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THE 
LAWS or STATICAL EQUILIBRIUM 
ANALYTICALLY INVESTIGATED. 
BY 
MR. JOHN GOUGH, 
COMMUNICATED BY DR. HOLME, 
Ox 
TT'HE theorem, which is frequently called 
the parallelogram of forces, contains the fun- 
damental principles of dynamics. On this 
account the young mathematician ought to use 
his best endeavours to acquire clear notions 
relative to the proposition in question ; be- 
cause it is of the first importance in the science 
_of mechanics. Many writers on this subject, 
more especially those on the continent, object 
to the common demonstration of the theorem, 
because motion is made use of in ‘demon- 
strating it, whereas the idea of Statical Equi- 
librium is in direct opposition to the idea of 
‘motion. In conformity with this objection 
the French mathematicians assume as an 
axiom, a proposition, which shall be pointed 
