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(83.) Any number of forces acting on the same point of a body may be replaced by a single force, which is mechanically equivalent to them, and which is, therefore, their resultant. This composition may be effected by the successive application of the parallelogram of forces. Let the several forces be called A, B, C, D, E, &c. Draw the parallelogram whose sides express the forces A and B, and let its diagonal be A′. The force expressed by A′ will be equivalent to A and B. Then draw the parallelogram whose sides express the forces A′ and C, and let its diagonal be B′. This diagonal will express a force mechanically equivalent to A′ and C. But A′ is mechanically equivalent to A and B, and therefore B′ is mechanically equivalent to A, B, and C. Next construct a parallelogram, whose sides express the forces B′ and D, and let its diagonal be C′. The force expressed by C′ will be mechanically equivalent to the forces B′ and D; but the force B′ is equivalent to A, B, C, and therefore C′ is equivalent to A, B, C, and D. By continuing this process it is evident, that a single force may be found, which will be equivalent to, and may be always substituted for, any number of forces which act upon the same point.