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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 197, page id 1041163592:0231
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PRINCIPTA MATHEMATICA.
197
cerrallo AD describitur, trahiunt corpus P versus A, eA uE arCa LIVen
TOta ATTTKL ducta in AF. Q. F. D
Corol. 1. Elinc si vires punctorum decrescunt in duplicata di
ctanciarum ratione, hoC CA, SI SIE F R ut P fi quad.  2EquC ad eo a-
rea ATIZK L. UE p A Y F; erit accractio corpusculi P in Circu
Ium UE F -
P F id eAt, uc P
Te
I
Corol. 2. Fx universalicer, E vires punctorum ad distantias D sInC.
reciproce ur distantiarum dienitas quaelibet Dn, hoc eAt, si SIC FR
UE
dn adCOquC area AFY YK L. UE ∞ An-1 D Hn - =  exIE AEETA
A
ctio corpusculi P in Circulum uE.p An - 2 P Fn - 1
Corol 3. F. F s diameter Circuli auseatur in intinitum, de nume
rus B Sic unitare major; aetractio corpusculi F in planum torum
intinicum crie reciproce uE P An -2, proprerea quod terminus al.
per VHn- eranelcet.
PROPOSITIO XCI PROBLEMA XLV.
Invenire attractionem corpusculi siti in axe Solidi rotundi, ad cujus
puncta sincula tendunt vires aequales centripetae in quacunque
distantiarum ratione decrescentes.
In Solidum A D F F G Era-
hatur corpusculum F, Sicum in
ejus aXC AB. Circulo quoli-
DEE R F S ad hune aZem per-
Pendiculari secetur hoc Solidum
ec in ejus diametro AS, in pla-
no aliquo P AL, K B per axem
cranscunte, capiatur (pEr PrOP.
XC) lonsicudo FR vi qua cOr-
pusculum F in circulum illum
accrahitur proxortionalis. Fangat autem punctum K curvam line-
am P RI Planis extimorum circulorum AI.  B P OcCurrentem i
ec T; e erit actractio corpusculi P in Solidum ut area L. AB l.
C. L.
P. RI MVS.
Corob.