Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/152.jpg" pagenum="124"/>
                    <arrow.to.target n="note100"/>
                  ut (
                    <emph type="italics"/>
                  mkXms/mt
                    <emph.end type="italics"/>
                  ) ad (
                    <emph type="italics"/>
                  rkq/2kC
                    <emph.end type="italics"/>
                  ), vel ut
                    <emph type="italics"/>
                  mkXms
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  rk
                    <emph.end type="italics"/>
                  quadratum; hoc eſt, ſi
                    <lb/>
                  capiantur datæ quantitates F, G in ea ratione ad invicem quam
                    <lb/>
                  habet angulus
                    <emph type="italics"/>
                  VCP
                    <emph.end type="italics"/>
                  ad angulum
                    <emph type="italics"/>
                  VCp,
                    <emph.end type="italics"/>
                  ut GG-FF ad FF. </s>
                  <s>Et
                    <lb/>
                  propterea, ſi centro
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  intervallo quovis
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  Cp
                    <emph.end type="italics"/>
                  deſcribatur
                    <lb/>
                  Sector circularis æqualis areæ toti
                    <emph type="italics"/>
                  VPC,
                    <emph.end type="italics"/>
                  quam corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  tempore
                    <lb/>
                  quovis in Orbe immobili revolvens radio ad centrum ducto de­
                    <lb/>
                  ſcrip ſit: differentia virium, quibus corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in Orbe immobili &
                    <lb/>
                  corpus
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  in Orbe mobili revolvuntur, erit ad vim centripetam qua
                    <lb/>
                  corpus aliquod radio ad centrum ducto Sectorem illum, eodem tem­
                    <lb/>
                  pore quo deſcripta ſit area
                    <emph type="italics"/>
                  VPC
                    <emph.end type="italics"/>
                  uniformiter deſeribere potuiſſet,
                    <lb/>
                  ut GG-FF ad FF. </s>
                  <s>Namque Sector ille & area
                    <emph type="italics"/>
                  pCk
                    <emph.end type="italics"/>
                  ſunt ad in­
                    <lb/>
                  vicem ut tempora quibus deſcribuntur. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note100"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Si Orbis
                    <emph type="italics"/>
                  VPK
                    <emph.end type="italics"/>
                  Ellipſis ſit umbilicum habens
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  & Ap­
                    <lb/>
                  ſidem ſummam
                    <emph type="italics"/>
                  V;
                    <emph.end type="italics"/>
                  eique ſimilis & æqualis ponatur Ellipſis
                    <emph type="italics"/>
                  upk,
                    <emph.end type="italics"/>
                    <lb/>
                  ita ut ſit ſemper
                    <emph type="italics"/>
                  pC
                    <emph.end type="italics"/>
                  æqualis
                    <emph type="italics"/>
                  PC,
                    <emph.end type="italics"/>
                  & angulus
                    <emph type="italics"/>
                  VCp
                    <emph.end type="italics"/>
                  ſit ad angulum
                    <lb/>
                    <emph type="italics"/>
                  VCP
                    <emph.end type="italics"/>
                  in data ratione G ad F; pro altitudine autem
                    <emph type="italics"/>
                  PC
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  pC
                    <emph.end type="italics"/>
                    <lb/>
                  ſcribatur A, & pro Ellipſeos latere recto ponatur 2 R: erit vis qua
                    <lb/>
                  corpus in Ellipſi mobili revolvi poteſt, ut (FF/AA)+(RGG-RFF/A
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  )
                    <lb/>
                  & contra. </s>
                  <s>Exponatur enim vis qua corpus revolvatur in immota
                    <lb/>
                  Ellipſi per quantitatem (FF/AA), & vis in
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  erit (FF/
                    <emph type="italics"/>
                  CV quad.
                    <emph.end type="italics"/>
                  ). Vis au­
                    <lb/>
                  tem qua corpus in Circulo ad diſtantiam
                    <emph type="italics"/>
                  CV
                    <emph.end type="italics"/>
                  ea cum velocitate
                    <lb/>
                  revolvi poſſet quam corpus in Ellipſi revolvens habet in
                    <emph type="italics"/>
                  V,
                    <emph.end type="italics"/>
                    <lb/>
                  eſt ad vim qua corpus in Ellipſi revolvens urgetur in Apſide
                    <emph type="italics"/>
                  V,
                    <emph.end type="italics"/>
                    <lb/>
                  ut dimidium lateris recti Ellipſeos. </s>
                  <s>ad Circuli ſemidiametrum
                    <emph type="italics"/>
                  CV,
                    <emph.end type="italics"/>
                    <lb/>
                  adeoque valet (RFF/
                    <emph type="italics"/>
                  CV cub.
                    <emph.end type="italics"/>
                  ): & vis quæ ſit ad hanc ut GG-FF ad
                    <lb/>
                  FF, valet (RGG-RFF/
                    <emph type="italics"/>
                  CV cub.
                    <emph.end type="italics"/>
                  ): eſtque hæc vis (per hujus Corol. </s>
                  <s>1.)
                    <lb/>
                  differentia virium in
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  quibus corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  in Ellipſi immota
                    <emph type="italics"/>
                  VPK,
                    <emph.end type="italics"/>
                    <lb/>
                  & corpus
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  in Ellipſi mobili
                    <emph type="italics"/>
                  upk
                    <emph.end type="italics"/>
                  revolvuntur. </s>
                  <s>Unde cum (per
                    <lb/>
                  hanc Prop.) differentia illa in alia quavis altitudine A ſit ad ſe­
                    <lb/>
                  ipſam in altitudine
                    <emph type="italics"/>
                  CV
                    <emph.end type="italics"/>
                  ut (1/A
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  ) ad (1/
                    <emph type="italics"/>
                  CV cub.
                    <emph.end type="italics"/>
                  ), eadem differentia
                    <lb/>
                  in omni altitudine. </s>
                  <s>A valebit (RGG-RFF/A
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  ). Igitur ad vim (FF/AA)
                    <lb/>
                  qua corpus revolvi poteſt in Ellipſi immobili
                    <emph type="italics"/>
                  VPK,
                    <emph.end type="italics"/>
                  addatur ex­
                    <lb/>
                  ceſſus (RGG-RFF/A
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  ) & componetur vis tota (FF/AA)+(RGG-RFF/A
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  ) </s>
                </p>
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          </chap>
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