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

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            <s xml:id="echoid-s3718" xml:space="preserve">
              <pb o="164" file="0234" n="257" rhead="CHRISTIANI HUGENII"/>
            2 a = b; </s>
            <s xml:id="echoid-s3719" xml:space="preserve">hoc eſt, ſi triangula affigi intelligantur in B, quod
              <lb/>
              <note position="left" xlink:label="note-0234-01" xlink:href="note-0234-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            longitudinem A L ſecet bifariam, erit y =
              <emph style="red">2 a a - x x.</emph>
              <lb/>
            quæ æquatio docet, quod ſi centro B, radio qui poſſit du-
              <lb/>
            plum B A, circumferentia deſcribatur, ea erit locus baſium
              <lb/>
            triangulorum acutiſſimorum B C, B D, quorum nempe,
              <lb/>
            ex A ſuſpenſorum, centrum oſcillationis erit L punctum.
              <lb/>
            </s>
            <s xml:id="echoid-s3720" xml:space="preserve">Cumque & </s>
            <s xml:id="echoid-s3721" xml:space="preserve">circulus totus, & </s>
            <s xml:id="echoid-s3722" xml:space="preserve">ſector ejus quilibet, axem
              <lb/>
            habens in recta A L, ex hujusmodi triangulorum paribus
              <lb/>
            componatur, manifeſtum eſt & </s>
            <s xml:id="echoid-s3723" xml:space="preserve">horum, ex A ſuſpenſorum,
              <lb/>
            centrum oſcillationis eſſe punctum L.</s>
            <s xml:id="echoid-s3724" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s3725" xml:space="preserve">Adeoque quilibet circuli ſector, ſuſpenſus à puncto quod
              <lb/>
            diſtet, à centro circuli ſui, ſemiſſe lateris quadrati circulo
              <lb/>
            inſcripti, pendulum iſochronum habebit toti eidem lateri æ-
              <lb/>
            quale. </s>
            <s xml:id="echoid-s3726" xml:space="preserve">Atque ita, hoc uno caſu, absque poſita dimenſione
              <lb/>
            arcus, pendulum ſectori iſochronum invenitur.</s>
            <s xml:id="echoid-s3727" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s3728" xml:space="preserve">Porro, ad univerſalem conſtructionem æquationis primæ,
              <lb/>
              <note position="left" xlink:label="note-0234-02" xlink:href="note-0234-02a" xml:space="preserve">TAB.XXV.
                <lb/>
              Fig. 3. & 4.</note>
            y =
              <emph style="red">2 a b - 2 a a - {8/3} a x + {4/3} b x - x x</emph>
            , dividatur A L bifariam
              <lb/>
            in E, & </s>
            <s xml:id="echoid-s3729" xml:space="preserve">adponatur ad B E pars ſui tertia E F; </s>
            <s xml:id="echoid-s3730" xml:space="preserve">eritque F
              <lb/>
            centrum deſcribendi circuli; </s>
            <s xml:id="echoid-s3731" xml:space="preserve">radius autem F O æqualis ſu-
              <lb/>
            mendus ei, quæ poteſt duplum differentiæ quadratorum
              <lb/>
            A E, E F.</s>
            <s xml:id="echoid-s3732" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s3733" xml:space="preserve">Si itaque, ex puncto B, ad deſcriptam circumferentiam
              <lb/>
            triangula duo paria acutiſſima conſtituantur, ut B C, B D;
              <lb/>
            </s>
            <s xml:id="echoid-s3734" xml:space="preserve">illorum, ex A ſuſpenſorum, centrum oſcillationis erit L. </s>
            <s xml:id="echoid-s3735" xml:space="preserve">
              <lb/>
            Quare & </s>
            <s xml:id="echoid-s3736" xml:space="preserve">portionis cujuslibet deſcripti circuli, cujus portio-
              <lb/>
            nis vertex ſit in B, axis vero in recta A L, quales ſunt u-
              <lb/>
            traque C B D; </s>
            <s xml:id="echoid-s3737" xml:space="preserve">poſita ſuſpenſione ex A; </s>
            <s xml:id="echoid-s3738" xml:space="preserve">centrum oſcilla-
              <lb/>
            tionis idem punctum L eſſe conſtat. </s>
            <s xml:id="echoid-s3739" xml:space="preserve">Atque adeo etiam cir-
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            culi ſegmentorum K O N, K M N, quæ facit recta K B N
              <lb/>
            perpendicularis ad A B.</s>
            <s xml:id="echoid-s3740" xml:space="preserve"/>
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            <s xml:id="echoid-s3741" xml:space="preserve">Et hæc quidem de motu laterali planorum, ac linearum,
              <lb/>
            animadvertiſſe ſufficiat. </s>
            <s xml:id="echoid-s3742" xml:space="preserve">Quibus hoc tantum addimus; </s>
            <s xml:id="echoid-s3743" xml:space="preserve">in-
              <lb/>
            ventis centris oſcillationis figurarum rectarum, ſeu quæ æ-
              <lb/>
            qualiter ad axem utrinque conſtitutæ ſunt; </s>
            <s xml:id="echoid-s3744" xml:space="preserve">ut trianguli iſo-
              <lb/>
            ſcelis, vel parabolicæ ſectionis rectæ etiam </s>
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