...represented by OA and AC, acting on a particle, give OC ; therefore, &c. 55. Triangle of Forces. — If three forces, represented in magnitude and direction by the sides of a plane triangle taken in order, act on a particle, they will equilibrate. (Fig. 8, p. 21.) For forces...

...Triangle of Forces is also true, viz. that If three forces acting at a point be in equilibrium they can be represented in magnitude and direction by the sides of a triangle taken in order. Let the three forces P, Q, and R, acting at a point 0, be in equilibrium. Measure off lengths OL and...

...squares of the other two forces. Tlic Triangle of Forces. — III. If three forces acting on a point be represented in magnitude and direction by the sides of a triangle taken in order, they will keep the point in equilibrium. Thus let P, Q, and V. (Fig. 5) represent three forces acting...

...momentum. But CO, OA, OB are equal and parallel to the sides of the triangle CO A taken in order. Therefore if three forces, represented in magnitude and direction...by the sides of a triangle taken in order, act on a particle, the particle will remain at rest ; or, if already moving, it will continue in motion along...

...opposite way, as at (rf). This result may be summed up thus, " If three forces acting at a point can be represented, in magnitude and direction, by the sides of a triangle taken in order, the forces will be in equilibrium;" that is, will exactly balance each other. The direction in the...

...equilibrium as if they acted on a particle at that point ; they must therefore be capable of being represented in magnitude and direction by the sides of a triangle taken in order. The conditions of equilibrium of three parallel forces will be investigated in Chap. VI. 54. The point...

...must act in their plane and be equal and opposite to the third. (3) J[f three concurring forces are represented in magnitude and direction by the sides of a triangle taken the same way round, the resultant is zero and the forces are in equilibrium. (4) Hence, if three concurring...

...[SUPPLEMENTAL}. (6) Triangle of forces : Medi. : A term applied to that proposition which asserts that if three forces, represented in magnitude and direction by the sides of a triangle taken in order, act upon a point, they will be in equilibrium ; and, conversely, if three forces acting upon a point, and...

...called the parallelepiped of forces. Tlie Triangle of Forces. — If three forces acting at a point are represented in magnitude and direction by the sides of a triangle taken in order, the three forces are in equilibrium. Any one of the forces is equal in magnitude, and in the opposite...

...taken in the reverse direction. Hence, if there be simultaneously impressed on a point three velocities represented in magnitude and direction by the sides of a triangle taken in order, then, the point will remain at rest.* Polygon of Velocities. — If several component velocities be...