Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/071.jpg" pagenum="43"/>
                  ac denique per punctum
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  agatur
                    <emph type="italics"/>
                  LR
                    <emph.end type="italics"/>
                  quæ ipſi
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  parallela
                    <lb/>
                  ſit & occurrat tum circulo in
                    <emph type="italics"/>
                  L
                    <emph.end type="italics"/>
                  tum tangenti
                    <emph type="italics"/>
                  PZ
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  R.
                    <emph.end type="italics"/>
                  Et
                    <lb/>
                  ob ſimilia triangula
                    <emph type="italics"/>
                  ZQR, ZTP, VPA
                    <emph.end type="italics"/>
                  ; erit
                    <emph type="italics"/>
                  RP quad.
                    <emph.end type="italics"/>
                  hoc
                    <lb/>
                  eſt
                    <emph type="italics"/>
                  QRL
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  QT quad.
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AV quad.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PV quad.
                    <emph.end type="italics"/>
                  Ideoque
                    <lb/>
                  (
                    <emph type="italics"/>
                  QRLXPV quad./AV quad.
                    <emph.end type="italics"/>
                  ) æquatur
                    <emph type="italics"/>
                  QT quad.
                    <emph.end type="italics"/>
                  Ducantur hæc æqualia in
                    <lb/>
                  (
                    <emph type="italics"/>
                  SP quad./QR
                    <emph.end type="italics"/>
                  ) &, punctis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  coeuntibus, ſcribatur
                    <emph type="italics"/>
                  PV
                    <emph.end type="italics"/>
                  pro
                    <emph type="italics"/>
                  RL.
                    <emph.end type="italics"/>
                    <lb/>
                  Sic fiet (
                    <emph type="italics"/>
                  SP quad.XPV cub./AV quad.
                    <emph.end type="italics"/>
                  ) æquale (
                    <emph type="italics"/>
                  SP quad.XQT quad./QR
                    <emph.end type="italics"/>
                  ) Ergo (per
                    <lb/>
                  Corol.1 & 5 Prop.VI.) vis centripeta eſt reciproce ut (
                    <emph type="italics"/>
                  SPqXPV cub./AV quad
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  id eſt, (ob datum
                    <emph type="italics"/>
                  AV quad.
                    <emph.end type="italics"/>
                  ) reciproce ut quadratum diſtantiæ ſeu
                    <lb/>
                  altitudinis
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  & cubus chordæ
                    <emph type="italics"/>
                  PV
                    <emph.end type="italics"/>
                  conjunctim.
                    <emph type="italics"/>
                  Q.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>Ad tangentem
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  productam demittatur perpendiculum
                    <emph type="italics"/>
                  SY,
                    <emph.end type="italics"/>
                    <lb/>
                  & ob ſimilia triangula
                    <emph type="italics"/>
                  SYP, VPA
                    <emph.end type="italics"/>
                  ; erit
                    <emph type="italics"/>
                  AV
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PV
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  ad
                    <lb/>
                    <emph type="italics"/>
                  SY,
                    <emph.end type="italics"/>
                  ideoque (
                    <emph type="italics"/>
                  SPXPV/AV
                    <emph.end type="italics"/>
                  ) æquale
                    <emph type="italics"/>
                  SY,
                    <emph.end type="italics"/>
                  & (
                    <emph type="italics"/>
                  SP quad.XPV cub./AV quad.
                    <emph.end type="italics"/>
                  ) æquale
                    <lb/>
                    <emph type="italics"/>
                  SY quad.XPV.
                    <emph.end type="italics"/>
                  Et propterea (per Corol.3 & 5 Prop.VI.) vis centri­
                    <lb/>
                  peta eſt reciproce ut (
                    <emph type="italics"/>
                  SPqXPV cub./AVq
                    <emph.end type="italics"/>
                  ) hoc eſt, ob datam
                    <emph type="italics"/>
                  AV,
                    <emph.end type="italics"/>
                  reci­
                    <lb/>
                  proce ut
                    <emph type="italics"/>
                  SPqXPV cub. </s>
                  <s>
                    <expan abbr="q.">que</expan>
                  E. I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſi punctum datum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad quod vis centripeta ſem­
                    <lb/>
                  per tendit, locetur in circumferentia hujus circuli, puta ad
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  ; erit
                    <lb/>
                  vis centripeta reciproce ut quadrato cubus altitudinis
                    <emph type="italics"/>
                  SP.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Vis qua corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in cir­
                    <lb/>
                    <figure id="id.039.01.071.1.jpg" xlink:href="039/01/071/1.jpg" number="17"/>
                    <lb/>
                  culo
                    <emph type="italics"/>
                  APTV
                    <emph.end type="italics"/>
                  circum virium centrum
                    <lb/>
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  revolvitur, eſt ad vim qua corpus
                    <lb/>
                  idem
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in eodem circulo & eodem
                    <lb/>
                  tempore periodico circum aliud quod­
                    <lb/>
                  vis virium centrum
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  revolvi poteſt,
                    <lb/>
                  ut
                    <emph type="italics"/>
                  RP quad.XSP
                    <emph.end type="italics"/>
                  ad cubum rectæ
                    <emph type="italics"/>
                  SG
                    <emph.end type="italics"/>
                    <lb/>
                  quæ a primo virium centro
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  ad or­
                    <lb/>
                  bis tangentem
                    <emph type="italics"/>
                  PG
                    <emph.end type="italics"/>
                  ducitur, & diſtan­
                    <lb/>
                  tiæ corporis a ſecundo virium centro
                    <lb/>
                  parallela eſt. </s>
                  <s>Nam, per conſtructionem hujus Propoſitionis, vis
                    <lb/>
                  prior eſt ad vim poſteriorem, ut
                    <emph type="italics"/>
                  RPqXPT cub.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  SPqXPV cub.
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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