Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/440.jpg" pagenum="412"/>
                    <arrow.to.target n="note441"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note441"/>
                  DE MUNDI
                    <lb/>
                  SYSTEMATE</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXXII. PROBLEMA XIII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Invenire motum medium Nodorum Lunæ.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Motus medius annuus eſt ſumma motuum omnium horariorum
                    <lb/>
                  mediocrium in anno. </s>
                  <s>Concipe Nodum verſari in
                    <emph type="italics"/>
                  N,
                    <emph.end type="italics"/>
                  & ſingulis
                    <lb/>
                  horis completis retrahi in locum ſuum priorem, ut non obſtante
                    <lb/>
                  motu ſuo proprio, datum ſemper ſervet ſitum ad Stellas Fixas. </s>
                  <s>
                    <lb/>
                  Interea vero Solem
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  per motum Terræ, progredi a Nodo, &
                    <lb/>
                  curſum annuum apparentem uniformiter complere. </s>
                  <s>Sit autem
                    <lb/>
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  arcus datus quam minimus, quem recta
                    <emph type="italics"/>
                  TS
                    <emph.end type="italics"/>
                  ad Solem ſemper
                    <lb/>
                  ducta, interſectione ſui & circuli
                    <emph type="italics"/>
                  NAn,
                    <emph.end type="italics"/>
                  dato tempore quam mi­
                    <lb/>
                  nimo deſcribit: & motus horarius mediocris (per jam oſtenſa)
                    <lb/>
                  erit ut
                    <emph type="italics"/>
                  AZq,
                    <emph.end type="italics"/>
                  id eſt (ob proportionales
                    <emph type="italics"/>
                  AZ, ZY
                    <emph.end type="italics"/>
                  ) ut rectan­
                    <lb/>
                  gulum ſub
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ZY,
                    <emph.end type="italics"/>
                  hoc eſt, ut area
                    <emph type="italics"/>
                  AZYa.
                    <emph.end type="italics"/>
                  Et ſumma om­
                    <lb/>
                  nium horariorum motuum mediocrium ab initio, ut ſumma om­
                    <lb/>
                  nium arearum
                    <emph type="italics"/>
                  aYZA,
                    <emph.end type="italics"/>
                  id eſt, ut area
                    <emph type="italics"/>
                  NAZ.
                    <emph.end type="italics"/>
                  Eſt autem maxima
                    <lb/>
                    <figure id="id.039.01.440.1.jpg" xlink:href="039/01/440/1.jpg" number="215"/>
                    <lb/>
                    <emph type="italics"/>
                  AZYa
                    <emph.end type="italics"/>
                  æqualis rectangulo ſub arcu
                    <emph type="italics"/>
                  Aa
                    <emph.end type="italics"/>
                  & radio circuli; & prop­
                    <lb/>
                  terea ſumma omnium rectangulorum in circulo toto ad ſummam
                    <lb/>
                  totidem maximorum, ut area circuli totius ad rectangulum ſub
                    <lb/>
                  circumferentia tota & radio; id eſt, ut 1 ad 2. Motus autem ho­
                    <lb/>
                  rarius, rectangulo maximo reſpondens, erat 16″. </s>
                  <s>16′. </s>
                  <s>37
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>42
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>Et
                    <lb/>
                  hic motus, anno toto ſidereo dierum 365.
                    <emph type="italics"/>
                  hor.
                    <emph.end type="italics"/>
                  6.
                    <emph type="italics"/>
                  min.
                    <emph.end type="italics"/>
                  9 fit
                    <lb/>
                  39
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  38′. </s>
                  <s>7″. </s>
                  <s>50′. </s>
                  <s>Ideoque hujus dimidium 19
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  49′. </s>
                  <s>3″. </s>
                  <s>55′. </s>
                  <s>eſt mo-</s>
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