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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PHILOSOPMIAE NATVRALIS
PROPOSITIO VIII TIEOREMA VIII.
Si Globorum duorum in se mutuo gravitantium materia undique,
in recionibus quae à centris aequaliter distant, bomocenea sit:
erit pondus Globi alterutrius in alterum reciproce ut quadra-
tum distantiae inter centra.
Postquam invenissem gravicatem in Planetam torum oriri et
componi ex graritatibus in partes; ec ese in partes singulas reci-
proce proportionalem quadratis distantiarum a parcibus: dubita-
bam an reciproca illa proportio duplicata obtineret accurate in vi
tota ex viribus pluribus compolita, an vero quam proxime. Nam
fieri poset ut proportio, quae in majoribus dictantiis latis accu-
race obtineret, prope superticiem Planctae ob inaquales particu-
larum distantias e situs dissimiles, notabiliter crraret. Pandem
VerO, PeT PEOD. LXXV. X LXXVI. Libri primi de iplarum C OrOI.
laria incellexi veritarem Propolicionis de qua hie agitur.
Corol. Z. Flinc inveniri de inter se comparari possunt pondera
corporum in diverios Planetas. Nam pondera corporum aqua-
lium circum Planetas in circulis revolrencium (unt (per COrol. 2.
erop. IV. Lib. l.) uc diameeri circulorum directe de quadrata tem-
porum periodicorum inrerse; et pondera ad superficies Planeta-
rum, aliasre qualvis a centro distantias, majora sune vel minora
(per hanc Proposicionem) in duplicaca racione distantiarum in-
verta. Sic ex temporibus periodicis Veneris circum Solem dic.
rum 224 e horarum 167, Satellitis extimi circumjorialis circum
Porem dierum 26 ex horarum 16,, Sacellicis Iugeniani circum
Sacurnum dierum 15 _ horarum 223, et Lunx circum Terram
dierum 27, BOr. 7. min. 43. Collacis cum distantia medioeri Vene-
ris a Sole ex cum elongationibus maximis heliocenericis Satellicis
extimi circumjorialis a centro foris 8. 212 Sacellicis Flugeniani
a CCNErO Saturni 3. 20, ec Lunx a Ferra 10, computum incundo
inreni quod corporum aequalium ec aSolc, Torc, Saturno ac Terra
aequalicer distantium pondera in Solem, lorem, Saturnum ac Per-
ram Forene ad invicem uC L3 1033 2410 ec 27s12 respective. FA enim
parallaxis solis ex obserrarionibus novistimis quasi 10 e al-
leius notter per emertiones foris de Satellicum c parre obscura
LUIn
DE MONVI
DYBTEMATE