Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/212.jpg" pagenum="184"/>
                    <arrow.to.target n="note160"/>
                  lineola illa
                    <emph type="italics"/>
                  Dd:
                    <emph.end type="italics"/>
                  at ſecundum lineam
                    <emph type="italics"/>
                  PS
                    <emph.end type="italics"/>
                  ad centrum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  tendentem
                    <lb/>
                  minor, in ratione
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PE,
                    <emph.end type="italics"/>
                  adeoque ut
                    <emph type="italics"/>
                  PDXDd.
                    <emph.end type="italics"/>
                  Dividi
                    <lb/>
                  jam intelligatur linea
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  in particulas innumeras æquales, quæ
                    <lb/>
                  ſingulæ nominentur
                    <emph type="italics"/>
                  Dd
                    <emph.end type="italics"/>
                  ; & ſuperficies
                    <emph type="italics"/>
                  FE
                    <emph.end type="italics"/>
                  dividetur in totidem
                    <lb/>
                  æquales annulos, quorum vires erunt ut ſumma omnium
                    <emph type="italics"/>
                  PDXDd,
                    <emph.end type="italics"/>
                    <lb/>
                  hoc eſt, ut 1/2
                    <emph type="italics"/>
                  PFq
                    <emph.end type="italics"/>
                  -1/2
                    <emph type="italics"/>
                  PDq,
                    <emph.end type="italics"/>
                  adeoque ut
                    <emph type="italics"/>
                  DE quad.
                    <emph.end type="italics"/>
                  Ducatur
                    <lb/>
                    <figure id="id.039.01.212.1.jpg" xlink:href="039/01/212/1.jpg" number="120"/>
                    <lb/>
                  jam ſuperficies
                    <emph type="italics"/>
                  FE
                    <emph.end type="italics"/>
                  in altitudinem
                    <emph type="italics"/>
                  Ef
                    <emph.end type="italics"/>
                  ; & fiet ſolidi
                    <emph type="italics"/>
                  EFfe
                    <emph.end type="italics"/>
                  vis ex­
                    <lb/>
                  ercita in corpuſculum
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  DEqXFf:
                    <emph.end type="italics"/>
                  puta ſi detur vis quam
                    <lb/>
                  particula aliqua data
                    <emph type="italics"/>
                  Ff
                    <emph.end type="italics"/>
                  in diſtantia
                    <emph type="italics"/>
                  PF
                    <emph.end type="italics"/>
                  exercet in corpuſculum
                    <lb/>
                    <emph type="italics"/>
                  P.
                    <emph.end type="italics"/>
                  At ſi vis illa non detur, fiet vis ſolidi
                    <emph type="italics"/>
                  EFfe
                    <emph.end type="italics"/>
                  ut ſolidum
                    <lb/>
                    <emph type="italics"/>
                  DEqXFf
                    <emph.end type="italics"/>
                  & vis illa non data conjunctim.
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                  E. D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note160"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXXX. THEOREMA XL.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si ad Sphæræ alicujus
                    <emph.end type="italics"/>
                  ABE,
                    <emph type="italics"/>
                  centro
                    <emph.end type="italics"/>
                  S
                    <emph type="italics"/>
                  deſcriptæ, particulas ſingu­
                    <lb/>
                  las æquales tendant æquales vires centripetæ, & ad Sphæræ
                    <lb/>
                  axem
                    <emph.end type="italics"/>
                  AB,
                    <emph type="italics"/>
                  in quo corpuſculum aliquod
                    <emph.end type="italics"/>
                  P
                    <emph type="italics"/>
                  locatur, erigantur de
                    <lb/>
                  punctis ſingulis
                    <emph.end type="italics"/>
                  D
                    <emph type="italics"/>
                  perpendicula
                    <emph.end type="italics"/>
                  DE,
                    <emph type="italics"/>
                  Sphæræ occurrentia in
                    <emph.end type="italics"/>
                  E,
                    <lb/>
                    <emph type="italics"/>
                  & in ipſis capiantur longitudines
                    <emph.end type="italics"/>
                  DN,
                    <emph type="italics"/>
                  quæ ſint ut quantitas
                    <emph.end type="italics"/>
                    <lb/>
                  (DE
                    <emph type="italics"/>
                  q
                    <emph.end type="italics"/>
                  XPS/PE)
                    <emph type="italics"/>
                  & vis quam Sphæræ particula ſita in axe ad di­
                    <lb/>
                  ſtantiam
                    <emph.end type="italics"/>
                  PE
                    <emph type="italics"/>
                  exercet in corpuſculum
                    <emph.end type="italics"/>
                  P
                    <emph type="italics"/>
                  conjunctim: dico quod
                    <lb/>
                  Vis tota, qua corpuſculum
                    <emph.end type="italics"/>
                  P
                    <emph type="italics"/>
                  trahitur verſus Sphæram, est ut
                    <lb/>
                  area comprehenſa ſub axe Sphæræ
                    <emph.end type="italics"/>
                  AB
                    <emph type="italics"/>
                  & linea curva
                    <emph.end type="italics"/>
                  ANB,
                    <lb/>
                    <emph type="italics"/>
                  quam punctum
                    <emph.end type="italics"/>
                  N
                    <emph type="italics"/>
                  perpetuo tangit.
                    <emph.end type="italics"/>
                  </s>
                </p>
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