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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 196, page id 1041163592:0230
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PHTLOSOPMTAE NATDRALIS
PROPOSITIO ZC. PROBLEMA ZLIV.
Si ad singula Circuli cujuscunque puncta tendant vires aequales cen-
tripetae, decrescentes in quacunque distantiarum ratione: inve-
nire vim qua corpusculum attrahitur ubivis positum in recta
quae plano circuli ad centrum ejus perpendiculariter insistit.
Centro A interrallo quoris AD, in plano cui recta AF per-
pendicularis est, describi incelligatur Circulus; et invenienda sIF vis
qua corpusculum quodris P in cundem accrahitur. A C irculi puncto
quoris F ad corpusculum atcrascum P agatur recta P P: In re-
eta P A Capiatur P F ipSI P F. X-
qualis, ex crigatur normalis PK,
quae sIC uc vis qua punctum F Er2-
hic corpusculum F. Sieque TRL
curra linca quam punctum R per-
Detuo tangit. Occurrat eadem Cir-
culi plano in L. In F A capiatE
FI aequalis F D, e crigatur per-
pendiculum IT I currae praedicta
Occurrens in L; _c erit corpuI-
culi F accractio in Circulum uE area
AITTL ducta in alcicudinem AF.
D. F. T.
tixenim in AF capiatur linea quam minima F. e. Jungatur Pe,
_c in P F, P A CapIaNEUF F C, F fipI F e aequales. Fc quoniam vis,
qua annuli punctum quodris P trahit ad sC CorpuS P, ponieur esse
UE FKL, ee inde ris qua punctum illud trahie corpus P versus  eA uE
3d viS qua annUIUS FOFUS EraHiE COrPUS Z verTuS A, ut
AFXFK
annulus ee
L
F
conjunctim; annulus aurem iste est uc rectan-
Sulum sub ractio F. ee laticudine P e, et hoc rectangulum (ob pro-
Portionales P F, _ AF FC _ CF) aequatur rectangulo P P. XC, F,
Ceu P F X FF; eric ris qua annulus ilte trahie corpuS F vertuS
A. UE P F. XFf e
AFXFK
conjunctim, id cst,. ut contencum
FFXFRX AP, SIVC UE area FRkf ducta in AF. EF prOpterca
Cumma ririum, quibus annuli omnes in Circulo, qui centro  ec in-
terrallo
DE NOTV
PORPORVML