70. Since the forces AP, BQ, CR (Fig. 22) are in equilibrium, it
follows that we may look on BQ as balancing in the position which it
occupies the two forces of AP and CR in their positions. This may
remind us of the numerous instances we have already met with, where one
force balanced two greater forces: in the present case AP and CR are
acting in opposite directions, and the force BQ which balances them is
equal to their difference. A force BT equal and opposite to BQ must
then be the resultant of CR and AP, since it is able to produce the
same effect. Notice that in this case the resultant of the two forces
is not between them, but that it lies on the side of the larger. When
the forces act in the same direction, the resultant is always between
them.
71. The actual position which the resultant of two opposite parallel
forces occupies is to be found by the following rule. Divide the
distance between the forces into as many equal parts as there are
pounds in their difference, then measure outwards from the point of
application of the larger force as many of these parts as there are
pounds in the smaller force; the point thus found determines the
position of the resultant. Thus, if the forces be 14 and 20, the
difference between them is 6, and therefore the distance between their
directions is divided into six parts; from the point of application of
the force of 20, 14 parts are measured outwards, and thus the position
of the resultant is determined. Hence we have the means of compounding
two parallel forces in general.