XIII. Demonstration of the Fundamental Property of the Lever. 
By Davip Brewster, LL. D. F.R.S. Evin. 
[Read December 3. 1810.} 
T isa fingular fact in the hiftory of {cience, that, after all 
the attempts of the moft eminent modern mathematicians, 
to obtain a fimple and fatisfactory demonftration of the funda- 
mental property of the leyer, the folution of this problem gi- 
ven by ArcuimepEs, fhould ftill be confidered as the moft legi- 
timate and elementary. Gatitro, Huycens, DE LA Hire, . 
Sir Isaac Newron, Macriaurin, Lanpen, and HAMILTON, 
have directed their attention to this important part of mecha- 
nics ; but their demonftrations are in general either tedious and 
abftrufe, or founded on affumptions too arbitrary to be recog- 
nifed as a proper bafis for mathematical reafoning. Even the 
demonftration given by Arcuimepes is not free from objec- 
tions, and is applicable only to the lever, confidered as a phy- 
fical body. Gaxteo, though his demonftration is fuperior in 
point of fimplicity to that of ARcHIMEDEs, reforts to the ine- 
legant contrivance, of fufpending a folid prifm from a mathe- 
matical lever, and of dividing the prifm into two unequal parts, 
which act as the power and the weight. The demonftration 
given by HuyceEns, aflumes as an axiom, that a given weight 
removed 
