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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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1II
PRINCIDIA MATHEMATICA.
EFOD. LXVL,) quam in ipsius aphelio. Acque hae sune inaequali. L1
cates insioniores ab AArOnOmIS HOTaTA.
Sunc etiam alix quaedam nondum obserrata inxqualitates, qui-
bus motus l. unares adeo perturbantur, uc nulla hactenus legc ad
Regulam aliquam certam reduei potuerint. Velocitates enim seu
motus horarii Aporeei et Nodorum Lunx, et corundem aequati-
ones, uc es dillerencia incer Lccentricicatem maximam in Syzygiis
ee minimam in Ouadraturis, ec inaequalicas quae Variatio dicitur,
augentur ac diminuuntur annuatim (per Corol. F4. PrOp. LXVL.)
in triplicata ratione diametri apparentis Solaris. Et Variatio Pra-
terea ausetur vel diminuitur in duplicata ratione temporis in-
ter quadraturas quam proxime (per Corol. 1. ec 2. LCm. X. ee
COrOl. 16. Prop. LXVI. Lib. l.) Scd haec inxqualicas in calculo
Atronomico, ad Protthaphaerelin Lunae reterri Colet, et cum ca
contundi.
PROPOSITIO ZXIII. PROBLEMA V.
Motus inaequales Satellitum fovis e Saturni a motibus Luna
ribus derivare.
Ex mocibus Lunxe noltrx motus analogi Lunarum seu Satelli-
cum foris sic derirantur. Mocus medius Nodorum Sacellitis ex-
timi Torialis, est ad motum medium Nodorum Lunxe nostra, in Fa-
tione compolita ex ratione duplicata temporis. Periodici Perrre
circa Solem ad cempus periodicum fovis circa Solem, de ratione
simplici cemporis periodici Sacellitis circa Jorem ad tempus perio.
dicum Lunx circa Terram: (per COrOl. 16. PFOP. LXVI.) adcoquo
annis centum conticit Nodus iste 8e. 24. in ancecedencia. NIOFUS
medii Nodorum Sacellicum inceriorum unt ad motum hujus, uE
illorum tempora periodica ad cempus periodicum hujus, per idem
Corollarium, de inde dantur. Motus autem Ausis Satellitis cu-
jusque in consequentia, eA ad mocum Nodorum iplius in antece.
dentia, uc motus Apogaei Lunae nostrae ad hujus mocum Nodo-
rum, (per idem Corol.) se inde datur. Diminui tamen debet
MOTUS Ausis sic inventus in ratione 5 2d 9 vel I ad 2 circiter, ob
causam quam hic exxonere non vacat. Aequationes maximae No-
dorum e Auxis Sacellicis cujusque Pere sune ad aequationes maxi-
mas Nodorum et augis Lunxe respectire, ut mocus Nodorum et
Aueis Satellicum tempore unius revolutionis aequationum prio.
rUMs
LERFIVS.
GHIIIIHIEIIIEIIMIIIMSHAMISMIIIIIIII