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I 
PROP. XXIII. 
Let AE (lig. 15 .) be a cyllndric canal, Infinitely 
continued beyond E; and let AF be a bent 
canal, meeting the other at A, and infinitely 
continued beyond F : let the fedlion of this ca- 
nal, in all parts of it, be equal to that of^ the 
■cylindric canal, and let both canals be filled 
with uniform fluid of the fame denfity ; the 
force with which a particle of fluid P, placed 
anyw'here at pleafure, repels the whole quan- 
tity of fluid in AF', in the diredfion of the ca- 
nal, is the fame with which it repels the fluid 
in the canal A E, in the diredfion A E. 
On the center P, draw two circular arches B D 
and b infinitely near to each other, cutting AE in 
B and and AF in D and I, and draw the radii 
P3 and P^. As PB = P D, the force with which 
P repels a particle at B, in the diredlion B /3, is to 
that with which it repels an equal particle at D, in 
the direaioii D I', as to or as i to ; and 
therefore, the force with which it repels the whole 
fluid in B /3, in the diredtion B /3, is the fame with 
which it repels the whole fluid in D in the direc- 
tion that is in the diredtion of the canal ; and 
therefore, the force with which it repels the whole 
fluid in AE, in the diredion AE, is the fame with 
which it repels the whole fluid in AF, in the direc- 
tion of the canal. 
C o R 0 L- 
