Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/189.jpg" pagenum="161"/>
                  ris periodici inverſe: patet hanc rationem compoſitam diminui per </s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note137"/>
                  actionem vis
                    <emph type="italics"/>
                  KL,
                    <emph.end type="italics"/>
                  adeoque tempus periodicum, ſi maneat Orbis
                    <lb/>
                  radius
                    <emph type="italics"/>
                  TP,
                    <emph.end type="italics"/>
                  augeri, idQ.E.I. ſubduplicata ratione qua vis illa cen­
                    <lb/>
                  tripeta diminuitur: auctoque adeo vel diminuto hoc Radio, tem­
                    <lb/>
                  pus periodicum augeri magis, vel diminui minus quam in Radii hu­
                    <lb/>
                  jus ratione ſeſquiplicata, per Corol. </s>
                  <s>6. Prop. </s>
                  <s>IV. </s>
                  <s>Si vis illa corporis
                    <lb/>
                  centralis paulatim langueſceret, corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  minus ſemper & minus
                    <lb/>
                  attractum perpetuo recederet longius a centro
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  ; & contra, ſi vis
                    <lb/>
                  illa augeretur, accederet propius. </s>
                  <s>Ergo ſi actio corporis longin­
                    <lb/>
                  qui
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  qua vis illa diminuitur, augeatur ac diminuatur per vices;
                    <lb/>
                  augebitur ſimul ac diminuetur Radius
                    <emph type="italics"/>
                  TP
                    <emph.end type="italics"/>
                  per vices, & tempus pe­
                    <lb/>
                  riodicum augebitur ac diminuetur in ratione compoſita ex ratione
                    <lb/>
                  ſeſquiplicata Radii & ratione ſubduplicata qua vis illa centripeta
                    <lb/>
                  corporis centralis
                    <emph type="italics"/>
                  T,
                    <emph.end type="italics"/>
                  per incrementum vel decrementum actionis
                    <lb/>
                  corporis longinqui
                    <emph type="italics"/>
                  S,
                    <emph.end type="italics"/>
                  diminuitur vel augetur. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note137"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  7. Ex præmiſſis conſequitur etiam quod Ellipſeos a cor­
                    <lb/>
                  pore
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  deſcriptæ Axis, ſeu Apſidum linea, quoad motum angula­
                    <lb/>
                  rem progreditur & regreditur per vices, ſed magis tamen progre­
                    <lb/>
                  ditur, & in ſingulis corporis revolutionibus per exceſſum progreſ­
                    <lb/>
                  ſionis fertur in conſequentia. </s>
                  <s>Nam vis qua corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  urgetur in
                    <lb/>
                  corpus
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  in Quadraturis, ubi vis
                    <emph type="italics"/>
                  MN
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                  evanuit, componitur ex vi
                    <lb/>
                    <emph type="italics"/>
                  LM
                    <emph.end type="italics"/>
                  & vi centripeta qua corpus
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  trahit corpus
                    <emph type="italics"/>
                  P.
                    <emph.end type="italics"/>
                  Vis prior
                    <emph type="italics"/>
                  LM,
                    <emph.end type="italics"/>
                    <lb/>
                  ſi augeatur diſtantia
                    <emph type="italics"/>
                  PT,
                    <emph.end type="italics"/>
                  augetur in eadem fere ratione cum hac
                    <lb/>
                  diſtantia, & vis poſterior decreſcit in duplicata illa ratione, adeo­
                    <lb/>
                  que ſumma harum virium decreſcit in minore quam duplicata ra­
                    <lb/>
                  tione diſtantiæ
                    <emph type="italics"/>
                  PT,
                    <emph.end type="italics"/>
                  & propterea (per Corol. </s>
                  <s>1. Prop. </s>
                  <s>XLV) efficit
                    <lb/>
                  ut Aux, ſeu Apſis ſumma, regrediatur. </s>
                  <s>In Conjunctione vero &
                    <lb/>
                  Oppoſitione, vis qua corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  urgetur in corpus
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  differentia eſt
                    <lb/>
                  inter vim qua corpus
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  trahit corpus
                    <emph type="italics"/>
                  P
                    <emph.end type="italics"/>
                  & vim
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  ; & differen­
                    <lb/>
                  tia illa, propterea quod vis
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  augetur quamproxime in ratione
                    <lb/>
                  diſtantiæ
                    <emph type="italics"/>
                  PT,
                    <emph.end type="italics"/>
                  decreſcit in majore quam duplicata ratione diſtan­
                    <lb/>
                  tiæ
                    <emph type="italics"/>
                  PT,
                    <emph.end type="italics"/>
                  adeoque (per Corol. </s>
                  <s>1. Prop.XLV) efficit ut Aux progre­
                    <lb/>
                  diatur. </s>
                  <s>In locis inter Syzygias & Quadraturas pendet motus Au­
                    <lb/>
                  gis ex cauſa utraque conjunctim, adeo ut pro hujus vel alterius
                    <lb/>
                  exceſſu progrediatur ipſa vel regrediatur. </s>
                  <s>Unde cum vis
                    <emph type="italics"/>
                  KL
                    <emph.end type="italics"/>
                  in
                    <lb/>
                  Syzygiis ſit quaſi duplo major quam vis
                    <emph type="italics"/>
                  LM
                    <emph.end type="italics"/>
                  in Quadraturis, ex­
                    <lb/>
                  ceſſus in tota revolutione erit penes vim
                    <emph type="italics"/>
                  KL,
                    <emph.end type="italics"/>
                  transferetque Au­
                    <lb/>
                  gem ſingulis revolutionibus in conſequentia. </s>
                  <s>Veritas autem hujus
                    <lb/>
                  & præcedentis Corollarii facilius intelligetur concipiendo Syſtema
                    <lb/>
                  corporum duorum
                    <emph type="italics"/>
                  T, P
                    <emph.end type="italics"/>
                  corporibus pluribus
                    <emph type="italics"/>
                  S, S, S,
                    <emph.end type="italics"/>
                  &c, in Or­
                    <lb/>
                  be
                    <emph type="italics"/>
                  ESE
                    <emph.end type="italics"/>
                  conſiſtentibus, undique cingi. </s>
                  <s>Namque horum actioni-</s>
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