Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/434.jpg" pagenum="406"/>
                  mus, ſunt ad invicem ut 1 ad 59,575. Ergo cum motus medius
                    <lb/>
                    <arrow.to.target n="note435"/>
                  horarius Lunæ (reſpectu fixarum) ſit 32′. </s>
                  <s>56″. </s>
                  <s>27′. </s>
                  <s>12
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  1/2, motus
                    <lb/>
                  horarius Nodi in hoc caſu erit 33″. </s>
                  <s>10′. </s>
                  <s>33
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>12
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>Aliis autem in
                    <lb/>
                  caſibus motus iſte horarius erit ad 33″. </s>
                  <s>10′. </s>
                  <s>33
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>12
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>ut conten­
                    <lb/>
                  tum ſub ſinubus angulorum trium
                    <emph type="italics"/>
                  TPI, PTN,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  STN
                    <emph.end type="italics"/>
                  (ſeu
                    <lb/>
                  diſtantiarum Lunæ a Quadratura, Lunæ a Nodo, & Nodi a Sole)
                    <lb/>
                  ad cubum Radii. </s>
                  <s>Et quoties ſignum anguli alicujus de affirmativo
                    <lb/>
                  in negativum, deque negativo in affirmativum mutatur, debebit
                    <lb/>
                  motus regreſſivus in progreſſivum & progreſſivus in regreſſivum
                    <lb/>
                  mutari. </s>
                  <s>Unde fit ut Nodi progrediantur quoties Luna inter Qua­
                    <lb/>
                  draturam alterutram & Nodum Quadraturæ proximum verſatur. </s>
                  <s>
                    <lb/>
                  Aliis in caſibus regrediuntur, & per exceſſum regreſſus ſupra pro­
                    <lb/>
                  greſſum, ſingulis menſibus ſeruntur in antecedentia. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note435"/>
                  DE MUNDI
                    <lb/>
                  SYSTEMATE</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc ſi a dati arcus quam minimi
                    <emph type="italics"/>
                  PM
                    <emph.end type="italics"/>
                  terminis
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                    <lb/>
                  &
                    <emph type="italics"/>
                  M
                    <emph.end type="italics"/>
                  ad lineam Quadraturas jungentem
                    <emph type="italics"/>
                  Qq
                    <emph.end type="italics"/>
                  demittantur perpen­
                    <lb/>
                  dicula
                    <emph type="italics"/>
                  PK, Mk,
                    <emph.end type="italics"/>
                  eademque producantur donec ſecent lineam
                    <lb/>
                  Nodorum
                    <emph type="italics"/>
                  Nn
                    <emph.end type="italics"/>
                  in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  d
                    <emph.end type="italics"/>
                  ; erit motus horarius Nodorum ut area
                    <lb/>
                    <emph type="italics"/>
                  MPDd
                    <emph.end type="italics"/>
                  & quadratum lineæ
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  conjunctim. </s>
                  <s>Sunto enim
                    <lb/>
                    <figure id="id.039.01.434.1.jpg" xlink:href="039/01/434/1.jpg" number="213"/>
                    <lb/>
                    <emph type="italics"/>
                  PK, PH
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  prædicti tres ſinus. </s>
                  <s>Nempe
                    <emph type="italics"/>
                  PK
                    <emph.end type="italics"/>
                  ſinus di­
                    <lb/>
                  ſtantiæ Lunæ a Quadratura,
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  ſinus diſtantiæ Lunæ a Nodo, &
                    <lb/>
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  ſinus diſtantiæ Nodi a Sole: & erit velocitas Nodi ut conten­
                    <lb/>
                  tum
                    <emph type="italics"/>
                  PKXPHXAZ.
                    <emph.end type="italics"/>
                  Eſt autem
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PK
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  PM
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  Kk,
                    <emph.end type="italics"/>
                    <lb/>
                  adeoque ob datas
                    <emph type="italics"/>
                  PT
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  PM
                    <emph.end type="italics"/>
                  eſt
                    <emph type="italics"/>
                  Kk
                    <emph.end type="italics"/>
                  ipſi
                    <emph type="italics"/>
                  PK
                    <emph.end type="italics"/>
                  proportionalis. </s>
                  <s>
                    <lb/>
                  Eſt &
                    <emph type="italics"/>
                  AT
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PD
                    <emph.end type="italics"/>
                  ut
                    <emph type="italics"/>
                  AZ
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  PH,
                    <emph.end type="italics"/>
                  & propterea
                    <emph type="italics"/>
                  PH
                    <emph.end type="italics"/>
                  rectangulo </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
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