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

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            <s xml:id="echoid-s3969" xml:space="preserve">
              <pb o="175" file="0251" n="277" rhead="HOROLOG. OSCILLATOR."/>
            gæ. </s>
            <s xml:id="echoid-s3970" xml:space="preserve">Quæritur jam, quo loco hoc virgæ imponendum, ut
              <lb/>
              <note position="right" xlink:label="note-0251-01" xlink:href="note-0251-01a" xml:space="preserve">
                <emph style="sc">De centro</emph>
                <lb/>
                <emph style="sc">OSCILLA-</emph>
                <lb/>
                <emph style="sc">TIONIS</emph>
              .</note>
            uno ſcrupulo primo acceleretur horologii motus, ſpatio 24
              <lb/>
            horarum. </s>
            <s xml:id="echoid-s3971" xml:space="preserve">Item, ubi collocandum, ut duorum ſcrupulorum
              <lb/>
            primorum ſit acceleratio; </s>
            <s xml:id="echoid-s3972" xml:space="preserve">item, ut trium, quatuor, atque
              <lb/>
            ita porro.</s>
            <s xml:id="echoid-s3973" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3974" xml:space="preserve">Ductis viginti quatuor horis ſexagies, fiunt 1440, quot
              <lb/>
            nempe ſcrupula prima una die continentur. </s>
            <s xml:id="echoid-s3975" xml:space="preserve">Ex his unum
              <lb/>
            aufer, quando unius ſcrupuli acceleratio quæritur: </s>
            <s xml:id="echoid-s3976" xml:space="preserve">ſuper-
              <lb/>
            ſunt 1439. </s>
            <s xml:id="echoid-s3977" xml:space="preserve">Ratio autem 1440 ad 1439 duplicata, proxime
              <lb/>
            eſt ea quæ 1440 ad 1438. </s>
            <s xml:id="echoid-s3978" xml:space="preserve">Ergo, ſi penduli ſimplicis, ſe-
              <lb/>
            cunda ſcrupula notantis, longitudo diviſa intelligatur in par-
              <lb/>
            tes æquales 1440, earumque 1438 alii pendulo tribuantur,
              <lb/>
            hoc præcedet alterum illud, in 24 horis, uno ſcrupulo pri-
              <lb/>
            mo. </s>
            <s xml:id="echoid-s3979" xml:space="preserve">Adeo ut hic p valeat partes 1438.</s>
            <s xml:id="echoid-s3980" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3981" xml:space="preserve">Quia autem pendulum horologii, ex virga metallica & </s>
            <s xml:id="echoid-s3982" xml:space="preserve">
              <lb/>
            pondere appenſo compoſitum, iſochronum ponitur pendulo
              <lb/>
            ſimplici partium 1440; </s>
            <s xml:id="echoid-s3983" xml:space="preserve">invenienda primum eſt virgæ illius
              <lb/>
            longitudo, ex æquatione ſuperius poſita. </s>
            <s xml:id="echoid-s3984" xml:space="preserve">Erat nempe
              <lb/>
            {{1/3} a b + a c/{1/2} b + c} æquale longitudini penduli ſimplicis, quod iſochro-
              <lb/>
            num compoſito ex virga habente longitudinem a, gravita-
              <lb/>
            tem b, & </s>
            <s xml:id="echoid-s3985" xml:space="preserve">pondere affixo cujus gravitas c. </s>
            <s xml:id="echoid-s3986" xml:space="preserve">Ergo ſi longitu-
              <lb/>
            do penduli ſimplicis iſochroni dicatur ſ. </s>
            <s xml:id="echoid-s3987" xml:space="preserve">Erit {{1/2} b ſ + c ſ/{1/3} b + c} = a.
              <lb/>
            </s>
            <s xml:id="echoid-s3988" xml:space="preserve">poſitoque, ut hic, c = 50; </s>
            <s xml:id="echoid-s3989" xml:space="preserve">b = 1; </s>
            <s xml:id="echoid-s3990" xml:space="preserve">ſ = 1440; </s>
            <s xml:id="echoid-s3991" xml:space="preserve">fiet, a = 1444 {4/5},
              <lb/>
            longitudo virgæ.</s>
            <s xml:id="echoid-s3992" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3993" xml:space="preserve">Jam, quia erat f = {1/2} p + vel @
              <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>
            ,
              <lb/>
            fiet f = {1/2} p + vel -
              <emph style="red">{1/4} p p + 72962 p - 105061210</emph>
            .
              <lb/>
            </s>
            <s xml:id="echoid-s3994" xml:space="preserve">Unde porro, ſi p ſit, uti diximus, partium 1438; </s>
            <s xml:id="echoid-s3995" xml:space="preserve">invenie-
              <lb/>
            tur f = 1331 {1/2}, qualium nempe ſ, ſeu pendulum ſimplex,
              <lb/>
            ſecunda ſcrupula oſcillationibus deſignans, continet 1440. </s>
            <s xml:id="echoid-s3996" xml:space="preserve">Cu-
              <lb/>
            jus longitudo ſi pedum trium ſtatuatur, quos horarios voca-
              <lb/>
            vimus, habebit f uncias 33, & </s>
            <s xml:id="echoid-s3997" xml:space="preserve">3 unciarum uncias, quas
              <lb/>
            lineas vocant. </s>
            <s xml:id="echoid-s3998" xml:space="preserve">Vel, auferendo hanc longitudinem f à tota
              <lb/>
            trium pedum longitudine, ſupererunt unciæ duæ, lineæ </s>
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