Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <pb xlink:href="039/01/045.jpg" pagenum="17"/>
              <s>COROLLARIUM IV.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Commune gravitas Centrum, corporum duorum vel plurimum, ab actio­
                <lb/>
              nibus corporum inter ſe non mutat ſtatum ſuum vel motus vel quie­
                <lb/>
              tis; & propterea corporum omnium in ſ mutuo agentium (excluſis
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              actionibus & impedimentis externis) commune Centrum gravitatis
                <lb/>
              vel quieſcit vel movetur uniformiter in directum.</s>
            </p>
            <p type="main">
              <s>Nam ſi puncta duo progrediantur uniformi cum motu in lineis
                <lb/>
              rectis, & diſtantia eorum dividatur in ratione data, punctum divi­
                <lb/>
              dens vel quieſcit vel progreditur uniformiter in linea recta. </s>
              <s>Hoc
                <lb/>
              poſtea in Lemmate XXIII demonſtratur, ſi corpora quotcunque moventur uNI­
                <lb/>
              formiter in lineis rectis, commune centrum gravitatis duorum quo­rumvis vel quieſcit vel progreditur uniformiter in linea recta; propterea quod linea, horum corporum centra in recta uniformiter
                <lb/>
              progredientia jungens, dividitur ab hoc centro communis corporum duo­
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              rum & centri communis tertii in data ratione.</s>
              <s>Eodem modo &
                <lb/>
              commune centrum horum trium & quarti cujuſvis vel quieſcit vel
                <lb/>
              progreditur uniformiter in linea recta; propterea quod ab eo divi­
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              ditur diſtantia inter centrum commune trium & centrum quarti in
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              data ratione, & ſic in infinitum.</s>
              <s>Igitur in ſyſtemate corporum quæ
                <lb/>
              actionibus in ſe invicem aliiſque omnibus in ſe extrinſecus impreſ­
                <lb/>
              ſis omnino vacant, adeoque moventur ſingula uniformiter in rectis
                <lb/>
              ſingulis, commune omnium centrum gravitatis vel quieſcit vel mo­
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              vetur uniformiter in directum.</s>
            </p>
            <p type="main">
              <s>Porro in ſyſtemate duorum corporum in ſe invicem agentium,
                <lb/>
              cum distantiæ centrorum utriusque a communi gravitatis centro ſint
                <lb/>
              reciproce ut corpora; erunt motus relativi corporum eorundem, vel
                <lb/>
              accedendi ad centrum illud vel ab eodem recedendi, æqualibus mutationibus in
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              partes contrarias factis, atque adeo ab actionibus horum corpo­
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              rum inter ſe, nec promovetur nec retardatur nec mutationem pa­
                <lb/>
              titur in ſtatu ſuo quoad motum vel quietem.</s>
              <s>In ſyſtemate autem
                <lb/>
              corporum plurimum, quoniam duorum quorumvis in ſe mutuo agen­
                <lb/>
              tium commune gravitatis centrum ob actionem illam nullatenus</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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