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

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              <pb o="174" file="0250" n="276" rhead="CHRISTIANI HUGENII"/>
              <note position="left" xlink:label="note-0250-01" xlink:href="note-0250-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            + vel -
              <emph style="red">{1/4} p p + {1/2} a b p + a a p - {1/3} a a b - a a c/d}</emph>
            . </s>
            <s xml:id="echoid-s3948" xml:space="preserve">Ubi animadverten-
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            dum, duas eſſe veras radices, ſi {1/2} a b p + c a p minus ſit
              <lb/>
            quam {1/3} a a b + a a c; </s>
            <s xml:id="echoid-s3949" xml:space="preserve">hoc eſt, ſi longitudo p minor ſit quam
              <lb/>
            {{1/3} a b + a c/{1/2} b + c}, quæ antea inventa fuit longitudo penduli iſochro-
              <lb/>
            ni, ſive diſtantia centri oſcillationis à ſuſpenſione, in pen-
              <lb/>
            dulo compoſito ex virga A C & </s>
            <s xml:id="echoid-s3950" xml:space="preserve">pondere C.</s>
            <s xml:id="echoid-s3951" xml:space="preserve"/>
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            <s xml:id="echoid-s3952" xml:space="preserve">Unde patet, ſi velimus efficere, ut, applicato pondere D,
              <lb/>
            acceleretur penduli motus; </s>
            <s xml:id="echoid-s3953" xml:space="preserve">poſſe duobus locis, inter A & </s>
            <s xml:id="echoid-s3954" xml:space="preserve">C,
              <lb/>
            illud diſponi, quorum utrolibet eadem celeritas pendulo
              <lb/>
            concilietur: </s>
            <s xml:id="echoid-s3955" xml:space="preserve">velut in D vel E. </s>
            <s xml:id="echoid-s3956" xml:space="preserve">Quæ loca æqualiter diſtabunt
              <lb/>
            à puncto N, quod abeſt ab A, ſemiſſe longitudinis p, hoc
              <lb/>
            eſt, ſemiſſe penduli ſimplicis, cui compoſitum hoc iſochro-
              <lb/>
            num poſtulabatur. </s>
            <s xml:id="echoid-s3957" xml:space="preserve">Apparet autem, quando hæc longitudo p
              <lb/>
            tantum exiguo minor ponitur quam A C, etiam punctum N
              <lb/>
            exiguo ſuperius eſſe puncto medio virgæ A C.</s>
            <s xml:id="echoid-s3958" xml:space="preserve"/>
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            <s xml:id="echoid-s3959" xml:space="preserve">Porro, ex æquatione ſuperiori, f = {1/2} p + vel -
              <lb/>
              <emph style="red">{1/4} p p + {1/2} a b p + a c p - {1/3} a a b - a a c/d}</emph>
            habetur determinatio longitudi-
              <lb/>
            nis p. </s>
            <s xml:id="echoid-s3960" xml:space="preserve">Patet enim, {1/4} p p + {1 a b p + a c p/2 d} non minus eſſe debere
              <lb/>
            quam {1 a a b - a a c/3 d}. </s>
            <s xml:id="echoid-s3961" xml:space="preserve">Unde non debebit eſſe minor quam
              <lb/>
            {a/d}
              <emph style="red">{4/3} b d + 4 c d + b b + 4 b c + 4 c c</emph>
            @ a b - 2 a c/d}. </s>
            <s xml:id="echoid-s3962" xml:space="preserve">Quod ſi p æquetur
              <lb/>
            huic quantitati, hoc eſt, ſi {1/4} p p + {1 a b p + a c p/2 d} fuerit æquale
              <lb/>
            {1 a a b + a a c/3 d}, erit jam, in eadem ſuperiori æquatione, f = {1/2} p,
              <lb/>
            hoc eſt, {a/2 d}
              <emph style="red">{4/3} b d + 4 c d + b b + 4 b c + 4 c c -</emph>
            {a b - 2 a c/2 d}. </s>
            <s xml:id="echoid-s3963" xml:space="preserve">Quo
              <lb/>
            determinatur diſtantia ponderis D à puncto A, ex qua ma-
              <lb/>
            xime omnium acceleret motum penduli.</s>
            <s xml:id="echoid-s3964" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3965" xml:space="preserve">Atque hæc ad horologiorum uſum ſic porro adhibentur.
              <lb/>
            </s>
            <s xml:id="echoid-s3966" xml:space="preserve">Sit, exempli gratia, pendulum horologii, quod ſingulis
              <lb/>
            oſcillationibus ſcrupula ſecunda notet. </s>
            <s xml:id="echoid-s3967" xml:space="preserve">Virgæ autem gravitas
              <lb/>
            ſit 50
              <unsure/>
            gravitatis appenſi ponderis in imo pendulo: </s>
            <s xml:id="echoid-s3968" xml:space="preserve">&</s>
            <s xml:id="echoid-s3969" xml:space="preserve">, præ-
              <lb/>
            ter hoc, ſit aliud exiguum pondus mobile ſecundum virgæ
              <lb/>
            longitudinem, cujus gravitas eadem ponatur quæ ipſius </s>
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