334 



i:'s TROOi DF 



Let forCCS P, Q, // ICtfag at the pom:-; .1. //. 



maintain a system in r.|iiilihrium ; let pullies In- fixed to the 

 M at till- ]">inN A, /!. <'.... and let the pullies a. /<. 

 '[ blocks, 80 that An may be the din 



of the force 1\ P>1 that of Q, and so on. Let a string have a 

 weight W attached to one ei:<l ; and be passed round the pully 

 ^and then round the pullies >/ and A a suHieient nuin' 

 times t" render the sum of the tensi-ms r(jual to /'. Let the 

 >;une >trinr then pass on to the pully //, and be passed round b 

 and B a sufficient number of times, until the sum of th 

 sions is equal to Q. The string is then passed on to c, and 

 round cC, and so on; the end of the string is fastened to a 

 fixed point .V. Thus the system of forces P, (J. //. ... may 

 be replaced by a single strinir. the tension of which is IT. \Vc 

 a.-sunn- that tlie. ; Q t /,'. ... are commensurable. 



\\ o proceed now to the proof, in which we follow 

 ds very closely. 



It is evident, in order that the system may remain in equi- 

 librium, that the weight II' must 'he incapable of descending 



indefinitely small displacement whatever i 

 the points of t .a ; for since the weight always lends to 



descend, if there w . displacement ot the system which 



