Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/068.jpg" pagenum="40"/>
                    <arrow.to.target n="note19"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note19"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Porro præcedentis propoſitionis & corollariorum ejus beneficio,
                    <lb/>
                  colligitur etiam proportio vis centripetæ ad vim quamlibet notam,
                    <lb/>
                  qualis eſt ea Gravitatis. </s>
                  <s>Nam ſi corpus in circulo Terræ concen­
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                  trico vi gravitatis ſuæ revolvatur, hæc gravitas eſt ipſius vis centri­
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                  peta. </s>
                  <s>Datur autem, ex deſcenſu gravium, & tempus revolutionis
                    <lb/>
                  unius, & arcus dato quovis tempore deſcriptus, per hujus Corol. </s>
                  <s>
                    <lb/>
                  IX. </s>
                  <s>Et hujuſmodi propoſitionibus
                    <emph type="italics"/>
                  Hugenius,
                    <emph.end type="italics"/>
                  in eximio ſuo Tracta­
                    <lb/>
                  tu
                    <emph type="italics"/>
                  de Horologio Oſcillatorio,
                    <emph.end type="italics"/>
                  vim gravitatis cum revolventium vi­
                    <lb/>
                  ribus centrifugis contulit. </s>
                </p>
                <p type="main">
                  <s>Demonſtrari etiam poſſunt præcedentia in hunc modum. </s>
                  <s>In cir­
                    <lb/>
                  culo quovis deſcribi intelligatur Polygonum laterum quotcunque. </s>
                  <s>
                    <lb/>
                  Et ſi corpus, in polygoni lateribus data cum velocitate movendo,
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                  ad ejus angulos ſingulos a circulo reflectatur; vis qua ſingulis re­
                    <lb/>
                  flexionibus impingit in circulum erit ut ejus velocitas: adeoque
                    <lb/>
                  ſumma virium in dato tempore erit ut velocitas illa & numerus re­
                    <lb/>
                  flexionum conjunctim: hoc eſt (ſi polygonum detur ſpecie) ut longi­
                    <lb/>
                  tudo dato illo tempore deſcripta & longitudo eadem applicata ad
                    <lb/>
                  Radium circuli; id eſt, ut quadratum longitudinis illius applicatum
                    <lb/>
                  ad Radium: adeoque, ſi polygonum lateribus infinite diminutis co­
                    <lb/>
                  incidat cum circulo, ut quadratum arcus dato tempore deſcripti ap­
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                  plicatum ad radium. </s>
                  <s>Hæc eſt vis centrifuga, qua corpus urget cir­
                    <lb/>
                  culum: & huic æqualis eſt vis contraria, qua circulus continuo re­
                    <lb/>
                  pellit corpus centrum verſus. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO. V. PROBLEMA I.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Data quibuſcunQ.E.I. locis velocitate, qua corpus figuram datam vi­
                    <lb/>
                  ribus ad commune aliquod centrum tendentibus deſcribit, centrum
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                  illud invenire.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Figuram deſcriptam tangant rectæ tres
                    <emph type="italics"/>
                  PT, TQV, VR
                    <emph.end type="italics"/>
                  in
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                  punctis totidem
                    <emph type="italics"/>
                  P, Q, R,
                    <emph.end type="italics"/>
                  concurrentes in
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  V.
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                  Ad tangentes
                    <lb/>
                  erigantur perpendicula
                    <emph type="italics"/>
                  PA, QB, RC,
                    <emph.end type="italics"/>
                  velocitatibus corporis in
                    <lb/>
                  punctis illis
                    <emph type="italics"/>
                  P, Q, R
                    <emph.end type="italics"/>
                  a quibus eriguntur reciproce proportionalia;
                    <lb/>
                  id eſt, ita ut ſit
                    <emph type="italics"/>
                  PA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  QB
                    <emph.end type="italics"/>
                  ut velocitas in
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  ad velocitatem in
                    <lb/>
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  QB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  RC
                    <emph.end type="italics"/>
                  ut velocitas in
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  ad velocitatem in
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                    <emph.end type="italics"/>
                  Per
                    <lb/>
                  perpendiculorum terminos
                    <emph type="italics"/>
                  A, B, C
                    <emph.end type="italics"/>
                  ad angulos rectos ducantur
                    <emph type="italics"/>
                  AD,
                    <lb/>
                  DBE, EC
                    <emph.end type="italics"/>
                  concurrentes in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  E:
                    <emph.end type="italics"/>
                  Et actæ
                    <emph type="italics"/>
                  TD, VE
                    <emph.end type="italics"/>
                  concur­
                    <lb/>
                  rent in centro qæſito
                    <emph type="italics"/>
                  S.
                    <emph.end type="italics"/>
                  </s>
                </p>
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        </body>
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