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

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        <div xml:id="echoid-div274" type="section" level="1" n="102">
          <p>
            <s xml:id="echoid-s3191" xml:space="preserve">
              <pb o="140" file="0202" n="221" rhead="CHRISTIANI HUGENII"/>
            & </s>
            <s xml:id="echoid-s3192" xml:space="preserve">- 2 ly = - 2 {ιι/θ} - 2 l
              <emph style="red">zz - xx + 2 {xμ/θ} - {μμ/θθ}</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s3193" xml:space="preserve">
              <note position="left" xlink:label="note-0202-01" xlink:href="note-0202-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">O@CILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            vel + θ yy = {ιι/θ} - 2 l
              <emph style="red">zz - xx + 2 {xμ/θ} - {μμ/θθ} + θ zz - θ x x
                <lb/>
              xm - {μμ/θ}</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s3194" xml:space="preserve">+ 2 & </s>
            <s xml:id="echoid-s3195" xml:space="preserve">- 2 ly = - 2{ιι/θ} + 2 l
              <emph style="red">zz - xx + 2 {xμ/θ} - {μμ/θθ}</emph>
            . </s>
            <s xml:id="echoid-s3196" xml:space="preserve">
              <lb/>
            Ac proinde, utroque caſu, pro θ y y - 2 l y habebitur - {ιι/θ}
              <lb/>
            + θ z z - θ x x + 2 x m - {μμ/θ}. </s>
            <s xml:id="echoid-s3197" xml:space="preserve">Quò appoſitis reliquis quantita-
              <lb/>
            tibus, ſumma prædicta contentis, θ x x - 2 x m + n n + k k,
              <lb/>
            fiet tota ſumma, nempe quadratorum F A, F B, F C, F D,
              <lb/>
            = θ z z + nn + k k - {μμ - ιι/θ}. </s>
            <s xml:id="echoid-s3198" xml:space="preserve">Quod apparet eſſe planum da-
              <lb/>
            tum, cum hæ quantitates omnes datæ ſint; </s>
            <s xml:id="echoid-s3199" xml:space="preserve">ſemperque idem
              <lb/>
            reperiri, ubicunque in circumferentia ſumptum fuerit pun-
              <lb/>
            ctum F. </s>
            <s xml:id="echoid-s3200" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s3201" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3202" xml:space="preserve">Quod ſi puncta data diverſas gravitates habere ponantur,
              <lb/>
            invicem commenſurabiles, ut ſi punctum A ponderet ut 2,
              <lb/>
            B ut 3, C ut 4, D ut 7, eorumque reperto gravitatis cen-
              <lb/>
            tro, circulus rurſus deſcribatur, ad cujus circumferentiæ
              <lb/>
            punctum, à datis punctis rectæ ducantur, ac ſingularum
              <lb/>
            quadrata multiplicia ſumantur ſecundum numerum ponderis
              <lb/>
            puncti ſui; </s>
            <s xml:id="echoid-s3203" xml:space="preserve">ut quadratum A F duplum, B F triplum, C F
              <lb/>
            quadruplum, D F ſeptuplum; </s>
            <s xml:id="echoid-s3204" xml:space="preserve">dico rurſus ſummam omnium
              <lb/>
            æqualem fore ſpatio dato, ſemperque eidem, ubicunque in
              <lb/>
            circumferentia punctum ſumptum fuerit. </s>
            <s xml:id="echoid-s3205" xml:space="preserve">Patet enim hoc ex
              <lb/>
            præcedenti demonſtratione, ſi imaginemur puncta ipſa mul-
              <lb/>
            tiplicia ſecundum numeros attributæ cuique gravitatis; </s>
            <s xml:id="echoid-s3206" xml:space="preserve">quaſi
              <lb/>
            nempe in A duo puncta conjuncta ſint, in B tria, in C qua-
              <lb/>
            tuor, in D ſeptem, atque illa omnia æqualiter gravia.</s>
            <s xml:id="echoid-s3207" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div279" type="section" level="1" n="103">
          <head xml:id="echoid-head129" xml:space="preserve">PROPOSITIO XIII.</head>
          <p style="it">
            <s xml:id="echoid-s3208" xml:space="preserve">SI figura plana, vel linea in plano exiſtens, ali-
              <lb/>
            ter atque aliter ſuſpendatur à punctis, quæ, in
              <lb/>
            eodem plano accepta, æqualiter à centro gravitatis
              <lb/>
            ſuæ diſtent; </s>
            <s xml:id="echoid-s3209" xml:space="preserve">agitatamotu in latus, ſibi ipſi iſochrona eſt.</s>
            <s xml:id="echoid-s3210" xml:space="preserve"/>
          </p>
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