Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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          <chap>
            <subchap1>
              <subchap2>
                <pb xlink:href="039/01/211.jpg" pagenum="183"/>
                <p type="main">
                  <s>Nam ſi linea
                    <emph type="italics"/>
                  Pe
                    <emph.end type="italics"/>
                  ſecet arcum
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  q
                    <emph.end type="italics"/>
                  ; & recta
                    <emph type="italics"/>
                  Ee,
                    <emph.end type="italics"/>
                  quæ cum
                    <lb/>
                    <arrow.to.target n="note159"/>
                  arcu evaneſcente
                    <emph type="italics"/>
                  Ee
                    <emph.end type="italics"/>
                  coincidit, producta occurrat rectæ
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  & ab
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  demittatur in
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  normalis
                    <emph type="italics"/>
                  SG:
                    <emph.end type="italics"/>
                  ob ſimilia triangula
                    <lb/>
                    <emph type="italics"/>
                  DTE, dTe, DES
                    <emph.end type="italics"/>
                  ; erit
                    <emph type="italics"/>
                  Dd
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Ee,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DT
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  TE,
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <figure id="id.039.01.211.1.jpg" xlink:href="039/01/211/1.jpg" number="119"/>
                    <lb/>
                    <emph type="italics"/>
                  ES
                    <emph.end type="italics"/>
                  ; & ob triangula
                    <emph type="italics"/>
                  Eeq, ESG
                    <emph.end type="italics"/>
                  (per Lem. </s>
                  <s>VIII, & Corol. </s>
                  <s>3.
                    <lb/>
                  Lem. </s>
                  <s>VII) ſimilia, erit
                    <emph type="italics"/>
                  Ee
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  eq
                    <emph.end type="italics"/>
                  ſeu
                    <emph type="italics"/>
                  Ff,
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  ES
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SG
                    <emph.end type="italics"/>
                  ; & ex
                    <lb/>
                  æquo,
                    <emph type="italics"/>
                  Dd
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Ff
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SG
                    <emph.end type="italics"/>
                  ; hoc eſt (ob ſimilia triangula
                    <lb/>
                    <emph type="italics"/>
                  PDE, PGS
                    <emph.end type="italics"/>
                  ) ut
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PS.
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note159"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXXIX. THEOREMA XXXIX.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si ſuperficies ob latitudinem infinite diminutam jamjam evaneſcens
                    <emph.end type="italics"/>
                    <lb/>
                  EF fe,
                    <emph type="italics"/>
                  convolutione ſui circa axem
                    <emph.end type="italics"/>
                  PS,
                    <emph type="italics"/>
                  deſcribat ſolidum
                    <lb/>
                  Sphæricum concavo convexum, ad cujus particulas ſingulas æqua­
                    <lb/>
                  les tendant æquales vires centripetæ: dico quod Vis, qua ſoli­
                    <lb/>
                  dum illud trahit corpuſculum ſitum in
                    <emph.end type="italics"/>
                  P,
                    <emph type="italics"/>
                  est in ratione compo­
                    <lb/>
                  ta ex ratione ſolidi
                    <emph.end type="italics"/>
                  DE
                    <emph type="italics"/>
                  q
                    <emph.end type="italics"/>
                  XFf
                    <emph type="italics"/>
                  & ratione vis qua particula
                    <lb/>
                  data in loco
                    <emph.end type="italics"/>
                  Ff
                    <emph type="italics"/>
                  traheret idem corpuſculum.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam ſi primo conſideremus vim ſuperficiei Sphæricæ
                    <emph type="italics"/>
                  FE,
                    <emph.end type="italics"/>
                  quæ
                    <lb/>
                  convolutione arcus
                    <emph type="italics"/>
                  FE
                    <emph.end type="italics"/>
                  generatur, & a linea
                    <emph type="italics"/>
                  de
                    <emph.end type="italics"/>
                  ubivis ſecatur in
                    <emph type="italics"/>
                  r
                    <emph.end type="italics"/>
                  ;
                    <lb/>
                  erit ſuperficiei pars annularis, convolutione arcus
                    <emph type="italics"/>
                  rE
                    <emph.end type="italics"/>
                  genita, ut
                    <lb/>
                  lineola
                    <emph type="italics"/>
                  Dd,
                    <emph.end type="italics"/>
                  manente Sphæræ radio
                    <emph type="italics"/>
                  PE,
                    <emph.end type="italics"/>
                  (uti demonſtravit
                    <emph type="italics"/>
                  Ar­
                    <lb/>
                  chimedes
                    <emph.end type="italics"/>
                  in Lib. </s>
                  <s>de
                    <emph type="italics"/>
                  Sphæra
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Cylindro.
                    <emph.end type="italics"/>
                  ) Et hujus vis ſecundum li­
                    <lb/>
                  neas
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  Pr
                    <emph.end type="italics"/>
                  undiQ.E.I. ſuperficie conica ſitas exercita, ut
                    <lb/>
                  hæc ipſa ſuperficiei pars annularis; hoc eſt, ut lineola
                    <emph type="italics"/>
                  Dd
                    <emph.end type="italics"/>
                  vel,
                    <lb/>
                  quod perinde eſt, ut rectangulum ſub dato Sphæræ radio
                    <emph type="italics"/>
                  PE
                    <emph.end type="italics"/>
                  & </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
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