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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINOIPIA MATHEMAEIC A.
1d9
PROPOSITIO LZXXII THIEOREMA XLI.
In Sphaera centro S intervallo S A descripta, si capiantur SI, S A,
Se continue proportionales: dico quod corpusculi intra Sphae-
ram in loco quovis  attractio est ad attractionem ipsius extra
Sphaeram in loco P, in ratione composita ex subduplicata ratione
distantiarum a centro 1S, PS  subduplicata ratione virium
centripetarum, in locis illis P ∞ I, ad centrum tendentium.
F E vires centripetae particularum Sphaerae sine reciproce ut di-
ctantix corpusculi a se actracti; ris, qua corpusculum situm in P.
trahitur a Sphaera eocas exit ad vim qua trahitur in P, in ratione
P RTMDS.
ComDOMCd ex Subduplicata ratione distanEix S L Ae MIILAHCTAn S+
ee ractone subduplicata vis centripetae in loco L, d Pal
in centro oriundae, ad vim contripetam in loco F ab eadem in cen
ero parcicula oriundam, id est, racione subduplicata dictantiarum
SE, SP ad inricem reciproce. IIxe duxe rationes lubduplicatae
componuntrationem requalicatis, ec proprerea artractiones in L ec X
a SPhaera tota Factxe aequantur. Simili computo, si vires particu.
larunt Spharae Cunc reciproce in duplicata ratione dictantiarum, col-
ligecite quod actractio in P sic ad accractionem in P, uc distantia SF
ad Shaerae semidiametrum S A: Si rires illae sunt reciproce in eri-
elicula ratione distanciarum, aractions  L d L El ali 
cula aliqua
lollu