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

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            <s xml:id="echoid-s3443" xml:space="preserve">
              <pb o="153" file="0217" n="237" rhead="HOROLOG. OSCILLATOR."/>
            qui ſit axi F parallelus . </s>
            <s xml:id="echoid-s3444" xml:space="preserve">Itaque rectangulum O T H
              <note position="right" xlink:label="note-0217-01" xlink:href="note-0217-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            cum plano Z, multiplicia ſecundum numerum particularum
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0217-02" xlink:href="note-0217-02a" xml:space="preserve">Prop. 47.
                <lb/>
              lib. 1. Eucl.</note>
            magnitudinis A B C D, æqualia erunt quadratis diſtantia-
              <lb/>
            rum ejusdem magnitudinis à dicto axe per E. </s>
            <s xml:id="echoid-s3445" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s3446" xml:space="preserve">planum
              <lb/>
            I, multiplex ſecundum eundem particularum numerum, æ-
              <lb/>
            quale poſitum fuit iisdem diſtantiarum quadratis. </s>
            <s xml:id="echoid-s3447" xml:space="preserve">Ergo pla-
              <lb/>
            num I æquale eſt rectangulo O T H & </s>
            <s xml:id="echoid-s3448" xml:space="preserve">plano Z ſimul ſum-
              <lb/>
            ptis. </s>
            <s xml:id="echoid-s3449" xml:space="preserve">quod oſtendendum ſupererat.</s>
            <s xml:id="echoid-s3450" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3451" xml:space="preserve">Hinc rurſus manifeſtum fit, quod propoſitione 16 demon-
              <lb/>
            ſtratum fuit; </s>
            <s xml:id="echoid-s3452" xml:space="preserve">nempe magnitudinem quamlibet, ſi aliter at-
              <lb/>
            que aliter ſuſpendatur atque agitetur, ab axibus parallelis,
              <lb/>
            qui à centro gravitatis ſuæ æqualiter diſtent, ſibi ipſi iſo-
              <lb/>
            chronam eſſe.</s>
            <s xml:id="echoid-s3453" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3454" xml:space="preserve">Sive enim magnitudo A B C D ſuſpendatur ab axe F, ſi-
              <lb/>
            ve ab axe L illi parallelo; </s>
            <s xml:id="echoid-s3455" xml:space="preserve">patet eadem utrobique eſſe qua-
              <lb/>
            drata diſtantiarum ab axe per E, qui ſit axibus F vel L pa-
              <lb/>
            rallelus. </s>
            <s xml:id="echoid-s3456" xml:space="preserve">Unde & </s>
            <s xml:id="echoid-s3457" xml:space="preserve">planum I, cujus multiplex, ſecundum
              <lb/>
            numerum particularum, æquatur quadratorum ſummæ, u-
              <lb/>
            troque caſu idem erit. </s>
            <s xml:id="echoid-s3458" xml:space="preserve">Hoc vero planum, applicatum ad di-
              <lb/>
            ſtantiam centri gravitatis ab axe oſcillationis, quæ utroque
              <lb/>
            caſu eadem ponitur, efficit diſtantiam qua centrum oſcilla-
              <lb/>
            tionis inferius eſt centro gravitatis; </s>
            <s xml:id="echoid-s3459" xml:space="preserve">Ergo etiam hæc diſtan-
              <lb/>
            tia utroque caſu eadem erit. </s>
            <s xml:id="echoid-s3460" xml:space="preserve">Velut ſi, facta ſuſpenſione ex
              <lb/>
            L, fuerit dicta diſtantia E Y, erit ipſa æqualis E G; </s>
            <s xml:id="echoid-s3461" xml:space="preserve">& </s>
            <s xml:id="echoid-s3462" xml:space="preserve">to-
              <lb/>
            ta Y L æqualis G F; </s>
            <s xml:id="echoid-s3463" xml:space="preserve">adeoque, in ſuſpenſione utraque,
              <lb/>
            idem pendulum ſimplex iſochronum fit magnitudini A B C D.</s>
            <s xml:id="echoid-s3464" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div302" type="section" level="1" n="109">
          <head xml:id="echoid-head135" xml:space="preserve">PROPOSITIO XIX.</head>
          <p style="it">
            <s xml:id="echoid-s3465" xml:space="preserve">SI magnitudo eadem, nunc brevius nunc longius
              <lb/>
            ſuſpenſa, agitetur; </s>
            <s xml:id="echoid-s3466" xml:space="preserve">erunt, ſicut diſtantiæ axi-
              <lb/>
            um oſcillationis à centro gravitatis inter ſe, ita
              <lb/>
            contraria ratione diſtantiæ centrorum oſcillationis
              <lb/>
            ab eodem gravitatis centro.</s>
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          </p>
          <p>
            <s xml:id="echoid-s3468" xml:space="preserve">Sit magnitudo, cujus centrum gravitatis A, ſuſpenſa pri-
              <lb/>
              <note position="right" xlink:label="note-0217-03" xlink:href="note-0217-03a" xml:space="preserve">TAB. XXII.
                <lb/>
              Fig. 3.</note>
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