Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/425.jpg" pagenum="397"/>
                  ſumma genita, id eſt, ut acceleratio deſcriptionis areæ
                    <emph type="italics"/>
                  CTP,
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                  ſeu
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                    <arrow.to.target n="note426"/>
                  incrementum momenti. </s>
                  <s>Vis qua Luna circa Terram quieſcentem
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                  ad diſtantiam
                    <emph type="italics"/>
                  TP,
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                  tempore ſuo periodico
                    <emph type="italics"/>
                  CADBC
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                  dierum 27.
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                    <emph type="italics"/>
                  hor.
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                  7.
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                  min.
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                  43. revolvi poſſet, efficeret ut corpus, tempore
                    <emph type="italics"/>
                  CT
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                    <lb/>
                  cadendo, deſcriberet longitudinem 1/2
                    <emph type="italics"/>
                  CT,
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                  & velocitatem ſimul
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                  acquireret æqualem velocitati, qua Luna in Orbe ſuo movetur. </s>
                  <s>
                    <lb/>
                  Patet hoc per Corol. </s>
                  <s>9. Prop. </s>
                  <s>IV. Lib. </s>
                  <s>I. </s>
                  <s>Cum autem perpen­
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                  diculum
                    <emph type="italics"/>
                  Kd
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                  in
                    <emph type="italics"/>
                  TP
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                  demiſſum ſit ipſius
                    <emph type="italics"/>
                  EL
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                  pars tertia, & ip­
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                  ſius
                    <emph type="italics"/>
                  TP
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                  ſeu
                    <emph type="italics"/>
                  ML
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                  in Octantibus pars dimidia, vis
                    <emph type="italics"/>
                  EL
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                  in Octan­
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                  tibus, ubi maxima eſt, ſuperabit vim
                    <emph type="italics"/>
                  ML
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                  in ratione 3 ad 2,
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                  adeoque erit ad vim illam, qua Luna tempore ſuo periodico circa
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                  Terram quieſcentem revolvi poſſet, ut 100 ad 2/3X17872 1/2 ſeu
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                  11915, & tempore
                    <emph type="italics"/>
                  CT
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                  velocitatem generare deberet quæ eſſet
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                  pars (100/11915) velocitatis Lunaris, tempore autem
                    <emph type="italics"/>
                  CPA
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                  velocitatem
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                  majorem generaret in ratione
                    <emph type="italics"/>
                  CA
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                  ad
                    <emph type="italics"/>
                  CT
                    <emph.end type="italics"/>
                  ſeu
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                  TP.
                    <emph.end type="italics"/>
                  Exponatur
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                  vis maxima
                    <emph type="italics"/>
                  EL
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                  in Octantibus per aream
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                  FKXKk
                    <emph.end type="italics"/>
                  rectangulo
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                  1/2
                    <emph type="italics"/>
                  TPXPp
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                  æqualem. </s>
                  <s>Et velocitas, quam vis maxima tempore
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                  quovis
                    <emph type="italics"/>
                  CP
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                  generare poſſet, erit ad velocitatem quam vis omnis
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                  minor
                    <emph type="italics"/>
                  EL
                    <emph.end type="italics"/>
                  eodem tempore generat, ut rectangulum 1/2
                    <emph type="italics"/>
                  TPXCP
                    <emph.end type="italics"/>
                    <lb/>
                  ad aream
                    <emph type="italics"/>
                  KCGF
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                  : tempore autem toto
                    <emph type="italics"/>
                  CPA,
                    <emph.end type="italics"/>
                  velocitates ge­
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                  nitæ erunt ad invicem ut rectangulum 1/2
                    <emph type="italics"/>
                  TPXCA
                    <emph.end type="italics"/>
                  & triangulum
                    <lb/>
                    <emph type="italics"/>
                  TCG,
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                  ſive ut arcus quadrantalis
                    <emph type="italics"/>
                  CA
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                  & radius
                    <emph type="italics"/>
                  TP.
                    <emph.end type="italics"/>
                  Ideoque
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                  (per Prop. </s>
                  <s>IX. Lib. </s>
                  <s>V. Elem.) velocitas poſterior, toto tempore
                    <lb/>
                  genita, erit pars (100/11915) velocitatis Lunæ. </s>
                  <s>Huic Lunæ velocitati,
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                  quæ areæ momento mediocri analoga eſt, addatur & auferatur
                    <lb/>
                  dimidium velocitatis alterius; & ſi momentum mediocre expona­
                    <lb/>
                  tur per numerum 11915, ſumma 11915+50 ſeu 11965 exhi­
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                  bebit momentum maximum areæ in Syzygia
                    <emph type="italics"/>
                  A,
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                  ac differentia
                    <lb/>
                  11915-50 ſeu 11865 ejuſdem momentum minimum in Quadra­
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                  turis. </s>
                  <s>Igitur areæ temporibus æqualibus in Syzygiis & Quadra­
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                  turis deſcriptæ, ſunt ad invicem ut 11965 ad 11865. Ad mo­
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                  mentum minimum 11865 addatur momentum, quod ſit ad mo­
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                  mentorum differentiam 100 ut trapezium
                    <emph type="italics"/>
                  FKCG
                    <emph.end type="italics"/>
                  ad triangu­
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                  lum
                    <emph type="italics"/>
                  TCG
                    <emph.end type="italics"/>
                  (vel quod perinde eſt, ut quadratum Sinus
                    <emph type="italics"/>
                  PK
                    <emph.end type="italics"/>
                  ad
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                  quadratum Radii
                    <emph type="italics"/>
                  TP,
                    <emph.end type="italics"/>
                  id eſt, ut
                    <emph type="italics"/>
                  Pd
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  TP
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                  ) & ſumma exhi­
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                  bebit momentum areæ, ubi Luna eſt in loco quovis interme­
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                  dio
                    <emph type="italics"/>
                  P.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note425"/>
                  DE MUNDI
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                  SYSTEMATE</s>
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                <p type="margin">
                  <s>
                    <margin.target id="note426"/>
                  LIBER
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                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>Hæc omnia ita ſe habent, ex Hypotheſi quod Sol & Terra qui­
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                  eſcunt, & Luna tempore Synodico dierum 27.
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                  hor.
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                  7.
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                  min.
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                  43. re­
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                  volvitur. </s>
                  <s>Cum autem periodus Synodica Lunaris vere ſit die-</s>
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