SIR J. COCKLE ON MATHEMATICAL HISTORY. 15 



drawn from the vertex of tlie triangle to the middle of its 

 base ; hence the transverse lever will have its fulcmm at 

 the middle point, and must, consequently, be equally loaded 

 at its two ends. Hence the load supported by the fulcrum 

 of the lever which forms the base of the triangle, and 

 which is loaded at its two ends with equal weights, will be 

 equal to the double weight at the vertex, and, consequently, 

 equal to the sum of the two weights.^' 



13. Whewell, in his 'Mechanical Euclid' (2nd ed. p. 

 170), says that it will be found that Lagrange's proof, if 

 distinctly stated, involves some such axiom as this : — that 

 " If two forces, acting at the extremities of a straight line, 

 and a single force acting at an intermediate point of the 

 straight line, produce the same effect to turn a body about 

 another line, the two forces produce at the intermediate 

 point an effect equal to the single force." He adds that 

 though this axiom may be self-evident, it will hardly be 

 considered more simple than the proposition to be proved. 

 Without discussing Whewell' s criticism, I observe that 

 Lagrange (Mec. An. i. i6, 19) regards forces as quantities 

 which can be added and subtracted, and which may be 

 regarded [ib. p. 18) as weights. De Morgan [loc. cit.) 

 seems to be of opinion that the proposition that the weight 

 of the whole is equal to the sum of the weights of all the 

 parts is known only by experience. 



" Oakwal," near Brisbane, 



Queensland, Australia, 

 July 22, 1875. 



