XIII. Demonstration of the Fundamental Property of the Lever. 

 By David Brewster, LL. D. F. R. S. Edin. 



[Read December 3. 1810.] 



IT is a lingular fact in the hiftory of fcience, that, after all 

 the attempts of the moft eminent modern mathematicians, 

 to obtain a fimple and fatisfa&ory demonftration of the funda- 

 mental property of the lever, the folution of this problem gi- 

 ven by Archimedes, mould Hill be confidered as the moft legi- 

 timate and elementary. Galileo, Huygens, De la Hire, . 

 Sir Isaac Newton, Maclaurin, Landen, 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 aflumptions too arbitrary to be recog- 

 nifed as a proper bafis for mathematical reafoning. Even the 

 dernonftration given by Archimedes is not free from objec- 

 tions, and is applicable only to the lever, confidered as a phy- 

 fical body. Galileo, 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 Huygens, aflumes as an axiom, that a given weight 



removed 



