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

Table of Notes

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              <pb o="163" file="0233" n="256" rhead="HOROLOG. OSCILLATOR."/>
            nas habeat pendulo ſimplici A N, etiam totum Ellipſeos
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              <note position="right" xlink:label="note-0233-01" xlink:href="note-0233-01a" 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>
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            planum, ex A ſuſpenſum & </s>
            <s xml:id="echoid-s3687" xml:space="preserve">in latus agitatum, ipſi A N
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            pendulo iſochronum fore. </s>
            <s xml:id="echoid-s3688" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s3689" xml:space="preserve">partem Ellipſeos quamli-
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            bet, quæ lineis una vel duabus, ad A N perpendicularibus,
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            abſcindetur.</s>
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            <s xml:id="echoid-s3691" xml:space="preserve">Cæterum adſcribemus & </s>
            <s xml:id="echoid-s3692" xml:space="preserve">aliud loci plani exemplum, in
              <lb/>
            quo nonnulla notatu digna occurrunt.</s>
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          <p>
            <s xml:id="echoid-s3694" xml:space="preserve">Sit virga A B ponderis expers, ſuſpenſa ex A; </s>
            <s xml:id="echoid-s3695" xml:space="preserve">oporteat-
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              <note position="right" xlink:label="note-0233-02" xlink:href="note-0233-02a" xml:space="preserve">TAB.XXIV.
                <lb/>
              Fig. 6.</note>
            que, ad datum in ea punctum B, affigere triangula duo pa-
              <lb/>
            ria, & </s>
            <s xml:id="echoid-s3696" xml:space="preserve">paribus angulis ab axe A B recedentia, quorum an-
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            guli ad B minimi, ſive infinite parvi exiſtimandi, quæque,
              <lb/>
            ita ſuſpenſa ab A, oſcillationes iſochronas faciant pendulo
              <lb/>
            ſimplici datæ longitudinis A L.</s>
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            <s xml:id="echoid-s3698" xml:space="preserve">Hic, ducta C G perpendiculari in B G, & </s>
            <s xml:id="echoid-s3699" xml:space="preserve">ponendo
              <lb/>
            A B = a; </s>
            <s xml:id="echoid-s3700" xml:space="preserve">A L = b; </s>
            <s xml:id="echoid-s3701" xml:space="preserve">B G = x; </s>
            <s xml:id="echoid-s3702" xml:space="preserve">C G = y: </s>
            <s xml:id="echoid-s3703" xml:space="preserve">invenitur æqua-
              <lb/>
            tio y =
              <emph style="red">2 a b - 2 a a - {8/3} a x + {4/3} b x - x x</emph>
            ex qua patet, baſes
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            triangulorum C, & </s>
            <s xml:id="echoid-s3704" xml:space="preserve">D, quæ baſes hic ut puncta conſide-
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            rantur, eſſe ad circuli circumferentiam; </s>
            <s xml:id="echoid-s3705" xml:space="preserve">quia nempe habetur
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            terminus ſimplex - x x.</s>
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            <s xml:id="echoid-s3707" xml:space="preserve">Licet autem hic animadvertere, quod ſi a ſit nihilo æqua-
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              <note position="right" xlink:label="note-0233-03" xlink:href="note-0233-03a" xml:space="preserve">TAB. XXV.
                <lb/>
              Fig. 1.</note>
            lis, hoc eſt, ſi punctum, ubi affiguntur trianguli B C,
              <lb/>
            B D, ſit idem cum puncto A; </s>
            <s xml:id="echoid-s3708" xml:space="preserve">tum futura ſit æquatio
              <lb/>
            y =
              <emph style="red">{4/3} b x - x x</emph>
            . </s>
            <s xml:id="echoid-s3709" xml:space="preserve">Ac proinde, hoc caſu, ſi ſumatur A O
              <lb/>
            = {2/3} b, hoc eſt, = {2/3} A L, centroque O per A circulus de-
              <lb/>
            ſcribatur A D N; </s>
            <s xml:id="echoid-s3710" xml:space="preserve">erunt baſes triangulorum A C, A D, ad
              <lb/>
            illius circumferentiam. </s>
            <s xml:id="echoid-s3711" xml:space="preserve">Cum igitur quælibet duo triangula
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            acutiſſima, quæ ex A ad circumferentiam A C N D conſti-
              <lb/>
            tuuntur, magnitudine & </s>
            <s xml:id="echoid-s3712" xml:space="preserve">ſitu ſibi reſpondentia, centrum
              <lb/>
            oſcillationis habeant punctum L, poſitâ A L = {3/4} diametri
              <lb/>
            A N; </s>
            <s xml:id="echoid-s3713" xml:space="preserve">cumque circulus totus ex ejusmodi triangulorum pa-
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            ribus componatur; </s>
            <s xml:id="echoid-s3714" xml:space="preserve">uti & </s>
            <s xml:id="echoid-s3715" xml:space="preserve">portio ejus quælibet, ut A C N D,
              <lb/>
            latera A C, A D æqualia habens; </s>
            <s xml:id="echoid-s3716" xml:space="preserve">manifeſtum eſt, tum cir-
              <lb/>
            culi totius, tum portionis qualem diximus, centrum oſcilla-
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            tionis eſſe in L.</s>
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            <s xml:id="echoid-s3718" xml:space="preserve">Rurſus, ſi in æquatione inventa ponatur {8/3} a = {4/3} b, ſeu
              <lb/>
              <note position="right" xlink:label="note-0233-04" xlink:href="note-0233-04a" xml:space="preserve">TAB. XXV.
                <lb/>
              Fig. 2.</note>
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