# Varignon theorem

From Encyclopedia of Mathematics

One of the fundamental theorems in the theory of sliding vectors (cf. Vector). According to Varignon's theorem, if a system of sliding vectors $F_{\nu}$ can be reduced to a single resultant $F$, the moment of the resultant about some point 0 (or axis $I$) is equal to the sum of the moments of the vectors constituting the system about this point (or axis): $$ \mathrm{mom}_0 F = \sum_{\nu} \mathrm{mom}_0 F_{\nu}\,;\ \ \ \mathrm{mom}_I F = \sum_{\nu} \mathrm{mom}_I F_{\nu} \ . $$

Established in 1687 by P. Varignon for a convergent system of forces. The theorem is extensively employed in geometrical statics, kinematics of rigid bodies and strength of materials.

**How to Cite This Entry:**

Varignon theorem.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Varignon_theorem&oldid=42610

This article was adapted from an original article by V.V. Rumyantsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article