Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
211
211 		212
212
213
213 		214
214
215
215 		216
216
217
217 		218
218
219
219 		220
220
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <pb xlink:href="039/01/216.jpg" pagenum="188"/>
                <p type="main">
                  <s>
                    <arrow.to.target n="note164"/>
                  bolicam; ſecunda 1/2
                    <emph type="italics"/>
                  SI
                    <emph.end type="italics"/>
                  aream 1/2
                    <emph type="italics"/>
                  ABXSI
                    <emph.end type="italics"/>
                  ; tertia (
                    <emph type="italics"/>
                  ALBXSI/2LDq
                    <emph.end type="italics"/>
                  ) are­
                    <lb/>
                  am
                    <emph type="italics"/>
                  (ALBXSI/2LA)-(ALBXSI/2LB),
                    <emph.end type="italics"/>
                  id eſt 1/2
                    <emph type="italics"/>
                  ABXSI.
                    <emph.end type="italics"/>
                  De prima ſub­
                    <lb/>
                  ducatur ſumma ſecundæ & tertiæ, &
                    <lb/>
                    <figure id="id.039.01.216.1.jpg" xlink:href="039/01/216/1.jpg" number="123"/>
                    <lb/>
                  manebit area quæſita
                    <emph type="italics"/>
                  ABNA.
                    <emph.end type="italics"/>
                  Un­
                    <lb/>
                  de talis emergit Problematis conſtru­
                    <lb/>
                  ctio. </s>
                  <s>Ad puncta
                    <emph type="italics"/>
                  L, A, S, B
                    <emph.end type="italics"/>
                  erige
                    <lb/>
                  perpendicula
                    <emph type="italics"/>
                  Ll, Aa, Ss, Bb,
                    <emph.end type="italics"/>
                  quo­
                    <lb/>
                  rum
                    <emph type="italics"/>
                  Ss
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  SI
                    <emph.end type="italics"/>
                  æquetur, perque pun­
                    <lb/>
                  ctum
                    <emph type="italics"/>
                  s
                    <emph.end type="italics"/>
                  Aſymptotis
                    <emph type="italics"/>
                  Ll, LB
                    <emph.end type="italics"/>
                  deſcri­
                    <lb/>
                  batur Hyperbola
                    <emph type="italics"/>
                  asb
                    <emph.end type="italics"/>
                  occurrens per­
                    <lb/>
                  pendiculis
                    <emph type="italics"/>
                  Aa, Bb
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  a
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  b
                    <emph.end type="italics"/>
                  ; & rect­
                    <lb/>
                  angulum 2
                    <emph type="italics"/>
                  ASI
                    <emph.end type="italics"/>
                  ſubductum de area
                    <lb/>
                  Hyperbolica
                    <emph type="italics"/>
                  AasbB
                    <emph.end type="italics"/>
                  reliquet aream
                    <lb/>
                  quæſitam
                    <emph type="italics"/>
                  ABNA.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note164"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Exempl.
                    <emph.end type="italics"/>
                  3. Si Vis centripeta, ad ſingulas Sphæræ particulas
                    <lb/>
                  tendens, decreſcit in quadruplicata ratione diſtantiæ a particulis;
                    <lb/>
                  ſcribe (
                    <emph type="italics"/>
                  PEqq/2AScub
                    <emph.end type="italics"/>
                  ) pro V, dein √2
                    <emph type="italics"/>
                  PSXLD
                    <emph.end type="italics"/>
                  pro
                    <emph type="italics"/>
                  PE,
                    <emph.end type="italics"/>
                  & fiet
                    <emph type="italics"/>
                  DN
                    <emph.end type="italics"/>
                  ut
                    <lb/>
                    <emph type="italics"/>
                  (SIqXSL/√2SI)X(1/√LDc),-(SIq/2√2SI)X(1/√LD),-(SIqXALB/2√2SI)X(1/√LDqc).
                    <emph.end type="italics"/>
                    <lb/>
                  Cujus tres partes ductæ in longitudinem
                    <emph type="italics"/>
                  AB,
                    <emph.end type="italics"/>
                  producunt areas tot­
                    <lb/>
                  idem,
                    <emph type="italics"/>
                  viz. (2SIqXSL/√2SI
                    <emph.end type="italics"/>
                  ) in
                    <emph type="italics"/>
                  (1/√LA)-(1/√LB); (SIq/√2SI)
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  √LB-√LA
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  & (
                    <emph type="italics"/>
                  SIqXALB/3√2SI
                    <emph.end type="italics"/>
                  ) in
                    <emph type="italics"/>
                  (1/√LAcub)-(1/√LBcub).
                    <emph.end type="italics"/>
                  Et hæ poſt debitam redu­
                    <lb/>
                  ctionem fiunt
                    <emph type="italics"/>
                  (2SIqXSL/LI), SIq,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  SIq+(2SIcub/3LI).
                    <emph.end type="italics"/>
                  Hæ vero, ſub­
                    <lb/>
                  ctis poſterioribus de priore, evadunt (
                    <emph type="italics"/>
                  4SIcub/3LI
                    <emph.end type="italics"/>
                  ). Igitur vis tota, qua
                    <lb/>
                  corpuſculum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in Sphæræ centrum trahitur, eſt ut
                    <emph type="italics"/>
                  (SIcub/PI),
                    <emph.end type="italics"/>
                  id eſt,
                    <lb/>
                  reciproce ut
                    <emph type="italics"/>
                  PS cubXPI.
                    <expan abbr="q.">que</expan>
                  E. I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Eadem Methodo determinari poteſt Attractio corpuſculi ſiti in­
                    <lb/>
                  tra Sphæram, ſed expeditius per Theorema ſequens. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum