Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
141
141 		142
142
143
143 		144
144
145
145 		146
146
147
147 		148
148
149
149 		150
150
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/142.jpg" pagenum="114"/>
                    <arrow.to.target n="note90"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note90"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Tempus quoQ.E.I.noteſcet erigendo ordinatam
                    <emph type="italics"/>
                  em
                    <emph.end type="italics"/>
                  re­
                    <lb/>
                  ciproce proportionalem lateri quadrato ex
                    <emph type="italics"/>
                  PQRD
                    <emph.end type="italics"/>
                  +vel-
                    <emph type="italics"/>
                  DFge,
                    <emph.end type="italics"/>
                    <lb/>
                  & capiendo tempus quo corpus deſcripſit lineam
                    <emph type="italics"/>
                  De
                    <emph.end type="italics"/>
                  ad tempus
                    <lb/>
                  quo corpus alterum vi uniformi cecidit a
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  & cadendo pervenit ad
                    <lb/>
                    <emph type="italics"/>
                  D,
                    <emph.end type="italics"/>
                  ut area curvilinea
                    <emph type="italics"/>
                  DLme
                    <emph.end type="italics"/>
                  ad rectangulum 2
                    <emph type="italics"/>
                  PDXDL.
                    <emph.end type="italics"/>
                  Nam­
                    <lb/>
                  que tempus quo corpus vi uniformi deſcendens deſcripſit lineam
                    <lb/>
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  eſt ad tempus quo corpus idem deſcripſit lineam
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  in ſub­
                    <lb/>
                  duplicata ratione
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PE,
                    <emph.end type="italics"/>
                  id eſt (lineola
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  jamjam naſcen­
                    <lb/>
                  te) in ratione
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  +1/2
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ſeu 2
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  ad 2
                    <emph type="italics"/>
                  PD+DE,
                    <emph.end type="italics"/>
                    <lb/>
                  & diviſim, ad tempus quo corpus idem deſcripſit lineolam
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                    <lb/>
                  ut 2
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DE,
                    <emph.end type="italics"/>
                  adeoque ut rectangulum 2
                    <emph type="italics"/>
                  PDXDL
                    <emph.end type="italics"/>
                  ad aream
                    <lb/>
                    <emph type="italics"/>
                  DLME
                    <emph.end type="italics"/>
                  ; eſtque tempus quo corpus utrumQ.E.D.ſcripſit lineo­
                    <lb/>
                  lam
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ad tempus quo corpus alterum inæquabili motu deſcrip­
                    <lb/>
                  ſit lineam
                    <emph type="italics"/>
                  De
                    <emph.end type="italics"/>
                  ut area
                    <emph type="italics"/>
                  DLME
                    <emph.end type="italics"/>
                  ad aream
                    <emph type="italics"/>
                  DLme,
                    <emph.end type="italics"/>
                  & ex æquo
                    <lb/>
                  tempus primum ad tempus ultimum ut rectangulum 2
                    <emph type="italics"/>
                  PDXDL
                    <emph.end type="italics"/>
                    <lb/>
                  ad aream
                    <emph type="italics"/>
                  DLme.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
              <subchap2>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  SECTIO VIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  De Inventione Orbium in quibus corpora Viribus quibuſcunque cen­
                    <lb/>
                  tripetis agitata revolvuntur.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XL. THEOREMA XIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si corpus, cogente Vi quacunque centripeta, moveatur utcunque, &
                    <lb/>
                  corpus aliud recta aſcendat vel deſcendat, ſintque eorum Velocita­
                    <lb/>
                  tes in aliquo æqualium altitudinum caſu æquales, Velocitates eorum
                    <lb/>
                  in omnibus æqualibus altitudinibus erunt æquales.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Deſcendat corpus aliquod ab
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  per
                    <emph type="italics"/>
                  D, E,
                    <emph.end type="italics"/>
                  ad centrum
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  moveatur corpus aliud a
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  in linea curva
                    <emph type="italics"/>
                  VIKk,
                    <emph.end type="italics"/>
                  Centro
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  in­
                    <lb/>
                  tervallis quibuſvis deſcribantur circuli concentrici
                    <emph type="italics"/>
                  DI, EK
                    <emph.end type="italics"/>
                  rectæ
                    <lb/>
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  E,
                    <emph.end type="italics"/>
                  curvæque
                    <emph type="italics"/>
                  VIK
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  K
                    <emph.end type="italics"/>
                  occurrentes. </s>
                  <s>Junga­
                    <lb/>
                  tur
                    <emph type="italics"/>
                  IC
                    <emph.end type="italics"/>
                  occurrens ipſi
                    <emph type="italics"/>
                  KE
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  N;
                    <emph.end type="italics"/>
                  & in
                    <emph type="italics"/>
                  IK
                    <emph.end type="italics"/>
                  demittatur perpendi­
                    <lb/>
                  culum
                    <emph type="italics"/>
                  NT
                    <emph.end type="italics"/>
                  ; ſitque circumferentiarum circulorum intervallum
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                    <lb/>
                  vel
                    <emph type="italics"/>
                  IN
                    <emph.end type="italics"/>
                  quam minimum, & habeant corpora in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  I
                    <emph.end type="italics"/>
                  velocita-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum