Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Page concordance

< >
Scan Original
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
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>
Impressum