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

Table of handwritten notes

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            <s xml:id="echoid-s3653" xml:space="preserve">
              <pb o="162" file="0232" n="255" rhead="CHRISTIANI HUGENII"/>
            jus centrum F, ubi A B bifariam dividitur, radius autem
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              <note position="left" xlink:label="note-0232-01" xlink:href="note-0232-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
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                <emph style="sc">OSCILLA-</emph>
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                <emph style="sc">TIONIS</emph>
              .</note>
            = {1/2} a, ſive F A. </s>
            <s xml:id="echoid-s3654" xml:space="preserve">Ergo, ubicunque in circumferentia
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            A C B D duo pondera æqualia, æqualiter ab A diſtantia,
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            ponentur, ea, ex A agitata, iſochrona erunt pendulo lon-
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            gitudinem habenti æqualem diametro A B.</s>
            <s xml:id="echoid-s3655" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3656" xml:space="preserve">Atque hinc manifeſtum quoque, & </s>
            <s xml:id="echoid-s3657" xml:space="preserve">circumferentiam
              <lb/>
            A C B D, ſi gravitas ei tribuatur, & </s>
            <s xml:id="echoid-s3658" xml:space="preserve">quamlibet ejus por-
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            tionem, æqualiter in A vel B diviſam, & </s>
            <s xml:id="echoid-s3659" xml:space="preserve">ab axe per A ſuſ-
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            penſam, eidem pendulo A B iſochronam eſſe.</s>
            <s xml:id="echoid-s3660" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3661" xml:space="preserve">Loci vero ſolidi exemplum eſto hujusmodi. </s>
            <s xml:id="echoid-s3662" xml:space="preserve">Sit A N linea
              <lb/>
              <note position="left" xlink:label="note-0232-02" xlink:href="note-0232-02a" xml:space="preserve">TAB.XXIV.
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              Fig. 5.</note>
            inflexilis ſine pondere. </s>
            <s xml:id="echoid-s3663" xml:space="preserve">Propoſitumque ſit, ad punctum in
              <lb/>
            ea acceptum, ut M, affigere ipſi ad angulos rectos lineam,
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            ſeu virgam, pondere præditam O M L, ad M bifariam divi-
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            ſam, cujus in latus agitatæ oſcillationes, ex ſuſpenſione A,
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            iſochronæ ſint pendulo ſimplici longitudinis A N.</s>
            <s xml:id="echoid-s3664" xml:space="preserve"/>
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            <s xml:id="echoid-s3665" xml:space="preserve">Ducatur O H parallela A N, & </s>
            <s xml:id="echoid-s3666" xml:space="preserve">A H parallela O M,
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            & </s>
            <s xml:id="echoid-s3667" xml:space="preserve">ſit O R æqualis {2/3} O L. </s>
            <s xml:id="echoid-s3668" xml:space="preserve">Itaque cunei ſuper recta O L,
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            abſciſſi plano per O H ducto, ſubcentrica erit O R. </s>
            <s xml:id="echoid-s3669" xml:space="preserve">Sed
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            cunei alterius ſuper eadem O L, abſciſſi plano per rectam
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            A H, (eſt autem cuneus hic nihil aliud quam rectangulum)
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            ſubcentrica erit ipſa A M. </s>
            <s xml:id="echoid-s3670" xml:space="preserve">Quare rectangulum illud, quod
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            ſupra Oſcillationis vocavimus, erit ſolum rectangulum O M R.
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            </s>
            <s xml:id="echoid-s3671" xml:space="preserve">quod nempe, applicatum ad longitudinem A M, dabit di-
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            ſtantiam centri oſcillationis lineæ O L, ex A ſuſpenſæ, in-
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            fra punctum M.</s>
            <s xml:id="echoid-s3672" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3673" xml:space="preserve">Sit jam A N = a: </s>
            <s xml:id="echoid-s3674" xml:space="preserve">A M = x: </s>
            <s xml:id="echoid-s3675" xml:space="preserve">M O vel M L = y. </s>
            <s xml:id="echoid-s3676" xml:space="preserve">Eſt
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            ergo rectangulum O M R = {1/3} yy. </s>
            <s xml:id="echoid-s3677" xml:space="preserve">quo applicato ad A M, fit
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            {1 y y/3x}. </s>
            <s xml:id="echoid-s3678" xml:space="preserve">quæ longitudo itaque ipſi M N æqualis eſſe debebit,
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            cum velimus centrum oſcillationis virgæ O L eſſe in N. </s>
            <s xml:id="echoid-s3679" xml:space="preserve">Fit
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            ergo æquatio {1 yy/3x} + x = a. </s>
            <s xml:id="echoid-s3680" xml:space="preserve">Unde y =
              <emph style="red">3 a x - 3 x x</emph>
            . </s>
            <s xml:id="echoid-s3681" xml:space="preserve">Quod
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            ſignificat puncta O & </s>
            <s xml:id="echoid-s3682" xml:space="preserve">L eſſe ad Ellipſin, cujus axis minor
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            A N; </s>
            <s xml:id="echoid-s3683" xml:space="preserve">latus rectum vero, ſecundum quod poſſunt ordinatim
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            ad axem hunc applicatæ, ipſius A N triplum.</s>
            <s xml:id="echoid-s3684" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s3685" xml:space="preserve">Hinc vero manifeſtum fit, cum omnis virga ipſi O L pa-
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            rallela, & </s>
            <s xml:id="echoid-s3686" xml:space="preserve">ad Ellipſin hanc terminata, oſcillationes </s>
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