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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINOIDIA MATHEMATICA.
57
eadem a viribus acceleratricibus ad alia corpora tendentibus, AUE. L. IBEK
non urgentur nisi leristime, aut urgentur aequaliter ec secundum li. PRIMOS.
neas ParalletaS QuAMPFOXIMC.
PROPOSITIO LXV THEOREMA XXVI.
Si Corpora tria, quorum vires decrescunt in duplicata ratione di
stantiarum, se mutuo trahant, e attractiones acceleratrices bi-
norum quorumcunque in tertium sint inter se reciproce ut qua
drata distantiarum; minora autem circa maximum revolvan-
cur: Dico quod interius circa intimum ex manimum, radiis
ad ipsum ductis, describet areas temporibus maris proportio-
nales, e Ficuram ad formam Ellipseos umbilicum in concur-
su radiorum habentis maeis accedentem, si corpus maximum
his attractionibus acitetur, quam si maximum illud vel a mi-
noribus non attractum quiescat, v el multo minus vel multo ma-
eis attractum aut multo minus aut multo maris acitetur.
Liguet Fere ex demonstratione Corollarii secundi Propoltionis
praecedentis; sed argumento magis distincto ec latius cogente sc
crincitur.
Cas. F. R evolvantur
corpora minora P e S
in eodem plano circa
maximum I, quorum
P deseribat Orbem in-
ceriorem F AB, _ S
exteriorem SF. Sit
SK medioeris distan-
tia corporum P e S;
de corporis F versus
Sactractio acceleratrix in medioeri illa distantia exxonatur per e-
andem. In duplicata ratione SH ad SF capiatur SL 2d SR, e c.
rit SL atcractio accelerarrix corporis F versus S in distantia quaris
SP. Junse P T, eique parallelam agc L. M Occurrentem SF in MB
ex aerractio SI relolvetur (per Legum Corol 2.) in acrractiones
M L.M. HC AC UrSCbITUT COrpUS P vi acceleracrice eriplici:
una