[ ”4 ] 
they are applied from the middle of the whole line) 
if then a third force or weight E, equal to the fum 
of the forces A and B, be applied to the point D, and 
ads on the line in an oppofite direction j I fay thefe 
three forces will fuftain each other, and keep the line 
in aequilibrio. For let us fuppofe the force E to be 
removed, and infteadof it another force, equal alfo to 
the fum of A and B, to be uniformly diffufed over 
the whole line G H, and to ad diredly againft the 
forces A and B, then the part of this force which ads 
on the fegment G L, will be equal to the force A, 
and therefore will be fuftained by it (poftulatum); and 
the other part, which is diffufed over the fegment LH, 
will be equal to and fuftained by the force B, fo that 
the forces A and B will fuftain this diffufed force 
and keep the line in aequilibrio. — Let now two other 
forces ad on this line in oppofite diredions, one of 
them the force E ading on the point D, as it was 
firft fuppofed to do, and the other an uniformly dif- 
fufed force equal to E (and confequently equal to the 
other diffufed force), then thefe two additional forces 
will alfo ballance each other, and therefore the aequi- 
librium will ft ill remain. So that the two forces A 
andB, and a diffufed force ading on one fide of the 
line fuftain the force E, and a diffufed force ading on 
the other fide : but it is manifeft, that, in this asquili— 
brium, the two diffufed forces ading on oppofite fides 
are perfedly equivalent, and therefore, if they are taken 
away from both fides, the aequilibrium muft ftill re- 
main. Hence it appears that the three weights or forces 
A, B and E, any two of which are (by the conflrudion) 
to each other inverfely astheir diftances from the third, 
will fuflain each other, and keep the line on which 
they 
