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

Table of contents

< >
< >
page |< < (234) of 434 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div434" type="section" level="1" n="177">
          <p>
            <s xml:id="echoid-s5126" xml:space="preserve">
              <pb o="234" file="0312" n="339" rhead="DE CENTRO OSCILL"/>
            præſentare altitudines, ad quas pondera ſejuncta redeunt.
              <lb/>
            </s>
            <s xml:id="echoid-s5127" xml:space="preserve">Non diſſentiet & </s>
            <s xml:id="echoid-s5128" xml:space="preserve">facile probari poteſt illud deductum eſſe
              <lb/>
            ex Principio, quod ſibi finxit, & </s>
            <s xml:id="echoid-s5129" xml:space="preserve">pro fundamento habet pro-
              <lb/>
            poſitionis ſuæ; </s>
            <s xml:id="echoid-s5130" xml:space="preserve">ſcilicet, celeritatem totalem Penduli compoſiti,
              <lb/>
            quæ inter partes diſtribuitur proportionaliter ad arcus, ques
              <lb/>
            ipſæ deſcribunt, ſemper æqualem eſſe ſummæ celeritatum, quas
              <lb/>
            eædem partes acquiſiviſſent, ſi ſejunctæ ſingulæ ſeparatim ex
              <lb/>
            iisdem altitudinibus, & </s>
            <s xml:id="echoid-s5131" xml:space="preserve">in eadem diſtantia ab Axe deſcendiſ-
              <lb/>
            ſent. </s>
            <s xml:id="echoid-s5132" xml:space="preserve">Ponit ergo, ut me refellat, principium hoc, quod fal-
              <lb/>
            ſum contendo; </s>
            <s xml:id="echoid-s5133" xml:space="preserve">in demonſtratione computationem memora-
              <lb/>
            tam ſequar.</s>
            <s xml:id="echoid-s5134" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5135" xml:space="preserve">D
              <emph style="super">nus</emph>
            Abbas novit & </s>
            <s xml:id="echoid-s5136" xml:space="preserve">concedit, detegi altitudinem, unde
              <lb/>
            commune ponderum gravitatis centrum deſcendit, ſi divi-
              <lb/>
            damus ſummam altitudinum 1. </s>
            <s xml:id="echoid-s5137" xml:space="preserve">& </s>
            <s xml:id="echoid-s5138" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5139" xml:space="preserve">(unde duo pondera ſi-
              <lb/>
            mul alligata deſcenderunt) per 2 numerum ponderum, quæ
              <lb/>
            ergo eſt {5/2}. </s>
            <s xml:id="echoid-s5140" xml:space="preserve">Concedit pariter, dari altitudinem, ad quam re-
              <lb/>
            vertitur commune eorum gravitatis centrum, ſcilicet {153/50}, vel
              <lb/>
            3{3/503}, ſi per numerum ponderum duo, dividamus ſummam al-
              <lb/>
            titudinum {9/25} & </s>
            <s xml:id="echoid-s5141" xml:space="preserve">{144/25}, ad quas pondera percuſſione ſeparata re-
              <lb/>
            deunt.</s>
            <s xml:id="echoid-s5142" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5143" xml:space="preserve">Centrum ergo gravitatis revertetur altius quam unde de-
              <lb/>
            ſcenderat, quantum 3{3/50} excedit 2{1/2}, quod primario adverſa-
              <lb/>
            tur Mechanices Principio. </s>
            <s xml:id="echoid-s5144" xml:space="preserve">Hoc ſi D
              <emph style="super">nu</emph>
            . </s>
            <s xml:id="echoid-s5145" xml:space="preserve">Abbas efficere poſ-
              <lb/>
            ſit, detectum habebit perpetuum mobile: </s>
            <s xml:id="echoid-s5146" xml:space="preserve">Quum ergo ejus
              <lb/>
            Principium ex quo falſa ſequitur concluſio, falſum ſit, ex-
              <lb/>
            inde nil quo mea labefactetur Propoſitio, poteſt inferri
              <lb/>
            vel deduci. </s>
            <s xml:id="echoid-s5147" xml:space="preserve">Quod ad alterum ejus Principium attinet,
              <lb/>
            quod pro fundamento habet regulæ generalis de determi-
              <lb/>
            nandis centris Oſcillationis, in eundem inducit errorem.
              <lb/>
            </s>
            <s xml:id="echoid-s5148" xml:space="preserve">Hoc Principium eſt, tempus Vibrationis Penduli compoſi-
              <lb/>
            ti eſſe medium inter tempora Vibrationum partium, id eſt,
              <lb/>
            æquale eſſe ſummæ illorum temporum, diviſæ per numerum
              <lb/>
            partium. </s>
            <s xml:id="echoid-s5149" xml:space="preserve">In Pendulo, quale conſideravimus, ubi ponderum
              <lb/>
            diſtantiæ, a puncto ſuſpenſionis, ſunt 1 & </s>
            <s xml:id="echoid-s5150" xml:space="preserve">4, ſi ponamus
              <lb/>
            tempus minoris ex partibus ſeparatis eſſe unum, (unde ſe-
              <lb/>
            quitur, tempus alterius partis ſeparatim agitatæ eſſe duo;)</s>
            <s xml:id="echoid-s5151" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum