Varignon's theorem[var·ən′yōnz ‚thir·əm]
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
Varignon’s theorem is used for solving a series of problems in mechanics (especially statics), resistance of materials, construction theories, and other areas.