Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/177.jpg" pagenum="149"/>
                  deſcribit, erit ſimilis & æqualis Curvis quas corpora
                    <emph type="italics"/>
                  S, P
                    <emph.end type="italics"/>
                  deſcri­
                    <lb/>
                    <arrow.to.target n="note125"/>
                  bunt circum ſe mutuo: proindeque (per Theor. </s>
                  <s>XX) ſimilis Curvis
                    <lb/>
                    <emph type="italics"/>
                  ST
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PQV,
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                  quas eadem corpora deſcribunt circum commune
                    <lb/>
                  gravitatis centrum
                    <emph type="italics"/>
                  C:
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                  id adeo quia proportiones linearum
                    <emph type="italics"/>
                  SC, CP
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  SP
                    <emph.end type="italics"/>
                  vel.
                    <emph type="italics"/>
                  sp
                    <emph.end type="italics"/>
                  ad invicem dantur. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note125"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  1. Commune illud gravitatis centrum
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  per Legum Co­
                    <lb/>
                  rollarium quartum, vel quieſcit vel movetur uniformiter in direc­
                    <lb/>
                  tum. </s>
                  <s>Ponamus primo quod id quieſcit, inque
                    <emph type="italics"/>
                  s
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  locentur cor­
                    <lb/>
                  pora duo, immobile in
                    <emph type="italics"/>
                  s,
                    <emph.end type="italics"/>
                  mobile in
                    <emph type="italics"/>
                  p,
                    <emph.end type="italics"/>
                  corporibus
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  ſimilia
                    <lb/>
                  & æqualia. </s>
                  <s>Dein tangant rectæ
                    <emph type="italics"/>
                  PR
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  pr
                    <emph.end type="italics"/>
                  Curvas
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  pq
                    <emph.end type="italics"/>
                  in
                    <lb/>
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  p,
                    <emph.end type="italics"/>
                  & producantur
                    <emph type="italics"/>
                  CQ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  sq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  r.
                    <emph.end type="italics"/>
                  Et, ob ſimilitudi­
                    <lb/>
                  nem Figurarum
                    <emph type="italics"/>
                  CPRQ, sprq,
                    <emph.end type="italics"/>
                  erit
                    <emph type="italics"/>
                  RQ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  rq
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  sp,
                    <emph.end type="italics"/>
                  ad­
                    <lb/>
                  eoQ.E.I. data ratione. </s>
                  <s>Proinde ſi vis qua corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  verſus cor­
                    <lb/>
                  pus
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  atque adeo verſus centrum intermedium
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  attrahitur, eſſet
                    <lb/>
                  ad vim qua corpus
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  verſus centrum
                    <emph type="italics"/>
                  s
                    <emph.end type="italics"/>
                  attrahitur in eadem illa ra­
                    <lb/>
                  tione data; hæ vires æqualibus temporibus attraherent ſemper cor­
                    <lb/>
                  pora de tangentibus
                    <emph type="italics"/>
                  PR, pr
                    <emph.end type="italics"/>
                  ad arcus
                    <emph type="italics"/>
                  PQ, pq,
                    <emph.end type="italics"/>
                  per intervalla ipſis
                    <lb/>
                  proportionalia
                    <emph type="italics"/>
                  RQ, rq;
                    <emph.end type="italics"/>
                  adeoque vis poſterior efficeret ut corpus
                    <lb/>
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  gyraretur in Curva
                    <emph type="italics"/>
                  pqv,
                    <emph.end type="italics"/>
                  quæ ſimilis eſſet Curvæ
                    <emph type="italics"/>
                  PQV,
                    <emph.end type="italics"/>
                  in qua
                    <lb/>
                  vis prior efficit ut corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  gyretur, & revolutiones iiſdem tem­
                    <lb/>
                  poribus complerentur. </s>
                  <s>At quoniam vires illæ non ſunt ad invi­
                    <lb/>
                  cem in ratione
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  sp,
                    <emph.end type="italics"/>
                  ſed (ob ſimilitudinem & æqualitatem
                    <lb/>
                  corporum
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  s, P
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  p,
                    <emph.end type="italics"/>
                  æqualitatem diſtantiarum
                    <emph type="italics"/>
                  SP, sp
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  ſibi mutuo æquales; corpora æqualibus temporibus æqualiter tra­
                    <lb/>
                  hentur de tangentibus: & propterea, ut corpus poſterius
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  trahatur
                    <lb/>
                  per intervallum majus
                    <emph type="italics"/>
                  rq,
                    <emph.end type="italics"/>
                  requiritur tempus majus, idQ.E.I. ſub­
                    <lb/>
                  duplicata ratione intervallorum; propterea quod (per Lemma de­
                    <lb/>
                  cimum) ſpatia, ipſo motus initio deſcripta, ſunt in duplicata ratione
                    <lb/>
                  temporum. </s>
                  <s>Ponatur igitur velocitas corporis
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  eſſe ad velocita­
                    <lb/>
                  tem corporis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in ſubduplicata ratione diſtantiæ
                    <emph type="italics"/>
                  sp
                    <emph.end type="italics"/>
                  ad diſtantiam
                    <lb/>
                    <emph type="italics"/>
                  CP,
                    <emph.end type="italics"/>
                  eo ut temporibus quæ ſint in eadem ſubduplicata ratione de­
                    <lb/>
                  ſcribantur arcus
                    <emph type="italics"/>
                  pq, PQ,
                    <emph.end type="italics"/>
                  qui ſunt in ratione integra: Et corpora
                    <lb/>
                    <emph type="italics"/>
                  P, p
                    <emph.end type="italics"/>
                  viribus æqualibus ſemper attracta deſcribent circum centra
                    <lb/>
                  quieſcentia
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  s
                    <emph.end type="italics"/>
                  Figuras ſimiles
                    <emph type="italics"/>
                  PQV, pqv,
                    <emph.end type="italics"/>
                  quarum poſterior
                    <lb/>
                    <emph type="italics"/>
                  pqv
                    <emph.end type="italics"/>
                  ſimilis eſt & æqualis Figuræ quam corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  circum corpus
                    <lb/>
                  mobile
                    <emph type="italics"/>
                  S
                    <emph.end type="italics"/>
                  deſcribit.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Ponamus jam quod commune gravitatis centrum, una
                    <lb/>
                  cum ſpatio in quo corpora moventur inter ſe, progreditur unifor­
                    <lb/>
                  miter in directum; &, per Legum Corollarium ſextum, motus
                    <lb/>
                  omnes in hoc ſpatio peragentur ut prius, adeoque corpora deſcri-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
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