Varignon theorem

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