Lami's Theorem

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The following theorem in mechanics, named after Bernard Lami, or Lamy (1640–1715):


Suppose that three forces act on a particle and that the resultant of the three forces is zero. Then the magnitude of each force is proportional to the sine of the angle between the other two forces.

In the given situation, the three forces are coplanar and the corresponding polygon of forces is a triangle. The lengths of the sides of this triangle are proportional to the magnitudes of the three forces and the result of the theorem is obtained by an application of the sine rule.

Subjects: Mathematics.

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