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

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        <div xml:id="echoid-div291" type="section" level="1" n="106">
          <pb o="149" file="0213" n="233" rhead="HOROLOG. OSCILLATOR."/>
          <p>
            <s xml:id="echoid-s3366" xml:space="preserve">Porrò ſummam quadratorum ab rectis, quæ ducuntur à
              <lb/>
              <note position="right" xlink:label="note-0213-01" xlink:href="note-0213-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            dictis punctis omnibus ad punctum F, eandem eſſe patet cum
              <lb/>
            ſumma quadratorum ab iis rectis, quæ à ſingulis particulis
              <lb/>
            magnitudinis propoſitæ ducuntur perpendiculares in axem
              <lb/>
            oſcillationis per F transeuntem; </s>
            <s xml:id="echoid-s3367" xml:space="preserve">quippe cum lineæ ipſæ,
              <lb/>
            quarum quadrata intelliguntur, utrobique eandem habeant
              <lb/>
            longitudinem. </s>
            <s xml:id="echoid-s3368" xml:space="preserve">Similiter etiam, cum ſuſpenſio eſt ex axe per
              <lb/>
            H, patet ſummam quadratorum ab rectis, quæ ab omnibus
              <lb/>
            punctis, in ſpatio A B C D ſignatis, ducuntur ad punctum
              <lb/>
            H, eandem eſſe cum ſumma quadratorum, ab iis quæ, à
              <lb/>
            particulis omnibus magnitudinis propoſitæ, ducuntur per-
              <lb/>
            pendiculares in axem oſcillationis per H transeuntem. </s>
            <s xml:id="echoid-s3369" xml:space="preserve">Ergo
              <lb/>
            utroque caſu, ſi ſumma quadratorum ab rectis quæ, à pun-
              <lb/>
            ctis omnibus prædictis, ducuntur ad puncta F vel H; </s>
            <s xml:id="echoid-s3370" xml:space="preserve">di-
              <lb/>
            vidatur per rectas E F vel E H, multiplices ſecundum nu-
              <lb/>
            merum particularum in quas magnitudo propoſita diviſa in-
              <lb/>
            telligitur, orietur ex applicatione hac longitudo penduli ſim-
              <lb/>
            plicis, quod magnitudini ſuſpenſæ ex F vel H iſochronum
              <lb/>
            fit. </s>
            <s xml:id="echoid-s3371" xml:space="preserve">Eſt autem ſumma quadratorum utroque caſu æqualis ;</s>
            <s xml:id="echoid-s3372" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0213-02" xlink:href="note-0213-02a" xml:space="preserve">Prop. 13.
                <lb/>
              huj.</note>
            & </s>
            <s xml:id="echoid-s3373" xml:space="preserve">rectæ quoque E F, E H, inter ſe æquales; </s>
            <s xml:id="echoid-s3374" xml:space="preserve">& </s>
            <s xml:id="echoid-s3375" xml:space="preserve">particu-
              <lb/>
            larum idem numerus. </s>
            <s xml:id="echoid-s3376" xml:space="preserve">Ergo, quum & </s>
            <s xml:id="echoid-s3377" xml:space="preserve">applicatæ quantitates,
              <lb/>
            & </s>
            <s xml:id="echoid-s3378" xml:space="preserve">quibus illæ applicantur, utrobique æquales ſint, etiam
              <lb/>
            longitudines ex applicatione ortæ æquales erunt, hoc eſt,
              <lb/>
            longitudines pendulorum iſochronorum magnitudini propoſi-
              <lb/>
            tæ ſuſpenſæ ex F vel ex H. </s>
            <s xml:id="echoid-s3379" xml:space="preserve">Quare conſtat propoſitum.</s>
            <s xml:id="echoid-s3380" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div294" type="section" level="1" n="107">
          <head xml:id="echoid-head133" xml:space="preserve">PROPOSITIO XVII.</head>
          <p style="it">
            <s xml:id="echoid-s3381" xml:space="preserve">DAto plano, cujus multiplex per numerum par-
              <lb/>
            ticularum, in quas ſuſpenſa figura diviſa in-
              <lb/>
            telligitur, æquetur quadratis omnium diſtantia-
              <lb/>
            rum ab axe oſcillationis; </s>
            <s xml:id="echoid-s3382" xml:space="preserve">ſi illud applicetur ad re-
              <lb/>
            ctam, æqualem diſtantiæ inter axem oſcillationis
              <lb/>
            & </s>
            <s xml:id="echoid-s3383" xml:space="preserve">centrum gravitatis ſuſpenſæ magnitudinis, orie-
              <lb/>
            tur longitudo penduli ſimplicis ipſi iſochroni.</s>
            <s xml:id="echoid-s3384" xml:space="preserve"/>
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