Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  PROPOSITIO III. THEOREMA III.
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                  LIBER
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                  TERTIUS.</s>
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                  Vim qua Luna retinetur in Orbe ſuo reſpicere Terram, & eſſe re­
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                  citroce ut quadratum diſtantiæ loeorum ab ipſius centro.
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                  <s>Patet aſſertionis pars prior per Phænomenon ſextum, & Propo­
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                  poſitionem ſecundam vel tertiam Libri primi: & pars poſterior
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                  per motum tardiſſimum Lunaris Apogæi. </s>
                  <s>Nam motus ille, qui
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                  ſingulis revolutionibus eſt graduum tantum trium & minutorum
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                  trium in conſequentia, contemni poteſt. </s>
                  <s>Patet enim (per Corol. 1.
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                  Prop. XLV. Lib.I.) quod ſi diſtantia Lunæ a centro Terræ ſit ad
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                  ſemidiametrum Terræ ut D ad 1; vis a qua motus talis oriatur ſit
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                  reciproce ut D (2 4/243), id eſt, reciproce ut ea ipſius D dignitas cu­
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                  jus index eſt (2 4/243), hoc eſt, in ratione diſtantiæ paulo majore quam
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                  duplicata inverſe, ſed quæ partibus 59 1/4 propius ad duplicatam
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                  quam ad triplicatam accedit. </s>
                  <s>Oritur vero ab actione Solis (uti
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                  poſthac dicetur) & propterea hic negligendus eſt. </s>
                  <s>Actio Solis
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                  quatenus Lunam diſtrahit a Terra, eſt ut diſtantia Lunæ a Terra
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                  quamproxime; ideoque (per ea quæ dicuntur in Corol. 2. Prop.
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                  XLV. Lib. I.) eſt ad Lunæ vim centripetam ut 2 ad 357,45 circi­
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                  ter, ſeu 1 ad (178 29/40). Et neglecta Solis vi tantilla, vis reliqua qua
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                  Luna retinetur in Orbe erit reciproce ut D
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                  2
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                  . Id quod etiam
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                  plenius conſtabit conferendo hanc vim cum vi gravitatis, ut fit
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                  in Propoſitione ſequente.
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                  Corol.
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                  Si vis centripeta mediocris qua Luna retinetur in Orbe,
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                  augeatur primo in ratione (177 29/40) ad (178 29/40), deinde etiam in rati­
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                  one duplicata ſemidiametri Terræ ad mediocrem diſtantiam centri
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                  Lunæ a centro Terræ: habebitur vis centripeta Lunaris ad ſuper­
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                  ficiem Terræ, poſito quod vis illa deſcendendo ad ſuperficiem
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                  Terræ, perpetuo augeatur in reciproca altitudinis ratione du­
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                  plicata.
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                  PROPOSITIO IV. THEOREMA IV.
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                  Lunam gravitare in Terram, & vi gravitatis retrahi ſemper a
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                  motu rectilineo, & in Orbe ſuo retineri.
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                  <s>Lunæ diſtantia mediocris a Terra in Syzygiis eſt ſemidiametro­
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                  rum terreſtrium, ſecundum pleroſque Aſtronomorum 59, ſecun­
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                  dum
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                  Vendelinum
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                  60, ſecundum
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                  Copernicum
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                  60 1/3, & ſecundum
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                  Ty-
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                  </s>
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