Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

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                  Solem. </s>
                  <s>Ea componitur ex partibus
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                  SM, LM,
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                  quarum
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                  LM
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                  &
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                  ipſius
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                  SM
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                  pars
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                  TM
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                  perturbat motum Lunæ, ut in Libri primi
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                  Prop. </s>
                  <s>LXVI. & ejus Corollariis expoſitum eſt. </s>
                  <s>Quatenus Terra
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                  & Luna circum commune gravitatis centrum revolvuntur, pertur­
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                  babitur etiam motus Terræ circa centrum illud a viribus conſimi­
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                  libus; ſed ſummas tam virium quam motuum referre licet ad Lu­
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                  nam, & ſummas virium per lineas ipſis analogas
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                  TM
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                  &
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                  ML
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                  deſignare. </s>
                  <s>Vis
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                  ML
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                  (in mediocri ſua quantitate) eſt ad vim
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                  centripetam, qua Luna in Orbe ſuo circa Terram quieſcentem ad
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                  diſtantiam
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                  PT
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                  revolvi poſſet, in duplicata ratione temporum
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                  periodieorum Lunæ circa Terram & Terræ circa Solem, (per
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                  Corol. </s>
                  <s>17. Prop. </s>
                  <s>LXVI. Lib.I.) hoc eſt, in duplicata ratione die­
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                  rum 27.
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                  hor.
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                  7.
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                  min.
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                  43. ad dies 365.
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                  hor.
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                  6.
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                  min.
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                  9. id eſt, ut 1000
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                  ad 178725, ſeu 1 ad (178 39/40). Invenimus autem in Propoſitione
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                  quarta quod, ſi Terra & Luna circa commune gravitatis centrum
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                  revolvantur, earum diſtantia mediocris ab invicem erit 60 1/2 ſemi­
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                  diametrorum mediocrium Terræ quamproxime. </s>
                  <s>Et vis qua Luna
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                  in Orbe circa Terram quieſcentem, ad diſtantiam
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                  PT
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                  ſemidiame­
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                  trorum terreſtrium 60 1/2 revolvi poſſet, eſt ad vim, qua eodem
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                  tempore ad diſtantiam ſemidiametrorum 60 revolvi poſſet, ut
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                  60 1/2 ad 60; & hæc vis ad vim gravitatis apud nos ut 1 ad
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                  60X60 quamproxime. </s>
                  <s>Ideoque vis mediocris
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                  ML
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                  eſt ad vim
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                  gravitatis in ſuperficie Terræ, ut 1X60 1/2 ad 60X60X60X(178 29/40),
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                  ſeu 1 ad 638092, 6. Vnde ex proportione linearum
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                  TM, ML,
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                  datur etiam vis
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                  TM:
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                  & hæ ſunt vires Solis quibus Lunæ motus
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                  perturbantur.
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                  Q.E.I.
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                <p type="margin">
                  <s>
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                  DE MUNDI
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                  SYSTEMATE</s>
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                <p type="margin">
                  <s>
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                  LIBER
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                  TERTIUS.</s>
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                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXVI. PROBLEMA VII.
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                  Invenire incrementum borarium areæ quam Luna, radio ad Ter­
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                  ram ducto, in Orbe circulari deſcribit.
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                  <s>Diximus aream, quam Luna radio ad Terram ducto deſcribit,
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                  eſſe tempori proportionalem, niſi quatenus motus Lunaris ab
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                  actione Solis turbatur. </s>
                  <s>Inæqualitatem momenti (vel incrementi
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                  horarii) hic inveſtigandam proponimus. </s>
                  <s>Ut computatio facilior
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                  reddatur, fingamus orbem Lunæ circularem eſſe, & inæqualitates
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                  omnes negligamus, ea ſola excepta, de qua hic agitur. </s>
                  <s>Ob in­
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                  gentem vero Solis diſtantiam, ponamus etiam lineas
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                  SP, ST
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                  ſibi
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                  invicem parallelas eſſe. </s>
                  <s>Hoc pacto vis
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                  LM
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                  reducetur ſemper </s>
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