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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 370, page id 1066518432:0398
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37ODE VIRIBOS ET MIOTIBOS CORDOROM. LIB. II.
EF permutando ac inrertendo PT. Ti: (FF = FC). FC F DL: =CR
Hk: CK (vel CD=). TIinc uLErO sequItuE PH. FC: (P F = F C)
FC, F DL = FC=: DC, atque inde elicitur P F = HC in FC, =DI
=FF. CL (vel, quia RF = FC: EF = P = N: P) aequatio P = N.
FC =DL = P. CT. Ouxe eadem est cum ca, in quam supra (5. 639.
incidimus; unde, quia in InguISIEIOne CUIEVX PDE, quam citatO lO-
co ellipun conicam esse ridimus, suppoluimus graritates absolutas
in E, D, _C. distantiis FC, DC proportionales esse, nunc illud
iplum, quod illic suppositio rel hrpochesis erat, tanquam conclu-
lio potuisset derirari ex principio, quod solicitationes acceleratri-
Ces in F _ D distantiis EC, DC HOTUM pANCEOrUM a CCNETO C FC-
ciproce proportionales SInE. Sed hac indirecta deductione non eA
opus, cum res directe probari posit. Nam, quia inrenimus (P = N
FO =DIE. (P = N) = P. CC, Crit (P =N). EC, + N. DP  = P
DE L P. CL = P. DC; dc, quia supra habuimus e D: eF = (P - VY)
FCE, + N. DL: P. DC. FC, crit ommino eD: eH = P. DCE: P. DC.
FC =DC: F. C. Ouod crat demonstrandum.
644. Idcirco insistendo principiis IIlustris Nertoni, atque Ccleb.
Cregorii, sectio telluris per axem erit elliplis conica, quam Pro-
POT. L. XXXII. determinarimus, critque adeo diameter terre le
cundum aequatorem ad diametrum per polos in subduplicata ratio-
nC P ad P = N, id est (5. 642.) = P: P = ; NV, id eAt, 2 578: 577. O1X
elliplis perparum distert a curra Flugeniana, quam propolicioni-
bus L. XXX. et L. XX XI. duabus diversis riis demonstratam dedi-
MuS.
645. Facta iterum CV = CP, ductaque Vb aequali lonsitudini
penduli in polo P secunda minuta notantis, atque per punctum b
delcripta hyperbola b0 inter alimptotas CF, CT, ejus ordinatx
Ka, FF praebebunt lonsitudines pendulorum ilochronorum, atque
ribrationibus suis secunda minuta indicantium in locis D et F.
NNam (5. 278.) rires centrales, quibus pendula ilochrOnA aSITANEUE,
Cunt pendulorum lonsitudinibus directe proportionales, unde cum
(secundum hrpothelin) Colicitationes acceleratrices in P, D ex F
distantiis horum punctorum à centro C reciproco proportionales sint
vel ex natura hyperbolae t’ab, directe, ordinatis respectiris Vb,
Ra, Ef; ex cum ordinata Vb jam repeaxesentet longitudinem pen-
duli in polo P secunda notcantis, reliquae Ra, Ef, ec. omnino in-
dicabune longitudines pendulorum iloctuonorum in locis D, F, dec.
TIOC