Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica
page |< < (245) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div439" type="section" level="1" n="180">
          <p>
            <s xml:id="echoid-s5361" xml:space="preserve">
              <pb o="245" file="0323" n="350" rhead="CONTROVERSIA."/>
            præciſe inveniatur quantum retardet, voco x quantitatem
              <lb/>
            motus corporis B in pendulo compoſito A D B, & </s>
            <s xml:id="echoid-s5362" xml:space="preserve">conſe-
              <lb/>
            quenter exceſſus reſiduus quantitatis ejus motus erit B x;
              <lb/>
            </s>
            <s xml:id="echoid-s5363" xml:space="preserve">ſed ob virgam B A, velocitas corporis A debet neceſſario
              <lb/>
            eſſe quarta pars velocitatis corporis B: </s>
            <s xml:id="echoid-s5364" xml:space="preserve">quantitas ergo ejus
              <lb/>
            motûs in pendulo compoſito erit {1/4} x (cum enim corpora A
              <lb/>
            & </s>
            <s xml:id="echoid-s5365" xml:space="preserve">B ſint æqualia quantitates motus ſunt proportionales ve-
              <lb/>
            locitatibus. </s>
            <s xml:id="echoid-s5366" xml:space="preserve">Illa autem motus quantitas produci non potuit,
              <lb/>
            niſi per reſiduum exceſſum quantitatis motus corporis B. </s>
            <s xml:id="echoid-s5367" xml:space="preserve">Pa-
              <lb/>
            tet ergo, quod ille exceſſus B - x debeat ſuperare quantitatem
              <lb/>
            motus corporis A inferiora verſus, & </s>
            <s xml:id="echoid-s5368" xml:space="preserve">eidem præterea imprimere
              <lb/>
            quantitatem motus {1/4} x ſuperiora verſus; </s>
            <s xml:id="echoid-s5369" xml:space="preserve">id eſt quod debeat
              <lb/>
            agere in corpus A ac ſi vis A + {1/4} x immediate applicita in
              <lb/>
            A, illud ſurſum propelleret. </s>
            <s xml:id="echoid-s5370" xml:space="preserve">Sed vis B x ob punctum fixum D
              <lb/>
            agit in A acſi vis 4 B - 4 x immediate applicita in A, illud ſurſum
              <lb/>
            propelleret; </s>
            <s xml:id="echoid-s5371" xml:space="preserve">dabitur ergo æqualitas inter 4 B - 4 x & </s>
            <s xml:id="echoid-s5372" xml:space="preserve">A + {1/4} x; </s>
            <s xml:id="echoid-s5373" xml:space="preserve">
              <lb/>
            unde deducitur quantitas x = {12/17} B, quæ præciſe exprimit
              <lb/>
            quantitatem motus corporis B in pendulo compoſito A D B,
              <lb/>
            Porro ſi fiat, ut {12/17}, velocitas corporis B in pendulo compo-
              <lb/>
            ſito, eſt ad 1, velocitatem corporis omnis gravis in extremi-
              <lb/>
            tate penduli ſimplicis, ita D B, 4. </s>
            <s xml:id="echoid-s5374" xml:space="preserve">eſt ad D G {17/3}, erit hæc
              <lb/>
            longitudo penduli ſimplicis Iſochroni.</s>
            <s xml:id="echoid-s5375" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5376" xml:space="preserve">Facile concluditur ex his omnibus, principium D
              <emph style="super">ni</emph>
            Ber-
              <lb/>
            noulli eſſe verum; </s>
            <s xml:id="echoid-s5377" xml:space="preserve">ſed eundem falli in concluſione quam in-
              <lb/>
            de deducit; </s>
            <s xml:id="echoid-s5378" xml:space="preserve">quoniam conſiderat velocitates acquiſitas corpo-
              <lb/>
            rum A & </s>
            <s xml:id="echoid-s5379" xml:space="preserve">B, cum conſiderare deberet, uti nos fecimus illo-
              <lb/>
            rum velocitates incipientes & </s>
            <s xml:id="echoid-s5380" xml:space="preserve">præterea motus quantitates.
              <lb/>
            </s>
            <s xml:id="echoid-s5381" xml:space="preserve">Alias enim nunquam poſſet applicari hoc principium, quod
              <lb/>
            non differt à principio, quod obtinet circa vectem, quum
              <lb/>
            corpora ſunt inæqualia; </s>
            <s xml:id="echoid-s5382" xml:space="preserve">Adeo ut credam me plane petitioni
              <lb/>
            ejus ſatis feciſſe, Rogantur hac occaſione eruditi & </s>
            <s xml:id="echoid-s5383" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5384" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5385" xml:space="preserve">Vides, quo pacto diverſæ viæ ducant ad cognitio-
              <lb/>
            nem ejusdem veritatis; </s>
            <s xml:id="echoid-s5386" xml:space="preserve">nolim tamen meam tuæ æquiparare,
              <lb/>
            quæ ultra omnem comparationem eruditior eſt & </s>
            <s xml:id="echoid-s5387" xml:space="preserve">magis Geo-
              <lb/>
            metrica; </s>
            <s xml:id="echoid-s5388" xml:space="preserve">Interim ſi exiſtimes, non inutile fore demonſtrare
              <lb/>
            rationes Phyſicas, quas hic affero, perfecte convenire </s>
          </p>
        </div>
      </text>
    </echo>
Impressum