Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="039/01/043.jpg" pagenum="15"/>
              geret illud hæc plana viribus
                <emph type="italics"/>
              pN, HN
                <emph.end type="italics"/>
              perpendiculariter, nimirun
                <lb/>
              planum
                <emph type="italics"/>
              pQ
                <emph.end type="italics"/>
              vi
                <emph type="italics"/>
              pN,
                <emph.end type="italics"/>
              & planum
                <emph type="italics"/>
              pG
                <emph.end type="italics"/>
              vi
                <emph type="italics"/>
              HN.
                <emph.end type="italics"/>
              Ideoque ſi tollatur pla­
                <lb/>
              num
                <emph type="italics"/>
              pQ,
                <emph.end type="italics"/>
              ut pondus tendat filum; quoniam filum ſuſtinendo pon
                <lb/>
              dus jam vicem præſtat plani ſublati, tendetur illud eadem vi
                <emph type="italics"/>
              pN,
                <emph.end type="italics"/>
                <lb/>
              qua planum antea urgebatur. </s>
              <s>Unde tenſio fili hujus obliqui erit
                <lb/>
              ad tenſionem ſili alterius perpendicularis
                <emph type="italics"/>
              PN,
                <emph.end type="italics"/>
              ut
                <emph type="italics"/>
              pN
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              pH.
                <emph.end type="italics"/>
              Id. </s>
              <s>
                <lb/>
              eoque ſi pondus
                <emph type="italics"/>
              p
                <emph.end type="italics"/>
              ſit ad pondus
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              in ratione quæ componitur ex
                <lb/>
              ratione reciproca minimarum diſtantiarum ſuorum ſuorum
                <emph type="italics"/>
              pN,
                <lb/>
              AM
                <emph.end type="italics"/>
              a centro rotæ, & ratione directa
                <emph type="italics"/>
              pH
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              pN
                <emph.end type="italics"/>
              ; pondera idem
                <lb/>
              valebunt ad rotam movendam, atque adeo ſe mutuo ſuſtinebunt,
                <lb/>
              ut quilibet experiri poteſt. </s>
            </p>
            <p type="main">
              <s>Pondus autem
                <emph type="italics"/>
              p,
                <emph.end type="italics"/>
              planis illis duobus obliquis incumbens, rationem
                <lb/>
              habet cunei inter corporis fiſſi facies internas: & inde vires cunei
                <lb/>
              & mallei innoteſcunt: utpote cum vis qua pondus
                <emph type="italics"/>
              p
                <emph.end type="italics"/>
              urget planum
                <lb/>
                <emph type="italics"/>
              pQ
                <emph.end type="italics"/>
              ſit ad vim, qua idem vel gravitate ſua vel ictu mallei impellitur
                <lb/>
              ſecundum lineam
                <emph type="italics"/>
              pH
                <emph.end type="italics"/>
              in plano, &c. </s>
              <s>ut
                <emph type="italics"/>
              pN
                <emph.end type="italics"/>
              and
                <emph type="italics"/>
              pH
                <emph.end type="italics"/>
              ; atque ad vim, qua
                <lb/>
              urget planum alterum
                <emph type="italics"/>
              pG,
                <emph.end type="italics"/>
              ut
                <emph type="italics"/>
              pN
                <emph.end type="italics"/>
              ad
                <emph type="italics"/>
              NH.
                <emph.end type="italics"/>
              Sed & vis Cochleæ per
                <lb/>
              ſimilem virium diviſionem colligitur; quippe quæ cuneus eſt a ve­
                <lb/>
              cte impulſus. </s>
              <s>Uſus igitur Corollarii hujus latiſſime patet, & late
                <lb/>
              patendo veritatem ſuam evincit; cum pendeat ex jam dictis Mecha­
                <lb/>
              nica tota ab Auctoribus diverſimode demonſtrata. </s>
              <s>Ex hiſce enim
                <lb/>
              facile derivantur vires Machinarum, quæ ex Rotis, Tympanis,
                <lb/>
              Trochleis, Vectibus, nervis tenſis & ponderibus directe vel obli­
                <lb/>
              que aſcendentibus, cæteriſque potentiis Mechanicis componi ſo­
                <lb/>
              lent, ut & vires Tendinum ad animalium oſſa movenda. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              COROLLARIUM III.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Quantitas motus quæ colligitur capiendo ſummam motuum factorum
                <lb/>
              ad eandem partem, & differentiam factorum ad contrarias, non
                <lb/>
              mutatur ab actione corporum inter ſe.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Etenim actio eique contraria reactio æquales ſunt per Legem 111,
                <lb/>
              adeoque per Legem 11 æquales in motibus efficiunt mutationes ver­
                <lb/>
              ſus contrarias partes. </s>
              <s>Ergo ſi motus fiunt ad eandem partem; quic­
                <lb/>
              quid additur motui corporis fugientis, ſubducetur motui corporis
                <lb/>
              inſequentis ſic, ut ſumma maneat eadem quæ prius. </s>
              <s>Sin corpora ob­
                <lb/>
              viam eant; æqualis erit ſubductio de motu utriuſque, adeoQ.E.D.ffe­
                <lb/>
              rentia motuum factorum in contrarias partes manebit eadem. </s>
            </p>
            <p type="main">
              <s>Ut ſi corpus ſphæricum
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              ſit triplo majus corpore ſphærico
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              ha­
                <lb/>
              beatQ.E.D.as velocitatis partes; &
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              ſequatur in eadem recta cum ve-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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