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contracted into the middle point of its axis j and there- 
fore, if the weights of thefe cylinders be contracted 
into thefe points, they will continue to fupport each 
as before. And thence it is concluded, that any two 
weights, aCting againft each other on a line fuftained 
at a fixed point, will counterpoife one another, when 
they are inverfely as the diftances of the points on 
which they aCt, from the point on which the line 
reds. To this argument there feems to be a manifeft: 
objection \ for, when the whole cylinder is diftinguifhed 
into two fegments, part of the weight of the greater 
fegment aCts on the fame fide of the fulcrum with the 
leffer fegment j and therefore when the whole weight 
of the greater fegment is contracted into its middle 
point on one fide of the fulcrum, and aCts all of it 
againft the leffer fegment, it requires at leaft fome 
proof to fhew, that this contracted weight will be 
ballanced by the weight of the leffer fegment. Mr. 
Hugens,inhisMifcellaneous Obfervations on Mechanics 
takes notice of this objection to Archimedes’s method, 
which, he fays,feveral mathematicians had endeavoured 
to remove,but without fuccefs. He therefore, inftead 
of this method, propofed one of his own, which de- 
pends on a poftu latum that he ufes in common with 
Archimedes, that I think ought not to be granted on 
this occafion ; it is this : “ When equal bodies are 
“ placed on the arms of a lever, the one which is 
“ furtheft from the fulcrum will prevail and raife the 
“ other up”. Now this is taking it for granted, in 
other words, that a fmall weight placed further from 
the fulcrum will fupport or raife a greater one. The 
caufe and reafon of which faCt muft be derived from the 
demonftration that follows, and therefore this demon- 
ftration 
