Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="039/01/050.jpg" pagenum="22"/>
                <arrow.to.target n="note10"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="note10"/>
              AXIOMATA
                <lb/>
              SIVE</s>
            </p>
            <p type="main">
              <s>In Attractionibus rem ſic breviter oſtendo. </s>
              <s>Corporibus duobus
                <lb/>
              quibuſvis
                <emph type="italics"/>
              A, B
                <emph.end type="italics"/>
              ſe mutuo trahentibus, concipe obſtaculum quodvis
                <lb/>
              interponi quo congreſſus eorum impediatur. </s>
              <s>Si corpus alterutrum
                <lb/>
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              magis trahitur verſus corpus alterum
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              quam illud alterum
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
                <lb/>
              in prius
                <emph type="italics"/>
              A,
                <emph.end type="italics"/>
              obſtaculum magis urgebitur preſſione corporis
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              quam
                <lb/>
              preſſione corporis
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              ; proindeque non manebit in æquilibrio. </s>
              <s>Præ­
                <lb/>
              valebit preſſio fortior, facietque ut ſyſtema corporum duorum &
                <lb/>
              obſtaculi moveatur in directum in partes verſus
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              motuQ.E.I. ſpatiis
                <lb/>
              liberis ſemper accelerato abeat in infinitum. </s>
              <s>Quod eſt abſurdum &
                <lb/>
              Legi primæ contrarium. </s>
              <s>Nam per Legem primam debebit ſyſtema
                <lb/>
              perſeverare in ſtatu ſuo quieſcendi vel movendi uniformiter in di­
                <lb/>
              rectum, proindeque corpora æqualiter urgebunt obſtaculum, & id­
                <lb/>
              circo æqualiter trahentur in invicem. </s>
              <s>Tentavi hoc in Magnete &
                <lb/>
              Ferro. </s>
              <s>Si hæc in vaſculis propriis ſeſe contingentibus ſeorſim po­
                <lb/>
              ſita, in aqua ſtagnante juxta fluitent; neutrum propellet alterum,
                <lb/>
              ſed æqualitate attractionis utrinque ſuſtinebunt conatus in ſe mu­
                <lb/>
              tuos, ac tandem in æquilibrio conſtituta quieſcent. </s>
            </p>
            <p type="main">
              <s>Sic etiam gravitas inter Terram & ejus partes, mutua eſt. </s>
              <s>Se­
                <lb/>
              cetur Terra
                <emph type="italics"/>
              FI
                <emph.end type="italics"/>
              plano quovis
                <emph type="italics"/>
              EG
                <emph.end type="italics"/>
              in partes duas
                <emph type="italics"/>
              EGF
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              EGI:
                <emph.end type="italics"/>
                <lb/>
              & æqualia erunt harum pondera in ſe mu­
                <lb/>
                <figure id="id.039.01.050.1.jpg" xlink:href="039/01/050/1.jpg" number="5"/>
                <lb/>
              tuo. </s>
              <s>Nam ſi plano alio
                <emph type="italics"/>
              HK
                <emph.end type="italics"/>
              quod priori
                <lb/>
                <emph type="italics"/>
              EG
                <emph.end type="italics"/>
              parallelum ſit, pars major
                <emph type="italics"/>
              EGI
                <emph.end type="italics"/>
              ſe­
                <lb/>
              cetur in partes duas
                <emph type="italics"/>
              EGKH
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              HKI,
                <emph.end type="italics"/>
                <lb/>
              quarum
                <emph type="italics"/>
              HKI
                <emph.end type="italics"/>
              æqualis ſit parti prius ab­
                <lb/>
              ſciſſæ
                <emph type="italics"/>
              EFG:
                <emph.end type="italics"/>
              manifeſtum eſt quod pars
                <lb/>
              media
                <emph type="italics"/>
              EGKH
                <emph.end type="italics"/>
              pondere proprio in neu­
                <lb/>
              tram partium extremarum propendebit,
                <lb/>
              ſed inter utramQ.E.I. æquilibrio, ut ita
                <lb/>
              dicam, ſuſpendetur, & quieſcet. </s>
              <s>Pars autem extrema
                <emph type="italics"/>
              HKI
                <emph.end type="italics"/>
              toto
                <lb/>
              ſuo pondere incumbet in partem mediam, & urgebit illam in
                <lb/>
              partem alteram extremam
                <emph type="italics"/>
              EGF
                <emph.end type="italics"/>
              ; ideoque vis qua partium
                <lb/>
                <emph type="italics"/>
              HKI
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              EGKH
                <emph.end type="italics"/>
              ſumma
                <emph type="italics"/>
              EGI
                <emph.end type="italics"/>
              tendit verſus partem tertiam
                <lb/>
                <emph type="italics"/>
              EGF,
                <emph.end type="italics"/>
              æqualis eſt ponderi partis
                <emph type="italics"/>
              HKI,
                <emph.end type="italics"/>
              id eſt ponderi partis ter­
                <lb/>
              tiæ
                <emph type="italics"/>
              EGF.
                <emph.end type="italics"/>
              Et propterea pondera partium duarum
                <emph type="italics"/>
              EGI, EGF
                <emph.end type="italics"/>
                <lb/>
              in ſe mutuo ſunt æqualia, uti volui oſtendere. </s>
              <s>Et niſi pondera illa
                <lb/>
              æqualia eſſent, Terra tota in libero æthere fluitans ponderi majori
                <lb/>
              cederet, & ab eo fugiendo abiret in infinitum. </s>
            </p>
            <p type="main">
              <s>Ut corpora in concurſu & reflexione idem pollent, quorum ve­
                <lb/>
              locitates ſunt reciproce ut vires inſitæ: ſic in movendis Inſtru­
                <lb/>
              mentis Mechanicis agentia idem pollent & conatibus contrariis ſe
                <lb/>
              mutuo ſuſtinent, quorum velocitates ſecundum determinationem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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