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

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        <div xml:id="echoid-div279" type="section" level="1" n="103">
          <pb o="141" file="0203" n="222" rhead="HOROLOG. OSCILLATOR."/>
          <p>
            <s xml:id="echoid-s3211" xml:space="preserve">Sit figura plana, vel linea in plano exiſtens A B C, cu-
              <lb/>
              <note position="right" xlink:label="note-0203-01" xlink:href="note-0203-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .
                <lb/>
              TAB. XX.
                <lb/>
              Fig. 6.</note>
            jus centrum gravitatis D. </s>
            <s xml:id="echoid-s3212" xml:space="preserve">quo eodem centro, circumferentia
              <lb/>
            circuli in eodem plano deſcribatur, E C F. </s>
            <s xml:id="echoid-s3213" xml:space="preserve">Dico, ſi à quo-
              <lb/>
            vis in illa puncto, ut E, C, vel G, ſuſpenſa figura agite-
              <lb/>
            tur in latus; </s>
            <s xml:id="echoid-s3214" xml:space="preserve">ſibi ipſi, ſive eidem pendulo ſimplici, iſochro-
              <lb/>
            nam eſſe.</s>
            <s xml:id="echoid-s3215" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3216" xml:space="preserve">Sit prima ſuſpenſio ex E puncto, quando autem eſt extra
              <lb/>
            figuram, ut hic, putandum eſt lineam E H, ex qua figura
              <lb/>
            pendet, rigidam eſſe, atque immobiliter ipſi affixam.</s>
            <s xml:id="echoid-s3217" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3218" xml:space="preserve">Intelligatur figura A B C diviſa in particulas minimas æ-
              <lb/>
            quales, à quarum omnium centris gravitatis, ad punctum
              <lb/>
            E, rectæ ductæ ſint; </s>
            <s xml:id="echoid-s3219" xml:space="preserve">quas quidem manifeſtum eſt, quum
              <lb/>
            moveatur figura motu in latus, eſſe ad axem agitationis per-
              <lb/>
            pendiculares. </s>
            <s xml:id="echoid-s3220" xml:space="preserve">Harum igitur omnium perpendicularium qua-
              <lb/>
            drata, diviſa per rectam E D, multiplicem ſecundum nu-
              <lb/>
            merum particularum in quas figura diviſa eſt, efficiunt lon-
              <lb/>
            gitudinem penduli ſimplicis, figuræ iſochroni , quæ ſit K L.</s>
            <s xml:id="echoid-s3221" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0203-02" xlink:href="note-0203-02a" xml:space="preserve">Prop. 6.
                <lb/>
              huj.</note>
            Suſpensâ autem figurâ ex puncto G, rurſus longitudo pen-
              <lb/>
            duli ſimplicis iſochroni invenitur, dividendo quadrata omnia
              <lb/>
            linearum, quæ à particulis figuræ ducuntur ad punctum G,
              <lb/>
            per rectam G D, multiplicem ſecundum earundem particu-
              <lb/>
            larum numerum . </s>
            <s xml:id="echoid-s3222" xml:space="preserve">Quum igitur puncta G & </s>
            <s xml:id="echoid-s3223" xml:space="preserve">E ſint in
              <note symbol="*" position="right" xlink:label="note-0203-03" xlink:href="note-0203-03a" xml:space="preserve">Prop. 6.
                <lb/>
              huj.</note>
            cumferentia deſcripta cetnro D, quod eſt centrum gravitatis
              <lb/>
            figuræ A B C, ſive centrum gravitatis punctorum omnium,
              <lb/>
            quæ centra ſunt particularum figuræ æqualium; </s>
            <s xml:id="echoid-s3224" xml:space="preserve">erit proinde
              <lb/>
            ſumma quadratorum à lineis, qnæ à dictis particulis ad pun-
              <lb/>
            ctum G ducuntur, æqualis ſummæ quadratorum à lineis quæ
              <lb/>
            ab iiſdem particulis ducuntur ad punctum E . </s>
            <s xml:id="echoid-s3225" xml:space="preserve">Hæ
              <note symbol="*" position="right" xlink:label="note-0203-04" xlink:href="note-0203-04a" xml:space="preserve">Prop.
                <lb/>
              præced.</note>
            quadratorum ſummæ, utraque ſuſpenſione, applicantur ad
              <lb/>
            magnitudines æquales: </s>
            <s xml:id="echoid-s3226" xml:space="preserve">quippe, in ſuſpenſione ex E, ad re-
              <lb/>
            ctam E D, multiplicem ſecundum numerum omnium par-
              <lb/>
            ticularum; </s>
            <s xml:id="echoid-s3227" xml:space="preserve">in ſuſpenſione autem ex G, ad rectam D G,
              <lb/>
            multiplicem ſecundum earundem particularum numerum.
              <lb/>
            </s>
            <s xml:id="echoid-s3228" xml:space="preserve">Ergo patet, ex applicatione hac poſteriori, quum nempe
              <lb/>
            ſuſpenſio eſt ex G, fieri longitudinem penduli iſochroni ean-
              <lb/>
            dem atque ex applicatione priori, hoc eſt, eandem ipſi K L.</s>
            <s xml:id="echoid-s3229" xml:space="preserve"/>
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