Varignon's Theorem:

Moment of a force about any point is equal to the sum of the moments of the components of that force about the same point.

To prove this theorem, consider the force R acting in the plane of the body shown in Fig. 1.4. The forces P and Q represent any two nonrectangular components of R. The moment of R about point O is M₀= r × R

Because R = P+Q, we may write

r × R = r × (P +Q)

Using the distributive law for cross products, we have

M₀ = r × R = r × P + r × Q

which says that the moment of R about O equals the sum of the moments about O of its components P and Q . This proves the theorem.

Varignon's theorem need not be restricted to the case of two components, but it applies equally well to three or more. where we take the clockwise moment sense to be positive.