Applied Mechanics and Graphic Statics
A point subjected to a number of forces will be in equilibrium, if

Sum of resolved parts in any two directions at right angles, are both zero
Algebraic sum of the moments of the forces about the point is zero
Two resolved parts in any two directions at right angles are equal
Algebraic sum of the forces is zero

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Applied Mechanics and Graphic Statics
Lami's theorem states that

Three coplanar forces acting at a point will be in equilibrium if each force is inversely proportional to the sine of the angle between the other two
Three coplanar forces acting at a point will be in equilibrium, if each force is proportional to the sine of the angle between the other two
If three forces acting on a point can be represented in magnitude and direction by the sides of a triangle, the point will be in the state of equilibrium
Three forces acting at a point are always in equilibrium

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