Newton, Isaac, Philosophia naturalis principia mathematica, 1713
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <pb xlink:href="039/01/287.jpg" pagenum="259"/>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                    <lb/>
                    <arrow.to.target n="note235"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note235"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>Cæterum hæc Propoſitio & ſuperiores, quæ ad Media inæquali­
                    <lb/>
                  ter denſa ſpectant, intelligendæ ſunt de motu corporum adeo par­
                    <lb/>
                  vorum, ut Medii ex uno corporis latere major denſitas quam ex al­
                    <lb/>
                  tero non conſideranda veniat. </s>
                  <s>Reſiſtentiam quoque cæteris paribus
                    <lb/>
                  denſitati proportionalem eſſe ſuppono. </s>
                  <s>Unde in Mediis quorum
                    <lb/>
                  vis reſiſtendi non eſt ut denſitas, debet denſitas eo uſque augeri vel
                    <lb/>
                  diminui, ut reſiſtentiæ vel tollatur exceſſus vel defectus ſuppleatur. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XVII. PROBLEMA IV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Invenire & vim centripetam & Medii reſiſtentiam qua corpus
                    <lb/>
                  in data Spirali, data velocitatis Lege, revolvi potest.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Sit Spiralis illa
                    <emph type="italics"/>
                  PQR.
                    <emph.end type="italics"/>
                  Ex velocitate qua corpus percurrit ar­
                    <lb/>
                  cum quam minimum
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  dabitur tempus, & ex altitudine
                    <emph type="italics"/>
                  TQ,
                    <emph.end type="italics"/>
                    <lb/>
                  quæ eſt ut vis centripeta & quadratum temporis, dabitur vis. </s>
                  <s>De­
                    <lb/>
                  inde ex arearum, æqualibus temporum particulis confectarum
                    <emph type="italics"/>
                  PSQ
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  QSR,
                    <emph.end type="italics"/>
                  differentia
                    <emph type="italics"/>
                  RSr,
                    <emph.end type="italics"/>
                  dabitur corporis retardatio, & ex re­
                    <lb/>
                  tardatione invenietur reſiſtentia ac denſitas Medii. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XVIII. PROBLEMA V.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Data Lege vis centripetæ, invenire Medii denſitatem in locis ſin­
                    <lb/>
                  gulis, qua corpus datam Spiralem deſcribet.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Ex vi centripeta invenienda eſt velocitas in locis ſingulis, de­
                    <lb/>
                  inde ex velocitatis retardatione quærenda Medii denſitas: ut in
                    <lb/>
                  Propoſitione ſuperiore. </s>
                </p>
                <p type="main">
                  <s>Methodum vero tractandi hæc Problemata aperui in hujus Pro­
                    <lb/>
                  poſitione decima, & Lemmate ſecundo; & Lectorem in hujuſmodi
                    <lb/>
                  perplexis diſquiſitionibus diutius detinere nolo. </s>
                  <s>Addenda jam
                    <lb/>
                  ſunt aliqua de viribus corporum ad progrediendum, deQ.E.D.nſi­
                    <lb/>
                  tate & reſiſtentia Mediorum, in quibus motus hactenus expoſiti &
                    <lb/>
                  his affines peraguntur. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum