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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 105, page id 1066518432:0133
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DE VFRFBUS ET NIOTIBAS CORPORUM. LIB. I. 105
Rciant atque adeo (5. 297.) unum CN alteri CP sinchronum aut
isochronum sIC; _ conversim, si haec pendula fynchrona sint, Colici
tationes ricariae R, S, eC. ex V similes crunt.
PROPOSITIOZXXV. PHEOREMA.
205. Si sinculae particulae cujusque penduli compositi derepente alicu-
bi vinculo solutae motum in altum convertant, unaquaeque ea celeritate
quam cum reliquis connexa oscillando acquisroit, commune omnium pen-
duli partium cravitatis centrum ad eam ipsam altitudinem ascendet, ex
qua delapsum erat descensu totius penduli compositi, cum scilicet omnes
penduli partes adhuc connexa essent.
I. Axim penduli compoliti ex situ horizontali C A in situm CM
delaplum esse ponamusinotu accelerato, particulas vero P, 9, etc.
rinculis solutas ascendere in rectis P2P, 929, ecc. unamquam que
celeritate iniciali, quam cum religuis olcillando acquisirie; ita ut
commune omnium gravitatis centrum M aCcendat per lincam NI2M.
Probandum est hanc N2M aequalem Fore ipADM, quae protundi-
tatem denotat, ex qua omnium penduli partium centrum graritatis
cecidit motu totius penduli compositi. Ouia nunc P, Q, N deno-
EANE MaCTAS COrPOrUM _E F. P, F. 9, _C. Cr. N corundem pondera,
horum summa, excepto pondere N, dicatur MI, hoc CA, M =P.
P + F. O + _EC., CrIEque (5. 48.) PrOPter centrum gravitatIS MI; F.
P. AC FF. O. BC =M. DC, nCC nON F. P. AP + F. O. BO +
EC. = M. DM; ac denique P. P. PZP + F. O. O2O F _EC. = M.
NI2MI.
TI. Sic insuper pendulum simplex CN composito sinchronum,
adeo ut id cum CMI congruat atque celeritates pondusculorum N,
P, C _c. Similes fInE; cruneque adeo (5. 204.) Colicitationes vi-
Cariae R, S, ec. V similes, rerim quia (5. F98.) Solicitationes vi-
carixe Colicitationibus graritatis centralibus F, F_c. C aequipol-
lene, atque cum hisce in requilibrio consistere queunt, crit (5. 56.)
F. P. AC + F. O. BC + _EC. id est (BUM. T.) =MI. DC = R. P. PC
+5. 9. OC + _C. _ C. N. YO = V. N. NC, atque HINC FCTUIEAE
analogia M. DC: G. N. YO =R. P. PC +S. O. OC +_C.: V. N.
NC (vel quia R, S, ec. et V radiis PC, OC, _EC. NC PFOPOr-
tionales (UINE) = P. PC + O. DC= + _C.: N. NO; at celeritates p.
Q, ec. n corpusculorum P, Q. N etiam radiis PC, OC, NC
proportionantur, erso M. DC: 6. N. YC, vel (proprer triangula
limi-