Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/072.jpg" pagenum="44"/>
                    <arrow.to.target n="note21"/>
                  id eſt, ut
                    <emph type="italics"/>
                  SPXRPq
                    <emph.end type="italics"/>
                  ad (
                    <emph type="italics"/>
                  SP cub.XPV cub/PT cub.
                    <emph.end type="italics"/>
                  ) ſive (ob ſimilia
                    <lb/>
                  triangula
                    <emph type="italics"/>
                  PSG, TPV
                    <emph.end type="italics"/>
                  ) ad
                    <emph type="italics"/>
                  SG cub.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note21"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Vis, qua corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in Orbe quocunque circum virium
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                  centrum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  revolvitur, eſt ad vim qua corpus idem
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in eodem
                    <lb/>
                  orbe eodemque tempore periodico circum aliud quodvis virium
                    <lb/>
                  centrum
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  revolvi poteſt, ut
                    <emph type="italics"/>
                  SPXRPq
                    <emph.end type="italics"/>
                  contentum utique ſub di­
                    <lb/>
                  ſtantia corporis a primo virium centro
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  & quadrato diſtantiæ ejus
                    <lb/>
                  a ſecundo virium centro
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  ad cubum rectæ
                    <emph type="italics"/>
                  SG
                    <emph.end type="italics"/>
                  quæ a primo vi­
                    <lb/>
                  rium centro
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad orbis tangentem
                    <emph type="italics"/>
                  PG
                    <emph.end type="italics"/>
                  ducitur, & corporis a ſe­
                    <lb/>
                  cundo virium centro diſtantiæ
                    <emph type="italics"/>
                  RP
                    <emph.end type="italics"/>
                  parallela eſt. </s>
                  <s>Nam vires in
                    <lb/>
                  hoc Orbe, ad ejus punctum quodvis
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  eædem ſunt ac in Circulo
                    <lb/>
                  ejuſdem curvaturæ. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO. VIII. PROBLEMA. III.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Moveatur corpus in Circulo
                    <emph.end type="italics"/>
                  PQA:
                    <emph type="italics"/>
                  ad hunc effectum requiritur Lex
                    <lb/>
                  vis centripetæ tendentis ad punctum adeo longinquum
                    <emph.end type="italics"/>
                  S,
                    <emph type="italics"/>
                  ut lineæ
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                  omnes
                    <emph.end type="italics"/>
                  PS, RS
                    <emph type="italics"/>
                  ad id ductæ, pro parallelis haberi poſſint.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>A Circuli centro
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  agatur ſemidiameter
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  parallelas iſtas
                    <lb/>
                  perpendiculariter ſecans in
                    <emph type="italics"/>
                  M
                    <emph.end type="italics"/>
                  &
                    <lb/>
                    <figure id="id.039.01.072.1.jpg" xlink:href="039/01/072/1.jpg" number="18"/>
                    <lb/>
                    <emph type="italics"/>
                  N,
                    <emph.end type="italics"/>
                  & jungatur
                    <emph type="italics"/>
                  CP.
                    <emph.end type="italics"/>
                  Ob ſimilia
                    <lb/>
                  triangula
                    <emph type="italics"/>
                  CPM, PZT
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  RZQ
                    <emph.end type="italics"/>
                    <lb/>
                  eſt
                    <emph type="italics"/>
                  CPq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PMq
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PRq
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  QTq
                    <emph.end type="italics"/>
                  & ex natura Circuli
                    <emph type="italics"/>
                  PRq
                    <emph.end type="italics"/>
                    <lb/>
                  æquale eſt rectangulo
                    <emph type="italics"/>
                  QRX√RN+QN
                    <emph.end type="italics"/>
                  &c.
                    <lb/>
                  </s>
                  <s>ſive coeuntibus punctis
                    <emph type="italics"/>
                  P, Q
                    <emph.end type="italics"/>
                  rect­
                    <lb/>
                  angulo
                    <emph type="italics"/>
                  QRX2PM.
                    <emph.end type="italics"/>
                  Ergo eſt
                    <lb/>
                    <emph type="italics"/>
                  CPq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PM quad.
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  QRX2PM
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  QT quad.
                    <emph.end type="italics"/>
                  adeoque (
                    <emph type="italics"/>
                  QT quad./QR
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  æquale (2
                    <emph type="italics"/>
                  PM cub./CP quad.
                    <emph.end type="italics"/>
                  ), & (
                    <emph type="italics"/>
                  QT quad.XSP quad./QR
                    <emph.end type="italics"/>
                  ) æquale (2
                    <emph type="italics"/>
                  PM cub.XSP qu./CP quad.
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  Eſt ergo (per Corol. </s>
                  <s>1 & 5 Prop. </s>
                  <s>VI.) vis centripeta reciproce ut
                    <lb/>
                  (2
                    <emph type="italics"/>
                  PMcub.XSP quad./CP quad.
                    <emph.end type="italics"/>
                  ) hoc eſt (neglecta ratione determinata (2
                    <emph type="italics"/>
                  SP quad./CP quad.
                    <emph.end type="italics"/>
                  ))
                    <lb/>
                  reciproce ut
                    <emph type="italics"/>
                  PM cub. </s>
                  <s>
                    <expan abbr="q.">que</expan>
                  E. I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Idem facile colligitur etiam ex Propoſitione præcedente. </s>
                </p>
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          </chap>
        </body>
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