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

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            <s xml:id="echoid-s3143" xml:space="preserve">
              <pb o="139" file="0201" n="220" rhead="HOROLOG. OSCILLATOR."/>
            datorum punctorum multitudinem exprimens, dicatur θ; </s>
            <s xml:id="echoid-s3144" xml:space="preserve">erit
              <lb/>
              <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            E R = {ι/θ}; </s>
            <s xml:id="echoid-s3145" xml:space="preserve">& </s>
            <s xml:id="echoid-s3146" xml:space="preserve">R G = {μ/θ}. </s>
            <s xml:id="echoid-s3147" xml:space="preserve">Cumque G S ſit x, erit R S ſive
              <lb/>
            F T = x - {μ/θ}; </s>
            <s xml:id="echoid-s3148" xml:space="preserve">vel {μ/θ} - x, ſi G R major quam G S; </s>
            <s xml:id="echoid-s3149" xml:space="preserve">& </s>
            <s xml:id="echoid-s3150" xml:space="preserve">ſem-
              <lb/>
            per quadratum F T = xx - 2 {xμ/θ} + {μμ/θθ}. </s>
            <s xml:id="echoid-s3151" xml:space="preserve">quo ablato ab qua-
              <lb/>
            drato F E = zz, relinquetur quadratum T E = zz - xx
              <lb/>
            + 2 {xμ/θ} - {μμ/θθ}. </s>
            <s xml:id="echoid-s3152" xml:space="preserve">Et proinde T E =
              <emph style="red">zz - xx + 2 {xμ/θ} - {μμ/θθ}</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s3153" xml:space="preserve">Erat autem E R = {ι/θ}. </s>
            <s xml:id="echoid-s3154" xml:space="preserve">Itaque T R = {ι/θ} + vel -
              <emph style="red">zz - xx
                <lb/>
              + 2 {xμ/θ} - {μμ/θθ}</emph>
            . </s>
            <s xml:id="echoid-s3155" xml:space="preserve">quæ T R, brevitatis gratia, dicatury y. </s>
            <s xml:id="echoid-s3156" xml:space="preserve">Colli-
              <lb/>
            gamus jam porro ſummam quadratorum omnium F A, F B,
              <lb/>
            F C, F D. </s>
            <s xml:id="echoid-s3157" xml:space="preserve">Quadratum A F æquatur quadratis A V, V F. </s>
            <s xml:id="echoid-s3158" xml:space="preserve">
              <lb/>
            Eſt autem A V æqualis differentiæ duarum V K, A K, ſi-
              <lb/>
            ve duarum S G, A K; </s>
            <s xml:id="echoid-s3159" xml:space="preserve">ac proinde A V = x - e vel e - x; </s>
            <s xml:id="echoid-s3160" xml:space="preserve">& </s>
            <s xml:id="echoid-s3161" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3162" xml:space="preserve">A V = xx - 2 ex + ee. </s>
            <s xml:id="echoid-s3163" xml:space="preserve">V F vero æqualis eſt differen-
              <lb/>
            tiæ duarum F S, V S ſive duarum F S, A L; </s>
            <s xml:id="echoid-s3164" xml:space="preserve">ac proinde
              <lb/>
            V F = y - a vel a - y; </s>
            <s xml:id="echoid-s3165" xml:space="preserve">& </s>
            <s xml:id="echoid-s3166" xml:space="preserve">qu. </s>
            <s xml:id="echoid-s3167" xml:space="preserve">V F = yy - 2 ay + aa. </s>
            <s xml:id="echoid-s3168" xml:space="preserve">Ad-
              <lb/>
            ditisque quadratis A V, V F, fit quadratum F A = xx - 2 ex
              <lb/>
            + ee + yy - 2 ay + aa. </s>
            <s xml:id="echoid-s3169" xml:space="preserve">Eodemque modo invenientur qua-
              <lb/>
            drata reliquarum F B, F C, F D; </s>
            <s xml:id="echoid-s3170" xml:space="preserve">atque omnia ordine diſ-
              <lb/>
            poſita erunt hæc; </s>
            <s xml:id="echoid-s3171" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3172" xml:space="preserve">F A = xx - 2 ex + ee + yy - 2 ay + aa. </s>
            <s xml:id="echoid-s3173" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3174" xml:space="preserve">F B = xx - 2 fx + ff + yy - 2 by + bb. </s>
            <s xml:id="echoid-s3175" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3176" xml:space="preserve">F C = xx - 2 gx + gg + yy - 2 cy + cc. </s>
            <s xml:id="echoid-s3177" xml:space="preserve">
              <lb/>
            qu. </s>
            <s xml:id="echoid-s3178" xml:space="preserve">F D = xx - 2 hx + hh + yy - 2 dy + dd.</s>
            <s xml:id="echoid-s3179" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3180" xml:space="preserve">Horum vero ſumma; </s>
            <s xml:id="echoid-s3181" xml:space="preserve">ſi ponamus quadrata ee + ff + gg
              <lb/>
            + hh = nn; </s>
            <s xml:id="echoid-s3182" xml:space="preserve">& </s>
            <s xml:id="echoid-s3183" xml:space="preserve">quadrata aa + bb, + cc + dd = kk;
              <lb/>
            </s>
            <s xml:id="echoid-s3184" xml:space="preserve">erit iſta, θ x x - 2 mx + nn + θ yy - 2 ly + kk. </s>
            <s xml:id="echoid-s3185" xml:space="preserve">Siquidem
              <lb/>
            θ erat numerus datorum punctorum ideoque & </s>
            <s xml:id="echoid-s3186" xml:space="preserve">quadratorum,
              <lb/>
            poſitumque fuerat e + f + g + h = m, & </s>
            <s xml:id="echoid-s3187" xml:space="preserve">a + b + c + d = l.</s>
            <s xml:id="echoid-s3188" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3189" xml:space="preserve">In iſta vero ſumma, ſi in terminis θ y y & </s>
            <s xml:id="echoid-s3190" xml:space="preserve">2 l y, pro y,
              <lb/>
            ponatur id cujus loco poſitum erat, nempe {ι/θ} + vel -
              <lb/>
              <emph style="red">zz - xx + 2 {xμ/θ} - {μμ/θθ}</emph>
              <lb/>
            fiet + θ y y = {ιι/θ} + 2 l
              <emph style="red">zz - xx + 2 {xμ/θ} - {μμ/θθ}</emph>
            + θ zz - θ xx
              <lb/>
            + 2 x m-{μμ/θ}.</s>
            <s xml:id="echoid-s3191" xml:space="preserve"/>
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