Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
171
171 		172
172
173
173 		174
174
175
175 		176
176
177
177 		178
178
179
179 		180
180
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <pb xlink:href="039/01/175.jpg" pagenum="147"/>
                <p type="main">
                  <s>Stantibus quæ in ſuperiore Propoſitione conſtructa ſunt, exeat
                    <lb/>
                    <arrow.to.target n="note123"/>
                  corpus de loco
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  in Trajectoriam inveniendam
                    <emph type="italics"/>
                  STtR
                    <emph.end type="italics"/>
                  ; &, ex da­
                    <lb/>
                  ta ejus velocitate in altitudine
                    <emph type="italics"/>
                  SC,
                    <emph.end type="italics"/>
                  dabitur ejus velocitas in alia
                    <lb/>
                  quavis altitudine
                    <emph type="italics"/>
                  TC.
                    <emph.end type="italics"/>
                  Ea cum velocitate, dato tempore quam
                    <lb/>
                  minimo, deſcribat corpus Trajectoriæ ſuæ particulam
                    <emph type="italics"/>
                  Tt,
                    <emph.end type="italics"/>
                  ſitque
                    <lb/>
                    <emph type="italics"/>
                  Pp
                    <emph.end type="italics"/>
                  veſtigium ejus in plano
                    <emph type="italics"/>
                  AOP
                    <emph.end type="italics"/>
                  deſcriptum. </s>
                  <s>Jungatur
                    <emph type="italics"/>
                  Op,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  Circelli centro
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  intervallo
                    <emph type="italics"/>
                  Tt
                    <emph.end type="italics"/>
                  in ſuperficie curva deſcripti ſit
                    <emph type="italics"/>
                  PpQ
                    <emph.end type="italics"/>
                    <lb/>
                  veſtigium Ellipticum in eodem plano
                    <emph type="italics"/>
                  OAPp
                    <emph.end type="italics"/>
                  deſcriptum. </s>
                  <s>Et ob
                    <lb/>
                  datum magnitudine & poſitione Circellum, dabitur Ellipſis illa
                    <lb/>
                    <emph type="italics"/>
                    <expan abbr="Ppq.">Ppque</expan>
                    <emph.end type="italics"/>
                  Cumque area
                    <emph type="italics"/>
                  POp
                    <emph.end type="italics"/>
                  ſit tempori proportionalis, atque ad­
                    <lb/>
                  eo ex dato tempore detur, dabitur
                    <emph type="italics"/>
                  Op
                    <emph.end type="italics"/>
                  poſitione, & inde dabitur
                    <lb/>
                  communis ejus & Ellipſeos interſectio
                    <emph type="italics"/>
                  p,
                    <emph.end type="italics"/>
                  una cum angulo
                    <emph type="italics"/>
                  OPp,
                    <emph.end type="italics"/>
                    <lb/>
                  in quo Trajectoriæ veſtigium
                    <emph type="italics"/>
                  APp
                    <emph.end type="italics"/>
                  ſecat lineam
                    <emph type="italics"/>
                  OP.
                    <emph.end type="italics"/>
                  Inde au­
                    <lb/>
                  tem invenietur Trajectoriæ veſtigium illud
                    <emph type="italics"/>
                  APp,
                    <emph.end type="italics"/>
                  eadem methodo
                    <lb/>
                  qua curva linea
                    <emph type="italics"/>
                  VIKk,
                    <emph.end type="italics"/>
                  in Propoſitione XLI, ex ſimilibus datis
                    <lb/>
                  inventa fuit. </s>
                  <s>Tum ex ſingulis veſtigii punctis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  erigendo ad pla­
                    <lb/>
                  num
                    <emph type="italics"/>
                  AOP
                    <emph.end type="italics"/>
                  perpendicula
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ſuperficiei curvæ occurrentia in
                    <emph type="italics"/>
                  T,
                    <emph.end type="italics"/>
                    <lb/>
                  dabuntur ſingula Trajectoriæ puncta
                    <emph type="italics"/>
                  T. Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note123"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
              </subchap2>
              <subchap2>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  SECTIO XI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  De Motu Corporum Viribus centripetis ſe mutuo petentium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Hactenus expoſui Motus corporum attractorum ad centrum Im­
                    <lb/>
                  mobile, quale tamen vix extat in rerum natura. </s>
                  <s>Attractiones enim
                    <lb/>
                  fieri ſolent ad corpora; & corporum trahentium & attractorum
                    <lb/>
                  actiones ſemper mutuæ ſunt & æquales, per Legem tertiam: ad­
                    <lb/>
                  eo ut neque attrahens poſſit quieſcere neque attractum, ſi duo ſint
                    <lb/>
                  corpora, ſed ambo (per Legum Corollarium quartum) quaſi at­
                    <lb/>
                  tractione mutua, circum gravitatis centrum commune revolvantur:
                    <lb/>
                  & ſi plura ſint corpora (quæ vel ab unico attrahantur vel omnia
                    <lb/>
                  ſe mutuo attrahant) hæc ita inter ſe moveri debeant, ut gravitatis
                    <lb/>
                  centrum commune vel quieſcat vel uniformiter moveatur in direc­
                    <lb/>
                  tum. </s>
                  <s>Qua de cauſa jam pergo Motum exponere corporum ſe mu­
                    <lb/>
                  tuo trahentium, conſiderando Vires centripetas tanquam Attractio­
                    <lb/>
                  nes, quamvis fortaſſe, ſi phyſice loquamur, verius dicantur Im­
                    <lb/>
                  pulſus. </s>
                  <s>In Mathematicis enim jam verſamur, & propterea miſſis
                    <lb/>
                  diſputationibus Phyſicis, familiari utimur ſermone, quo poſſimus
                    <lb/>
                  a Lectoribus Mathematicis facilius intelligi. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum