Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  LIBER
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                  TERTIUS.</s>
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                  Scholium.
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                  <s>Hiſce motuum Lunarium computationibus oſtendere volui,
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                  quod motus Lunares, per Theoriam Gravitatis, a cauſis ſuis com­
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                  putari poſſint. </s>
                  <s>Per eandem Theoriam inveni præterea quod Æ­
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                  quatio Annua medii motus Lunæ oriatur a varia dilatatione Or­
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                  bis Lunæ per vim Solis, juxta Corol. </s>
                  <s>6. Prop. </s>
                  <s>LXVI. Lib. </s>
                  <s>I. </s>
                  <s>Hæc
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                  vis in Perigæo Solis major eſt, & Orbem Lunæ dilatat; in Apo­
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                  gæo ejus minor eſt, & Orbem illum contrahi permittit. </s>
                  <s>In Orbe
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                  dilatato Luna tardius revolvitur, in contracto citius; & Æquatio
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                  Annua per quam hæc inæqualitas compenſatur, in Apogæo &
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                  Perigæo Solis nulla eſt, in mediocri Solis a Terra diſtantia ad
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                  11′. </s>
                  <s>50″ circiter aſcendit, in aliis locis Æquationi centri Solis
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                  proportionalis eſt; & additur medio motui Lunæ ubi Terra per­
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                  git ab Aphelio ſuo ad Perihelium, & in oppoſita Orbis parte, ſub­
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                  ducitur. </s>
                  <s>Aſſumendo radium Orbis magni 1000 & Eccentricita­
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                  tem Terræ 16 7/8, hæc Æquatio ubi maxima eſt, per Theoriam Gra­
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                  vitatis prodiit 11′. </s>
                  <s>49″. </s>
                  <s>Sed Eccentricitas Terræ paulo major eſſe
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                  videtur, & aucta Eccentricitate hæc Æquatio augeri debet in ea­
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                  dem ratione. </s>
                  <s>Sit Eccentricitas (16 11/16), & Æquatio maxima erit
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                  11′. </s>
                  <s>52″. </s>
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                  <s>Inveni etiam quod in Perihelio Terræ, propter majorem vim
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                  Solis, Apogæum & Nodi Lunæ velocius moventur quam in Aphe­
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                  lio ejus, idQ.E.I. triplicata ratione diſtantiæ Terræ a Sole inverſe,
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                  Et inde oriuntur Æquationes Annuæ horum motuum Æquationi
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                  centri Solis proportionales. </s>
                  <s>Motus autem Solis eſt in duplicata
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                  ratione diſtantiæ Terræ a Sole inverſe, & maxima centri Æquatio
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                  quam hæc inæqualitas generat, eſt 1
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                  gr.
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                  56′. </s>
                  <s>26″ prædictæ Solis
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                  Eccentricitati (16 15/16) congruens. </s>
                  <s>Quod ſi motus Solis eſſet in tri­
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                  plicata ratione diſtantiæ inverſe, hæc inæqualitas generaret Æqua­
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                  tionem maximam 2
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                  gr.
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                  56′. </s>
                  <s>9″. </s>
                  <s>Et propterea Æquationes maxi­
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                  mæ quas inæqualitates motuum Apogæi & Nodorum Lunæ gene­
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                  rant, ſunt ad 2
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                  gr.
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                  56′. </s>
                  <s>9″, ut motus medius diurnus Apogæi &
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                  motus medius diurnus Nodorum Lunæ ſunt ad motum medium
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                  diurnum Solis. </s>
                  <s>Unde prodit Æquatio maxima medii motus
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                  Apogæi 19′. </s>
                  <s>52″: & Æquatio maxima medii motus Nodorum
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                  9′. </s>
                  <s>27″. </s>
                  <s>Additur vero Æquatio prior & ſubducitur poſterior, ubi
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                  Terra pergit a Perihelio ſuo ad Aphelium: & contrarium fit in
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                  oppoſita Orbis parte. </s>
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