The Laws of Statical Equilibrium. 388 
opposite directions, in the same right line, 
produce an equilibrium, by counteracting 
each other's effects: but no two forces, whe- 
ther equal or unequal, can maintain an equi- 
librium, the directions of which include an 
angle ; for in the latter hypothesis the direct 
opposition is wanting, which alone gives the 
title of an axiom to the preceding assertion. 
_ Art. 5. Suppose F and G to represent two 
forces in magnitude, which act conjointly 
upon a material point B, in the directions 
(or rightlines) AB and CB, Fig. 1. including 
the angle ABC. These things being stated, 
it follows that if F or G were to act separately, 
B would be urged in AB or CB by Art. 3, 
but F and G act conjointly: therefore B is 
urged in neither of these directions by Art. 2, 
moreover AB and CB include an angle ABC ; 
consequently F and G do not keep the point 
in eqnilibrio by Art. 4.; hence B is urged in 
a right line by Art. 3; let this be DB. 
Draw SC meeting DB at right angles at D; 
now since F and G urge B towards different 
parts, while this point remains in DB, it is 
evident from Art. 4, that Bis retained 
in DB by two equal and contrary forces, act- 
ing at the angle B parallel to AC, in the op 
posite directions AD, CD; therefore DB is 
in the plane BAC ; and it divides the angle 
