Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Page concordance

< >
Scan Original
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <pb xlink:href="039/01/073.jpg" pagenum="45"/>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Et ſimili argumento corpus movebitur in Ellipſi vel etiam in
                    <lb/>
                  Hyperbola vel Parabola, vi centripeta quæ ſit reciproce ut cu­
                    <lb/>
                  bus ordinatim applicatæ ad centrum virium maxime longinquum
                    <lb/>
                  tendentis. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO IX. PROBLEMA IV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Gyretur corpus in Spirali
                    <emph.end type="italics"/>
                  PQS
                    <emph type="italics"/>
                  ſecante radios omnes
                    <emph.end type="italics"/>
                  SP, SQ,
                    <emph type="italics"/>
                  &c.
                    <emph.end type="italics"/>
                    <lb/>
                    <figure id="id.039.01.073.1.jpg" xlink:href="039/01/073/1.jpg" number="19"/>
                    <lb/>
                    <emph type="italics"/>
                  in angulo dato: requiritur Lex
                    <lb/>
                  vis centripetæ tendentis ad
                    <lb/>
                  centrum Spiralis.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Detur angulus indefinite par­
                    <lb/>
                  vus
                    <emph type="italics"/>
                  PSQ,
                    <emph.end type="italics"/>
                  & ob datos omnes
                    <lb/>
                  angulos dabitur ſpecie figura
                    <emph type="italics"/>
                  SPQRT.
                    <emph.end type="italics"/>
                  Ergo datur ratio (
                    <emph type="italics"/>
                  QT/QR
                    <emph.end type="italics"/>
                  ), eſtque
                    <lb/>
                  (
                    <emph type="italics"/>
                  QT quad./QR
                    <emph.end type="italics"/>
                  ) ut
                    <emph type="italics"/>
                  QT,
                    <emph.end type="italics"/>
                  hoc eſt ut
                    <emph type="italics"/>
                  SP.
                    <emph.end type="italics"/>
                  Mutetur jam uteunque angulus
                    <emph type="italics"/>
                  PSQ,
                    <emph.end type="italics"/>
                    <lb/>
                  & recta
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  angulum contactus
                    <emph type="italics"/>
                  QPR
                    <emph.end type="italics"/>
                  ſubtendens mutabitur (per
                    <lb/>
                  Lemma XI.) in duplicata ratione ipſius
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  QT.
                    <emph.end type="italics"/>
                  Ergo manebit
                    <lb/>
                  (
                    <emph type="italics"/>
                  QT quad./QR
                    <emph.end type="italics"/>
                  ) eadem quæ prius, hoc eſt ut
                    <emph type="italics"/>
                  SP.
                    <emph.end type="italics"/>
                  Quare (
                    <emph type="italics"/>
                  QTq.XSPq/QR
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  eſt ut
                    <emph type="italics"/>
                  SP cub.
                    <emph.end type="italics"/>
                  adeoque (per Corol. </s>
                  <s>1 & 5 Prop. </s>
                  <s>VI.) vis centripeta eſt
                    <lb/>
                  reciproce ut cubus diſtantiæ
                    <emph type="italics"/>
                  SP.
                    <expan abbr="q.">que</expan>
                  E. I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Idem aliter.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Perpendiculum
                    <emph type="italics"/>
                  SY
                    <emph.end type="italics"/>
                  in tangentem demiſſum, & circuli Spiralem
                    <lb/>
                  tangentis chorda
                    <emph type="italics"/>
                  PV
                    <emph.end type="italics"/>
                  ſunt ad altitudinem
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  in datis rationibus;
                    <lb/>
                  ideoque
                    <emph type="italics"/>
                  SP cub.
                    <emph.end type="italics"/>
                  eſt ut
                    <emph type="italics"/>
                  SYqXPV,
                    <emph.end type="italics"/>
                  hoc eſt (per Corol. </s>
                  <s>3 & 5 Prop.VI.)
                    <lb/>
                  reciproce ut vis centripeta. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  LEMMA XII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Parallelogramma omnia, circa datæ Ellipſeos vel Hyperbolæ diametros
                    <lb/>
                  quaſvis conjugatas deſcripta, eſſe inter ſe æqualia.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Conſtat ex Conicis. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum