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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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AIII
PRINOIPTA MATHIEMATTCA.
PROPOSITIOXV. PROBLEMA I
Invenire Orbium principales diametros.
Capiendae sunt hxe in ratione subse squiplicata temporum perio-
dicorum, per ProD. ZV. Lib. I. deinde sigillatim augendae in rati
one summae massarum Solis ex Planetx cujusque revolveneis ad
primam duarum medie proporcionalium inter summam illam et
Solem, Per PrOD. LX. Lib. L.
PROPOSITIOZVI. PROBLEMA II.
Tnvenire Orbium Eccentricitates  Aphelia.
Problema COntit per PrOP. XVIIT. Lib. I.
PROPOSTTIO XVII. THTEOREMA XV
Planetarum motus diurnos uniformes esse, e librationem Lunae
ex ipsius motu diurno oriri.
PateE per motus Legem I, e Corol. 22. PrOD. LXVT. Lib. I.
Duoniam vero Lunae, circa axem Cuum unitormiter revolventis,
dies menstruus est; hujus Facies eadem ulteriorem umbilicum or-
bis ipsius semper respiciet, e propterea pro situ umbilici illius
deriabie hinc inde a Terra. FIxec est libracio in lonsitudinem.
Nam libratio in lacicudinem orta cs ex inclinatione axis Lunaris
2d planum orbis. Porro hxec ita se habere, ex Phaenomenis mani-
fectum eAt.
PROPOSITTO XVHI TTTEOREMA XVI.
Axees Planetarum diametris quae ad eosdem axes normaliter du-
cuntur minores esse.
elanetae sublato omni motu circulari diurno figuram Sphaericam,
ob aequalem undique partium graritatem, affectare deberent. P’er
mocum illum circularem Ac ut partes ab adC recedentes juxta
aequatorem ascendere conentur. Ideoque materia si Auida lE
CCC
alcentu
L EBER
TBRXIVC
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