut 5 pedibus,) ſummas altitudinum, ad quas adſcendunt pon-
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            dera in exemplo propoſito, non eſſe æqualem ſummæ alti-
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            tudinum unde deſcendunt, quam æqualitatem D
              <emph style="super">us</emph>
            . </s>
            <s xml:id="echoid-s5187" xml:space="preserve">Huge-
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            nius ponit in generali propoſitione, quâ utitur pro princi-
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            pio in ſuo tractatu de centro Oſcillationis.</s>
            <s xml:id="echoid-s5188" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5189" xml:space="preserve">D
              <emph style="super">us</emph>
            . </s>
            <s xml:id="echoid-s5190" xml:space="preserve">Bernoulli reſpondet, quadrata numerorum, qui
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            exprimunt velocitates ponderum, tantum exprimere pro-
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            portionem altitudinum, ad quas revertuntur poſt illo-
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            rum ſeparationem, & </s>
            <s xml:id="echoid-s5191" xml:space="preserve">non ipſas altitudines, quæ qui-
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            dem inter ſe habere poſſunt rationem, {144/25} ad {9/25} dum ta-
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            men harum ſumma eſt 5, quæ eſt ſumma altitudinum,
              <lb/>
            unde pondera deſcenderunt. </s>
            <s xml:id="echoid-s5192" xml:space="preserve">Nam altitudines, ad quas
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            revertuntur ſeparata, ſunt juxta illum 4{12/17} & </s>
            <s xml:id="echoid-s5193" xml:space="preserve">{5/17}, quarum
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            ſumma valet 5, ut ſumma primarum altitudinum 1. </s>
            <s xml:id="echoid-s5194" xml:space="preserve">& </s>
            <s xml:id="echoid-s5195" xml:space="preserve">4.
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            </s>
            <s xml:id="echoid-s5196" xml:space="preserve">Iterum reſpondere non difficile erit. </s>
            <s xml:id="echoid-s5197" xml:space="preserve">Rogatum velim
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            D
              <emph style="super">um</emph>
            . </s>
            <s xml:id="echoid-s5198" xml:space="preserve">Bernoulli, dum contendit, proportionem quadra-
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            torum numerorum, qui velocitates exprimunt, tantum
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            conſiderandam eſſe, quâ motus lege, & </s>
            <s xml:id="echoid-s5199" xml:space="preserve">per quodnam
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            principium Mechanicum pondera, de quibus agimus, po-
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            tius redeant ad altitudines, quas ille notavit, &</s>
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