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V. Observations on the fundamental Property of the Lever ; 
with a Proof of the Principle assumed by Archimedes, in his 
Demonstration. By the Rev. S. Vince, A. M. F. R. S. 
Read December 19, 1793. 
The want of a demonstration of the property of the lever, 
upon clear and self-evident principles, has justly been consi- 
dered as a great desideratum in the science of mechanics, as 
the most important parts of that branch of natural philosophy 
are founded upon it. Archimedes was, I believe, the first 
who attempted it. He supposes, that if two equal bodies - be 
placed upon a lever, their effect to turn it about any point is 
the same as if they were placed in the middle point between 
them. This proposition is by no means self-evident, and 
therefore the investigation which is founded upon it has been 
rejected as imperfect. Huygens observes, that some mathe- 
maticians, not satisfied with the principle here taken for 
granted, have, by altering the form of the demonstration, en- 
deavoured to render its defects less sensible, but without suc- 
cess. He then attempts a demonstration of his own, in which 
he takes for granted, that if the same weight be removed to a 
greater distance from the fulcrum, the effect to turn about the 
lever will be greater ; this is a principle by no means to be 
admitted, when we are supposed to be totally ignorant of the 
effects of weights upon a lever at different distances from the 
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