Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/191.jpg" pagenum="163"/>
                  & maxima fit ubi Apſides ſunt in Syzygiis. </s>
                  <s>Si Apſides conſtituan­
                    <lb/>
                    <arrow.to.target n="note139"/>
                  tur in Quadraturis, ratio prope Apſides minor eſt & prope Syzy­
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                  gias major quam duplicata diſtantiarum, & ex ratione illa majori
                    <lb/>
                  oritur Augis motus velociſſimus, uti jam dictum eſt. </s>
                  <s>At ſi con­
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                  ſideretur ratio incrementi vel decrementi totius in progreſſu inter
                    <lb/>
                  Apſides, hæc minor eſt quam duplicata diſtantiarum. </s>
                  <s>Vis in Ap­
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                  ſide ima eſt ad vim in Apſide ſumma in minore quam duplicata
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                  ratione diſtantiæ Apſidis ſummæ ab umbilico Ellipſeos ad di­
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                  ſtantiam Apſidis imæ ab eodem umbilico: & e contra, ubi
                    <lb/>
                  Apſides conſtituuntur in Syzygiis, vis in Apſide ima eſt ad vim
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                  in Apſide ſumma in majore quam duplicata ratione diſtantiarum. </s>
                  <s>
                    <lb/>
                  Nam vires
                    <emph type="italics"/>
                  LM
                    <emph.end type="italics"/>
                  in Quadraturis additæ viribus corporis
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  compo­
                    <lb/>
                  nunt vires in ratione minore, & vires
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  in Syzygiis ſubductæ
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                  viribus corporis
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  relinquunt vires in ratione majore. </s>
                  <s>Eſt igi­
                    <lb/>
                  tur ratio decrementi & incrementi totius, in tranſitu inter Apſides,
                    <lb/>
                  minima in Quadraturis, maxima in Syzygiis: & propterea in tran­
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                  ſitu Apſidum a Quadraturis ad Syzygias perpetuo augetur, auget­
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                  que Excentricitatem Ellipſeos; inque tranſitu a Syzygiis ad
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                  Quadraturas perpetuo diminuitur, & Excentricitatem diminuit. </s>
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                <p type="margin">
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                    <margin.target id="note139"/>
                  LIBER
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                  PRIMUS.</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  10. Ut rationem ineamus errorum in Latitudinem, finga­
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                  mus planum Orbis
                    <emph type="italics"/>
                  EST
                    <emph.end type="italics"/>
                  immobile manere; & ex errorum expo­
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                  ſita cauſa manifeſtum eſt quod, ex viribus
                    <emph type="italics"/>
                  NM, ML,
                    <emph.end type="italics"/>
                  quæ ſunt
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                  cauſa illa tota, vis
                    <emph type="italics"/>
                  ML
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                  agendo ſemper ſecundum planum Orbis
                    <lb/>
                    <emph type="italics"/>
                  PAB,
                    <emph.end type="italics"/>
                  nunquam perturbat motus in Latitudinem; quodque vis
                    <emph type="italics"/>
                  NM,
                    <emph.end type="italics"/>
                    <lb/>
                  ubi Nodi ſunt in Syzygiis, agendo etiam ſecundum idem Orbis
                    <lb/>
                  planum, non perturbat hos motus; ubi vero ſunt in Quadraturis
                    <lb/>
                  eos maxime perturbat, corpuſque
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  de plano Orbis ſui perpetuo
                    <lb/>
                  trahendo, minuit inclinationem plani in tranſitu corporis a Qua­
                    <lb/>
                  draturis ad Syzygias, augetque viciſſim eandem in tranſitu a Syzy­
                    <lb/>
                  giis ad Quadraturas. </s>
                  <s>Unde fit ut corpore in Syzygiis exiſtente in­
                    <lb/>
                  clinatio evadat omnium minima, redeatque ad priorem magnitudi­
                    <lb/>
                  nem circiter, ubi corpus ad Nodum proximum accedit. </s>
                  <s>At ſi Nodi
                    <lb/>
                  conſtituantur in Octantibus poſt Quadraturas, id eſt, inter
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  A,
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                  D
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                  intelligetur ex modo expoſitis quod, in tranſitu corporis
                    <lb/>
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  a Nodo alterutro ad gradum inde nonageſimum, inclinatio pla­
                    <lb/>
                  ni perpetuo minuitur; deinde in tranſitu per proximos 45 gradus,
                    <lb/>
                  uſque ad Quadraturam proximam, inclinatio augetur, & poſtea de­
                    <lb/>
                  nuo in tranſitu per alios 45 gradus, uſque ad Nodum proximum,
                    <lb/>
                  diminuitur. </s>
                  <s>Magis itaQ.E.D.minuitur inclinatio quam augetur, &
                    <lb/>
                  propterea minor eſt ſemper in Nodo ſubſequente quam in præce-</s>
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