# Varignon's Theorem

## Varignon's theorem

[var·ən′yōnz ‚thir·əm]
(mechanics)
The theorem that the moment of a force is the algebraic sum of the moments of its vector components acting at a common point on the line of action of the force.

## Varignon’s Theorem

a theorem in mechanics that establishes the dependence between moments of forces of a given system and the moment of their resultant force. This theorem was first formulated and proved by the French scientist P. Varignon. According to Varignon’s theorem, if a system of forces Fi has a resultant force R, then the moment M0(R) of the resultant force relative to any center O (or z-axis) is equal to the sum of the moments M0(Fi) of the component forces relative to the same center O (or the same z-axis). Mathematically, Varignon’s theorem is expressed by the formulas

M0(R) =ΣM0(Fi)

or

Mz(R)Mz(Fi)

Varignon’s theorem is used for solving a series of problems in mechanics (especially statics), resistance of materials, construction theories, and other areas.

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