Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Page concordance

< >
Scan Original
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/209.jpg" pagenum="181"/>
                  trahitur verſus centrum
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  eſt ut planum illud ductum in diſtantiam </s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note157"/>
                  ſuam
                    <emph type="italics"/>
                  Pg,
                    <emph.end type="italics"/>
                  ſive ut huic æquale planum
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  ductum in diſtantiam
                    <lb/>
                  illam
                    <emph type="italics"/>
                  Pg
                    <emph.end type="italics"/>
                  ; & ſumma virium plani utriuſque ut planum
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  duc­
                    <lb/>
                  tum in ſummam diſtantiarum
                    <emph type="italics"/>
                  PG+Pg,
                    <emph.end type="italics"/>
                  id eſt, ut planum illud
                    <lb/>
                  ductum in duplam centri & corpuſculi diſtantiam
                    <emph type="italics"/>
                  PS,
                    <emph.end type="italics"/>
                  hoc eſt, ut
                    <lb/>
                  duplum planum
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  ductum in diſtantiam
                    <emph type="italics"/>
                  PS,
                    <emph.end type="italics"/>
                  vel ut ſumma æ­
                    <lb/>
                  qualium planorum
                    <emph type="italics"/>
                  EF+ef
                    <emph.end type="italics"/>
                  ducta in diſtantiam eandem. </s>
                  <s>Et ſi­
                    <lb/>
                  mili argumento, vires omnium planorum in Sphæra tota, hinc in­
                    <lb/>
                  de æqualiter a centro Sphæræ diſtantium, ſunt ut ſumma planorum
                    <lb/>
                  ducta in diſtantiam
                    <emph type="italics"/>
                  PS,
                    <emph.end type="italics"/>
                  hoc eſt, ut Sphæra tota ducta in diſtan­
                    <lb/>
                  tiam centri ſui
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  a corpuſculo
                    <emph type="italics"/>
                  P.
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note157"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Trahat jam corpuſculum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  Sphæram
                    <emph type="italics"/>
                  AEBF.
                    <emph.end type="italics"/>
                  Et eo­
                    <lb/>
                  dem argumento probabitur quod vis, qua Sphæra illa trahitur, erit:
                    <lb/>
                  ut diſtantia
                    <emph type="italics"/>
                  PS.
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  3. Componatur jam Sphæra altera ex corpuſculis innume­
                    <lb/>
                  ris
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ; & quoniam vis; qua corpuſculum unumquodque trahitur,
                    <lb/>
                  eſt ut diſtantia corpuſculi a centro Sphæræ primæ ducta in Sphæ­
                    <lb/>
                  ram eandem, atque adeo eadem eſt ac ſi prodiret tota de corpuſ­
                    <lb/>
                  culo unico in centro Sphæræ; vis tota qua corpuſcula omnia in
                    <lb/>
                  Sphæra ſecunda trahuntur, hoc eſt, qua Sphæra illa tota trahitur,
                    <lb/>
                  eadem erit ac ſi Sphæra illa traheretur vi prodeunte de corpuſculo
                    <lb/>
                  unico in centro Sphæræ primæ, & propterea proportionalis eſt di­
                    <lb/>
                  ſtantiæ inter centra Sphærarum.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  4. Trahant Sphæræ ſe mutuo, & vis geminata proportio­
                    <lb/>
                  nem priorem ſervabit.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  5. Locetur jam corpuſculum
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  intra Sphæram
                    <emph type="italics"/>
                  AEBF
                    <emph.end type="italics"/>
                  ; &
                    <lb/>
                  quoniam vis plani
                    <emph type="italics"/>
                  ef
                    <emph.end type="italics"/>
                  in corpuſculum eſt ut contentum ſub plano
                    <lb/>
                  illo & diſtantia
                    <emph type="italics"/>
                  pg
                    <emph.end type="italics"/>
                  ; & vis contraria plani
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  ut contentum ſub
                    <lb/>
                  plano illo & diſtantia
                    <emph type="italics"/>
                  pG
                    <emph.end type="italics"/>
                  ; erit vis ex utraque compoſita ut diffe­
                    <lb/>
                  rentia contentorum, hoc eſt, ut ſumma æqualium planorum ducta
                    <lb/>
                  in ſemiſſem differentiæ diſtantiarum, id eſt, ut ſumma illa ducta in
                    <lb/>
                    <emph type="italics"/>
                  pS
                    <emph.end type="italics"/>
                  diſtantiam corpuſculi a centro Sphæræ. </s>
                  <s>Et ſimili argumento,
                    <lb/>
                  attractio planorum omnium
                    <emph type="italics"/>
                  EF, ef
                    <emph.end type="italics"/>
                  in Sphæra tota, hoc eſt, at­
                    <lb/>
                  tractio Sphæræ totius, eſt ut ſumma planorum omnium, ſeu Sphæra
                    <lb/>
                  tota, ducta in
                    <emph type="italics"/>
                  pS
                    <emph.end type="italics"/>
                  diſtantiam corpuſculi a centro Sphæræ.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  6. Et ſi ex corpuſculis innumeris
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  componatur Sphæra
                    <lb/>
                  nova, intra Sphæram priorem
                    <emph type="italics"/>
                  AEBF
                    <emph.end type="italics"/>
                  ſita; probabitur ut prius
                    <lb/>
                  quod attractio, ſive ſimplex Sphæræ unius in alteram, ſive mutua
                    <lb/>
                  utriuſQ.E.I. ſe invicem, erit ut diſtantia centrorum
                    <emph type="italics"/>
                  pS. Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum