Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

< >
[Figure 141]
[Figure 142]
[Figure 143]
[Figure 144]
[Figure 145]
[Figure 146]
[Figure 147]
[Figure 148]
[Figure 149]
[Figure 150]
[Figure 151]
[Figure 152]
[Figure 153]
[Figure 154]
[Figure 155]
[Figure 156]
[Figure 157]
[Figure 158]
[Figure 159]
[Figure 160]
[Figure 161]
[Figure 162]
[Figure 163]
[Figure 164]
[Figure 165]
[Figure 166]
[Figure 167]
[Figure 168]
[Figure 169]
[Figure 170]
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/276.jpg" pagenum="248"/>
                    <arrow.to.target n="note224"/>
                  ut velocitas & pars altera ut
                    <lb/>
                    <figure id="id.039.01.276.1.jpg" xlink:href="039/01/276/1.jpg" number="162"/>
                    <lb/>
                  velocitatis quadratum, fit re­
                    <lb/>
                  ſiſtentia tota in
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AP quad
                    <emph.end type="italics"/>
                    <lb/>
                  +2
                    <emph type="italics"/>
                  BAP.
                    <emph.end type="italics"/>
                  Jungantur
                    <emph type="italics"/>
                  DA,
                    <lb/>
                  DP
                    <emph.end type="italics"/>
                  Circulum ſecantes in
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                    <lb/>
                  ac
                    <emph type="italics"/>
                  T,
                    <emph.end type="italics"/>
                  & exponatur gravitas per
                    <lb/>
                    <emph type="italics"/>
                  DA quad,
                    <emph.end type="italics"/>
                  ita ut ſit gravitas ad
                    <lb/>
                  reſiſtentiam in
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DAq
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  APq
                    <emph.end type="italics"/>
                  +2
                    <emph type="italics"/>
                  BAP:
                    <emph.end type="italics"/>
                  & tempus
                    <lb/>
                  aſcenſus omnis ſuturi erit ut
                    <lb/>
                  Circuli ſector
                    <emph type="italics"/>
                  EDTE.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note224"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Agatur enim
                    <emph type="italics"/>
                  DVQ,
                    <emph.end type="italics"/>
                  ab­
                    <lb/>
                  ſcindens & velocitatis
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                    <lb/>
                  momentum
                    <emph type="italics"/>
                  PQ,
                    <emph.end type="italics"/>
                  & Sectoris
                    <lb/>
                    <emph type="italics"/>
                  DET
                    <emph.end type="italics"/>
                  momentum
                    <emph type="italics"/>
                  DTV
                    <emph.end type="italics"/>
                  da­
                    <lb/>
                  to temporis momento reſpondens: & velocitatis decrementum il­
                    <lb/>
                  lud
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  erit ut ſumma virium gravitatis
                    <emph type="italics"/>
                  DAq
                    <emph.end type="italics"/>
                  & reſiſtentiæ
                    <lb/>
                    <emph type="italics"/>
                  APq
                    <emph.end type="italics"/>
                  +2
                    <emph type="italics"/>
                  BAP,
                    <emph.end type="italics"/>
                  id eſt (per Prop. </s>
                  <s>12, Lib. </s>
                  <s>2. Elem.) ut
                    <emph type="italics"/>
                  DPquad.
                    <emph.end type="italics"/>
                    <lb/>
                  Proinde area
                    <emph type="italics"/>
                  DPQ,
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  proportionalis, eſt ut
                    <emph type="italics"/>
                  DP quad
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  & area
                    <emph type="italics"/>
                  DTV,
                    <emph.end type="italics"/>
                  (quæ eſt ad aream
                    <emph type="italics"/>
                  DPQ
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DTq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  DPq
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  eſt ut datum
                    <emph type="italics"/>
                  DTQ
                    <emph.end type="italics"/>
                  Decreſcit igitur area
                    <emph type="italics"/>
                  EDT
                    <emph.end type="italics"/>
                  uniformiter ad mo­
                    <lb/>
                  dum temporis futuri, per ſubductionem datarum particularum
                    <emph type="italics"/>
                  DTV,
                    <emph.end type="italics"/>
                    <lb/>
                  & propterea tempori aſcenſus futuri proportionalis eſt.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Caſ.
                    <emph.end type="italics"/>
                  2. Si veloci­
                    <lb/>
                    <figure id="id.039.01.276.2.jpg" xlink:href="039/01/276/2.jpg" number="163"/>
                    <lb/>
                  tas in aſcenſu cor­
                    <lb/>
                  poris exponatur per
                    <lb/>
                  longitudinem
                    <emph type="italics"/>
                  AP
                    <emph.end type="italics"/>
                    <lb/>
                  ut prius, & reſiſten­
                    <lb/>
                  tia ponatur eſſe ut
                    <lb/>
                    <emph type="italics"/>
                  APq
                    <emph.end type="italics"/>
                  +2
                    <emph type="italics"/>
                  BAP,
                    <emph.end type="italics"/>
                  &
                    <lb/>
                  ſi vis gravitatis mi­
                    <lb/>
                  nor ſit quam quæ per
                    <lb/>
                    <emph type="italics"/>
                  DAq
                    <emph.end type="italics"/>
                  exponi poſ­
                    <lb/>
                  ſit; capiatur
                    <emph type="italics"/>
                  BD
                    <emph.end type="italics"/>
                    <lb/>
                  jus longitudinis, ut
                    <lb/>
                  ſit
                    <emph type="italics"/>
                  ABq-BDq
                    <emph.end type="italics"/>
                    <lb/>
                  gravitati proportio­
                    <lb/>
                  nale, ſitque
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  ipſi
                    <lb/>
                    <emph type="italics"/>
                  DB
                    <emph.end type="italics"/>
                  perpendicularis & æqualis, & per verticem
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  deſcribatur Hy­
                    <lb/>
                  perbola
                    <emph type="italics"/>
                  FTVE
                    <emph.end type="italics"/>
                  cujus ſemidiametri conjugatæ ſint
                    <emph type="italics"/>
                  DB
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DF,
                    <emph.end type="italics"/>
                    <lb/>
                  quæque ſecet
                    <emph type="italics"/>
                  DA
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  E,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DP, DQ
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  ; & crit tempus
                    <lb/>
                  aſcenſus futuri ut Hyperbolæ ſector
                    <emph type="italics"/>
                  TDE.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>