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# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 266, page id 1040780814:0284
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266
ASTRONOMLE PAYSTCA
Lib. III.
tionem rectae Sr ad Pa: Onde Ouantitas Mrateria in S ost ad Onan.
titarem Materia in P in ratione composita ex triplicata ratione sv ad
ead duplicata ratione Temporis periodici Satellitis a circa P ad
Tempus periodicum Primarii r circa Solem. Vtraque autem com-
Donens ratio datur; nempe ratio sr ad e a per praemistuum Lemma,
 ipla Tempora periodica per obserrationem: non latebit isitur
ratio composica; nempe ratio Ouantitatis Materia in Sole ad Ouan.
titatem Materix in Primario P.
Frinc invenietur ratio Ouanticatis Materia in Planetis tribus Sa-
tellitio donatis; inveniendo sc. rationem Ouantitaris Mlateria in il-
lorum unoquoque ad Ouantitatem Materix in Solc.
SCHOLTOM.
Similiter inrenietur ratio Graritatis Acceleratricis in Superticie
Solis ad Graritarem Acceleratricem in Puperficie cujurris Planetae
Satellitem habentis. HTabentur enim ratio Crravitatis in superticie
Solis ad Craritatem in V, duplicata sc. rationis Dictantia sr ad
Semidiametrum Solis ex praecedentibus cognita, et ratio Gravi
tatis in r versus solem ad Graritatem in A vertuS Planetam, in-
renta ut supra; item ratio Graritatis in a ad Graritatem in Cuper.
ficie Planeta e, duplicata nota rationis quam habet Semidiameter
Planeta ad Distantiam Satellitis à Primario. Liguet iam rationem
ex tribus hisce notis rationibus compositam eandem ese cum ra-
tione Craritatis in superticie Solis ad Graritatem in superticie Pla
neta P. Et hinc rursus, ex aquo, determinabitur rario CTravitatis
in superticie unius Planctae ad Graritatem in superticie alteriuS,
si uterque Satellite saudet.
PROPOSITIO ZLIX.
Dvenire rationem Densitatis Sols ad Densitatem Planetae eu
Ljusvis Primarii, circa quem Satelles revolvitur.
Si duo COrpOra A _ B sinE ejusdem magnicudinis, patet quanti-
tatem materiae in a eAe ad quancitatem materiae in B ut dentitas
iptius a ad densitatem ipsus e: FF si ejusdem Fuerint densitatis,
quantitas materix in a est ad quantitatem materia in B ut COrPO.
ris a magnitudo ad magnitudinem corporis B: EF isitur, licet
neque magnitudines neque dentitates aequentur, ratio quantitatis
materiae in a ad quantirarem materia in B componitur ex directa
ratione densitatum ec directa ratione masnitudinum corundem.
Unde ratio densitatis corporis a ad densitatem corporis B compo.
nitur ex ratione quantitatis materia in a ad quantitatem materia
in B, _ ratione masnitudinis corporis B ad magnitudinem corporis
A; hoc cA (in casu praesenti) Densitas Solis est ad Denlitatem
Planeta in ratione composita ex ratione Ouantitatis Materia in
Sole ad Ouantitatem Materia in dicto Plancta, _ ratione MaSHI
tudinis Planeta ad Magnicudinem Solis. Sed (per PTOP. PFaC.) da
cur componentium rationum prior, s Planera Satellite saudet;
dri
it