Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Page concordance

< >
Scan Original
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
< >
page |< < of 524 > >|
    <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>
Impressum