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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 14, page id 1066518432:0042
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16: 3.
L4 DE V PRFBUS ET MOTFBUS CORPORUM. L 1B. I.
que distantiam à plano positione dato a P d ducantur, erunt omnium fa-
eta aequalia facto ex aecrecato omnium corporum in distantiam L c
centri eorum gravitatis e a dato plano; in casut quo omnia corpora ad
eandem plani a P d partem sita sunt.
Sin vero nonnulla corpora A, B eEC. posita fuerint ad unam plant
P partem, ex reliqua C, D ad alteram partem: F. xcessus, quo facta
ex corporibus ad partes centri omnium eravitatis F. sitis, in suas homo-
losas a plano P distantias, superant facta ex corporibus reliquis in
suas ab eodem plano distantias, aequabitur facto ex omnibus corporibus
simul sumtis in distantiam cP, communis omnium centri cravitatis F. d
plano P.
Calu primo ostendi debet, quod, Politis A + B + C + D L _C.
=M, sIE A. Aa + B. BB + C. CC + D. Dd =MI. EC. FF secundo Ca-
Su, esse C. CP + D. AP = A. aP = B. bP = M. CP, designantibus CP,
AF, aP, bF distantiaS COrPOrUM C, D, A, B ec. a plano PO.
Demonstr. I. Per centrum graritatis li omnium corporum trans-
cant ad parallela plano ae, ex et. parallela plano PO alteri ad re-
eto, e ad considerari porest tanquam axis equilibrii ponderum A,
B, C, D, acque adeo erit ob casum aequilibrii A. Aa L D. Dd = B.
BB + C. Cn, vel quod eodem recidit, B. BB + C. Cn - A. A~ -- D.
Dd = 0. TEem A. 2c + B. bC = C. CC + D. de, vel C. Cc + D. de = A.
ac = B. bC = 0 respectu axis aequilibrii cF.
TI. Onia A2 = aa = a A = F, C = Aa, Bb = FC + BB, CC =FC = Cn,
de Dd = EC = Dd, eriE A. A2 + B. Bb + C. CC + D. Dd = A. F C + B.
FC. + C. Ec + D. EC F B. BB + C. Cn = A. Aa = D. Dd =MI. E C, quia
A + B + C + D = NI, _E (AUM. THujuS.) B. BB L C. Cn = A. A~ =D.
Dd = 0. Ouod est primum.
TII. Ouia 2P = 20 = cP, bP = bC = cP, cP = cC + cP; de dF =
dc = CF, erit C. CF + D. dF - A. aF = B. BF = C. CF + D. CF + A.
cF = B. CF +. C. ce + D. de = A. ac = B. BC =MI. CP, quia (RAMI. E
hujuS.) CAt C. Cc = D. de = A. ac = B. bC = 0, e C + D + A + B = HI
UE anECa. Ouxe omnia crane demonstranda.
C O R OL F A R F U M I.
4). Si COrpOTa reCta alcendant in lineis Aa, BB, CC, Dd _C.
Rorizonti perpendrcularibus, corumque cenerum graritatis R in
recta DC illis parallela, erit A. Aa +. B. BB + C. CC + D. Dd =MI.
FC. Nam dueta ut libet recta ad ipsis A2, Bb eC. Perpendiculari,
exirque (5. 44.) A. Aa + B. BB + C. Cia + D. Dd =M. Ecy de A. ad +
1.15. 6.