Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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PROPOSITIO XV. PROBLEMA I.
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Invenire Orbium principales diametros.
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LIBER
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TERTIUS.</
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>Capiendæ ſunt hæ in ratione ſubſeſquiplicata temporum perio
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dieorum, per Prop. XV. Lib. I. deinde ſigillatim augendæ in rati
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one ſummæ maſſarum Solis & Planetæ cujuſque revolventis ad
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primam duarum medie proportionalium inter ſummam illam &
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Solem, per Prop. LX. Lib. I.
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PROPOSITIO XVI. PROBLEMA II.
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Invenire Orbium Eccentricitates & Aphelia.
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>Problema confit per Prop. XVIII. Lib. I.
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PROPOSITIO XVII. THEOREMA XV.
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Planetarum motus diurnos uniformes eſſe, & librationem Lunæ
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ex ipſius motu diurno oriri.
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>Patet per motus Legem I, & Corol. 22. Prop. LXVI. Lib. I.
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Quoniam vero Lunæ, circa axem ſuum uniformiter revolventis,
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dies menſtruus eſt; hujus facies eadem ulteriorem umbilicum or
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bis ipſius ſemper reſpiciet, & propterea pro ſitu umbilici illius
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deviabit hinc inde a Terra. </
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>Hæc eſt libratio in longitudinem.
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Nam libratio in latitudinem orta eſt ex inclinatione axis Lunaris
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ad planum orbis. </
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feſtum eſt.
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PROPOSITIO XVIII. THEOREMA XVI.
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Axes Planetarum diametris quæ ad eoſdem axes normaliter du
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cuntur minores eſſe.
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>Planetæ ſublato omni motu circulari diurno figuram Sphæricam,
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ob æqualem undique partium gravitatem, affectare deberent. </
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motum illum circularem fit ut partes ab axe recedentes juxta
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æquatorem aſcendere conentur. </
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