Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

< >
[Figure 31]
[Figure 32]
[Figure 33]
[Figure 34]
[Figure 35]
[Figure 36]
[Figure 37]
[Figure 38]
[Figure 39]
[Figure 40]
[Figure 41]
[Figure 42]
[Figure 43]
[Figure 44]
[Figure 45]
[Figure 46]
[Figure 47]
[Figure 48]
[Figure 49]
[Figure 50]
[Figure 51]
[Figure 52]
[Figure 53]
[Figure 54]
[Figure 55]
[Figure 56]
[Figure 57]
[Figure 58]
[Figure 59]
[Figure 60]
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <pb xlink:href="039/01/102.jpg" pagenum="74"/>
                <p type="main">
                  <s>
                    <arrow.to.target n="note50"/>
                  ctum
                    <emph type="italics"/>
                  M
                    <emph.end type="italics"/>
                  perpetuo tangit lineam Rectam. </s>
                  <s>Ergo duæ ſectiones Co­
                    <lb/>
                  nicæ tranſibunt per eadem quinque puncta, contra Corol. </s>
                  <s>3. Lem. </s>
                  <s>
                    <lb/>
                  xx. </s>
                  <s>Igitur punctum
                    <emph type="italics"/>
                  M
                    <emph.end type="italics"/>
                  verſari in linea Curva abſurdum eſt.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note50"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXII. PROBLEMA. XIV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Trajectoriam per data quinque puncta deſcribere.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Dentur puncta quinque
                    <emph type="italics"/>
                  A, B, C, P, D.
                    <emph.end type="italics"/>
                  Ab eorum aliquo
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                  alia duo quævis
                    <emph type="italics"/>
                  B, C,
                    <emph.end type="italics"/>
                  quæ poli nominentur, age rectas
                    <emph type="italics"/>
                  AB, AC,
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.102.1.jpg" xlink:href="039/01/102/1.jpg" number="48"/>
                    <lb/>
                  hiſque parallelas
                    <emph type="italics"/>
                  TPS, PRQ
                    <emph.end type="italics"/>
                  per punctum quartum
                    <emph type="italics"/>
                  P.
                    <emph.end type="italics"/>
                  De­
                    <lb/>
                  inde a polis duobus
                    <emph type="italics"/>
                  B, C
                    <emph.end type="italics"/>
                  age per punctum quintum
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  infiNI­
                    <lb/>
                  tas duas
                    <emph type="italics"/>
                  BDT, CRD,
                    <emph.end type="italics"/>
                  noviſſime ductis
                    <emph type="italics"/>
                  TPS, PRQ
                    <emph.end type="italics"/>
                  (prio­
                    <lb/>
                  rem priori & poſteriorem poſteriori) occurrentes in
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  R.
                    <emph.end type="italics"/>
                  De­
                    <lb/>
                  niQ.E.D. rectis
                    <emph type="italics"/>
                  PT, PR,
                    <emph.end type="italics"/>
                  acta recta
                    <emph type="italics"/>
                  tr
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  TR
                    <emph.end type="italics"/>
                  parallela, ab­
                    <lb/>
                  ſcinde quaſvis
                    <emph type="italics"/>
                  Pt, Pr
                    <emph.end type="italics"/>
                  ipſis
                    <emph type="italics"/>
                  PT, PR
                    <emph.end type="italics"/>
                  proportionales; & ſi per
                    <lb/>
                  earum terminos
                    <emph type="italics"/>
                  t, r
                    <emph.end type="italics"/>
                  & polos
                    <emph type="italics"/>
                  B, C
                    <emph.end type="italics"/>
                  actæ
                    <emph type="italics"/>
                  Bt, Cr
                    <emph.end type="italics"/>
                  concurrant in
                    <lb/>
                    <emph type="italics"/>
                  d,
                    <emph.end type="italics"/>
                  locabitur punctum illud
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  in Trajectoria quæſita. </s>
                  <s>Nam punc­
                    <lb/>
                  tum illud
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  (per Lemma xx) verſatur in Conica Sectione per
                    <lb/>
                  puncta quatuor
                    <emph type="italics"/>
                  A, B, C, P
                    <emph.end type="italics"/>
                  tranſeunte; &, lineis
                    <emph type="italics"/>
                  Rr, Tt
                    <emph.end type="italics"/>
                  evane­
                    <lb/>
                  ſcentibus, coit punctum
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  cum puncto
                    <emph type="italics"/>
                  D.
                    <emph.end type="italics"/>
                  Tranſit ergo ſectio Co­
                    <lb/>
                  nica per puncta quinque
                    <emph type="italics"/>
                  A, B, C, P, D. Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>