Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  DE MUNDI
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                  SYSTEMATE</s>
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                  PROPOSITIO XXXII. PROBLEMA XIII.
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                  Invenire motum medium Nodorum Lunæ.
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                  <s>Motus medius annuus eſt ſumma motuum omnium horariorum
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                  mediocrium in anno. </s>
                  <s>Concipe Nodum verſari in
                    <emph type="italics"/>
                  N,
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                  & ſingulis
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                  horis completis retrahi in locum ſuum priorem, ut non obſtante
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                  motu ſuo proprio, datum ſemper ſervet ſitum ad Stellas Fixas. </s>
                  <s>
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                  Interea vero Solem
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                  S,
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                  per motum Terræ, progredi a Nodo, &
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                  curſum annuum apparentem uniformiter complere. </s>
                  <s>Sit autem
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                    <emph type="italics"/>
                  Aa
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                  arcus datus quam minimus, quem recta
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                  TS
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                  ad Solem ſemper
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                  ducta, interſectione ſui & circuli
                    <emph type="italics"/>
                  NAn,
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                  dato tempore quam mi­
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                  nimo deſcribit: & motus horarius mediocris (per jam oſtenſa)
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                  erit ut
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                  AZq,
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                  id eſt (ob proportionales
                    <emph type="italics"/>
                  AZ, ZY
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                  ) ut rectan­
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                  gulum ſub
                    <emph type="italics"/>
                  AZ
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                  &
                    <emph type="italics"/>
                  ZY,
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                  hoc eſt, ut area
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                  AZYa.
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                  Et ſumma om­
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                  nium horariorum motuum mediocrium ab initio, ut ſumma om­
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                  nium arearum
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                  aYZA,
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                  id eſt, ut area
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                  NAZ.
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                  Eſt autem maxima
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                    <emph type="italics"/>
                  AZYa
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                  æqualis rectangulo ſub arcu
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                  Aa
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                  & radio circuli; & prop­
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                  terea ſumma omnium rectangulorum in circulo toto ad ſummam
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                  totidem maximorum, ut area circuli totius ad rectangulum ſub
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                  circumferentia tota & radio; id eſt, ut 1 ad 2. Motus autem ho­
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                  rarius, rectangulo maximo reſpondens, erat 16″. </s>
                  <s>16′. </s>
                  <s>37
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                  iv
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                  . </s>
                  <s>42
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                  v
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                  . </s>
                  <s>Et
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                  hic motus, anno toto ſidereo dierum 365.
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                  hor.
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                  6.
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                  min.
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                  9 fit
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                  39
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                  gr.
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                  38′. </s>
                  <s>7″. </s>
                  <s>50′. </s>
                  <s>Ideoque hujus dimidium 19
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                  gr.
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                  49′. </s>
                  <s>3″. </s>
                  <s>55′. </s>
                  <s>eſt mo-</s>
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