Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/153.jpg" pagenum="125"/>
                  qua corpus in Ellipſi mobili
                    <emph type="italics"/>
                  upk
                    <emph.end type="italics"/>
                  iiſdem temporibus revolvi
                    <lb/>
                    <arrow.to.target n="note101"/>
                  poſſit. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note101"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Ad eundem modum colligetur quod, ſi Orbis immo­
                    <lb/>
                  bilis
                    <emph type="italics"/>
                  VPK
                    <emph.end type="italics"/>
                  Ellipſis ſit centrum habens in virium centro
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  ; ei­
                    <lb/>
                  que ſimilis, æqualis & concentrica ponatur Ellipſis mobilis
                    <emph type="italics"/>
                  upk;
                    <emph.end type="italics"/>
                    <lb/>
                  ſitque 2 R Ellipſeos hujus latus rectum principale, & 2T latus
                    <lb/>
                  tranſverſum ſive axis major, atque angulus
                    <emph type="italics"/>
                  VCp
                    <emph.end type="italics"/>
                  ſemper ſit ad
                    <lb/>
                  angulum
                    <emph type="italics"/>
                  VCP
                    <emph.end type="italics"/>
                  ut G ad F; vires quibus corpora in Ellipſi im­
                    <lb/>
                  mobili & mobili temporibus æqualibus revolvi poſſunt, erunt ut
                    <lb/>
                  (FFA/T
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  ) & (FFA/T
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  )+(RGG-RFF/A
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  ) reſpective. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  4. Et univerſaliter, ſi corporis altitudo maxima
                    <emph type="italics"/>
                  CV
                    <emph.end type="italics"/>
                  no­
                    <lb/>
                  minetur T, & radius curvaturæ quam Orbis
                    <emph type="italics"/>
                  VPK
                    <emph.end type="italics"/>
                  habet in
                    <emph type="italics"/>
                  V,
                    <emph.end type="italics"/>
                  id
                    <lb/>
                  eſt radius Circuli æqualiter curvi, nominetur R, & vis centripeta
                    <lb/>
                  qua corpus in Trajectoria quacunQ.E.I.mobili
                    <emph type="italics"/>
                  VPK
                    <emph.end type="italics"/>
                  revolvi po­
                    <lb/>
                  teſt, in loco
                    <emph type="italics"/>
                  V
                    <emph.end type="italics"/>
                  dicatur (VFF/TT), atque aliis in locis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  indefinite dica­
                    <lb/>
                  tur X, altitudine
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                  nominata A, & capiatur G ad F in data
                    <lb/>
                  ratione anguli
                    <emph type="italics"/>
                  VCp
                    <emph.end type="italics"/>
                  ad angulum
                    <emph type="italics"/>
                  VCP:
                    <emph.end type="italics"/>
                  erit vis centripeta qua
                    <lb/>
                  corpus idem eoſdem motus in eadem Trajectoria
                    <emph type="italics"/>
                  upk
                    <emph.end type="italics"/>
                  circula­
                    <lb/>
                  riter mota temporibus iiſdem peragere poteſt, ut ſumma virium
                    <lb/>
                  X+(VRGG-VRFF/A
                    <emph type="italics"/>
                  cub.
                    <emph.end type="italics"/>
                  ). </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  5. Dato igitur motu corporis in Orbe quocunQ.E.I.mo­
                    <lb/>
                  bili, augeri vel minui poteſt ejus motus angularis circa centrum
                    <lb/>
                  virium in ratione data, & inde inveniri novi Orbes immobiles in
                    <lb/>
                  quibus corpora novis viribus centripetis gyrentur. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  6. Igitur ſi ad rectam
                    <emph type="italics"/>
                  CV
                    <emph.end type="italics"/>
                  po­
                    <lb/>
                    <figure id="id.039.01.153.1.jpg" xlink:href="039/01/153/1.jpg" number="95"/>
                    <lb/>
                  ſitione datam erigatur perpendiculum
                    <lb/>
                    <emph type="italics"/>
                  VP
                    <emph.end type="italics"/>
                  longitudinis indeterminatæ, jun­
                    <lb/>
                  gaturque
                    <emph type="italics"/>
                  CP,
                    <emph.end type="italics"/>
                  & ipſi æqualis agatur
                    <lb/>
                    <emph type="italics"/>
                  Cp,
                    <emph.end type="italics"/>
                  conſtituens angulum
                    <emph type="italics"/>
                  VCp,
                    <emph.end type="italics"/>
                  qui ſit
                    <lb/>
                  ad angulum
                    <emph type="italics"/>
                  VCP
                    <emph.end type="italics"/>
                  in data ratione;
                    <lb/>
                  vis qua corpus gyrari poteſt in Curva
                    <lb/>
                  illa
                    <emph type="italics"/>
                  Vpk
                    <emph.end type="italics"/>
                  quam punctum
                    <emph type="italics"/>
                  p
                    <emph.end type="italics"/>
                  perpetuo
                    <lb/>
                  tangit, erit reciproce ut cubus altitu­
                    <lb/>
                  dinis
                    <emph type="italics"/>
                  Cp.
                    <emph.end type="italics"/>
                  Nam corpus
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  per vim inertiæ, nulla alia vi urgente,
                    <lb/>
                  uniformiter progredi poteſt in recta
                    <emph type="italics"/>
                  VP.
                    <emph.end type="italics"/>
                  Addatur vis in centrum
                    <lb/>
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  cubo altitudinis
                    <emph type="italics"/>
                  CP
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  Cp
                    <emph.end type="italics"/>
                  reciproce proportionalis, & (per
                    <lb/>
                  jam demonſtrata) detorQ.E.I.ur motus ille rectilineus in lineam </s>
                </p>
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