Newton, Isaac, Philosophia naturalis principia mathematica, 1713
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="039/01/041.jpg" pagenum="13"/>
            <p type="main">
              <s>
                <emph type="center"/>
              LEX III.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Actioni contrariam ſemper & æqualem eſſe reactionem: ſive cor­
                <lb/>
              porum duorum actiones in ſe mutuo ſemper eſſe æquales & in par­
                <lb/>
              tes contrarias dirigi.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Quicquid premit vel trahit alterum, tantundem ab eo premitur
                <lb/>
              vel trahitur. </s>
              <s>Si quis lapidem digito premit, premitur & hujus
                <lb/>
              digitus a lapide. </s>
              <s>Si equus lapidem funi alligatum trahit, retrahe­
                <lb/>
              tur etiam & equus (ut ita dicam) æqualiter in lapidem: nam funis
                <lb/>
              utrinQ.E.D.ſtentus eodem relaxandi ſe conatu urgebit equum ver­
                <lb/>
              ſus lapidem, ac lapidem verſus equum; tantumQ.E.I.pediet pro­
                <lb/>
              greſſum unius quantum promovet progreſſum alterius. </s>
              <s>Si corpus
                <lb/>
              aliquod in corpus aliud impingens, motum ejus vi ſua quomodo­
                <lb/>
              cunque mutaverit, idem quoque viciſſim in motu proprio eandem
                <lb/>
              mutationem in partem contrariam vi alterius ob æqualitatem preſ­
                <lb/>
              ſionis mutuæ) ſubibit. </s>
              <s>His actionibus æquales fiunt mutationes,
                <lb/>
              non velocitatum, ſed motuum; ſcilicet in corporibus non aliunde
                <lb/>
              impeditis. </s>
              <s>Mutationes enim velocitatum, in contrarias itidem
                <lb/>
              partes factæ, quia motus æqualiter mutantur, ſunt corporibus re­
                <lb/>
              ciproce proportionales. </s>
              <s>Obtinet etiam hæc Lex in Attractionibus,
                <lb/>
              ut in Scholio proximo probabitur. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              COROLLARIUM I.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
                <emph type="italics"/>
              Corpus viribus conjunctis diagonalem parallelogrammi eodem tem­
                <lb/>
              pore deſcribere, quo latera ſeparatis.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Si corpus dato tempore, vi ſola
                <lb/>
                <figure id="id.039.01.041.1.jpg" xlink:href="039/01/041/1.jpg" number="1"/>
                <lb/>
                <emph type="italics"/>
              M
                <emph.end type="italics"/>
              in loco
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              impreſſa, ferretur uNI­
                <lb/>
              formi cum motu ab
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              ; & vi
                <lb/>
              ſola
                <emph type="italics"/>
              N
                <emph.end type="italics"/>
              in eodem loco impreſſa, fer­
                <lb/>
              retur ab
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              C:
                <emph.end type="italics"/>
              compleatur pa­
                <lb/>
              rallelogrammum
                <emph type="italics"/>
              ABDC,
                <emph.end type="italics"/>
              & vi utra­
                <lb/>
              que feretur id eodem tempore in diagonali ab
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              D.
                <emph.end type="italics"/>
              Nam quo­
                <lb/>
              niam vis
                <emph type="italics"/>
              N
                <emph.end type="italics"/>
              agit ſecundum lineam
                <emph type="italics"/>
              AC
                <emph.end type="italics"/>
              ipſi
                <emph type="italics"/>
              BD
                <emph.end type="italics"/>
              parallelam, hæc vis per
                <lb/>
              Legem 11 nihil mutabit velocitatem accedendi ad lineam illam
                <emph type="italics"/>
              BD
                <emph.end type="italics"/>
                <lb/>
              a vi altera genitam. </s>
              <s>Accedet igitur corpus eodem tempore ad lineam
                <lb/>
                <emph type="italics"/>
              BD,
                <emph.end type="italics"/>
              ſive vis
                <emph type="italics"/>
              N
                <emph.end type="italics"/>
              imprimatur, ſive non; atque adeo in fine illius tempo­
                <lb/>
              ris reperietur alicubi in linea illa
                <emph type="italics"/>
              BD.
                <emph.end type="italics"/>
              Eodem argumento in fine tem­
                <lb/>
              poris ejuſdem reperietur alicubi in linea
                <emph type="italics"/>
              CD,
                <emph.end type="italics"/>
              & idcirco in utriuſque
                <lb/>
              lineæ concurſu
                <emph type="italics"/>
              D
                <emph.end type="italics"/>
              reperiri neceſſe eſt. </s>
              <s>Perget autem motu rectili­
                <lb/>
              neo ab
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              D
                <emph.end type="italics"/>
              per Legem 1. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum