Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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Solem. </
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>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. </
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>LXVI. & ejus Corollariis expoſitum eſt. </
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<
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>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. </
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<
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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. </
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>17. Prop. </
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>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. </
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<
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>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. </
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<
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>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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DE MUNDI
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SYSTEMATE</
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LIBER
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TERTIUS.</
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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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<
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>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. </
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>Inæqualitatem momenti (vel incrementi
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horarii) hic inveſtigandam proponimus. </
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<
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>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. </
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<
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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. </
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<
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>Hoc pacto vis
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LM
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reducetur ſemper </
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