The case of two forces may be specially noticed. Let AB be the shortest distance between the lines of action, and let AA´, BB´ (fig. 42) represent the forces. Let [alpha], [beta] be the angles which AA´, BB´ make with the direction of the vector-sum, on opposite sides. Divide AB in O, so that AA´·cos [alpha]·AO = BB´·cos [beta]·OB, (1) and draw OC parallel to the vector-sum. Resolving AA´, BB´ each into two components parallel and perpendicular to OC, we see that the former components have a single resultant in OC, of amount R = AA´ cos [alpha] + BB´ cos [beta], (2) whilst the latter components form a couple of moment G = AA´·AB·sin [alpha] = BB´·AB·sin [beta]. (3) Conversely it is seen that any wrench can be replaced in an infinite number of ways by two forces, and that the line of action of one of these may be chosen quite arbitrarily. Also, we find from (2) and (3) that G·R = AA´·BB´·AB·sin ([alpha] + [beta]). (4) The right-hand expression is six times the volume of the tetrahedron of which the lines AA´, BB´ representing the forces are opposite edges; and we infer that, in whatever way the wrench be resolved into two forces, the volume of this tetrahedron is invariable. To define the _moment_ of a force _about an axis_ HK, we project the force orthogonally on a plane perpendicular to HK and take the moment of the projection about the intersection of HK with the plane (see § 4). Some convention as to sign is necessary; we shall reckon the moment to be positive when the tendency of the force is right-handed as regards the direction from H to K. Since two concurrent forces and their resultant obviously project into two concurrent forces and their resultant, we see that the sum of the moments of two concurrent forces about any axis HK is equal to the moment of their resultant. Parallel forces may be included in this statement as a limiting case. Hence, in whatever way one system of forces is by successive steps replaced by another, no change is made in the sum of the moments about any assigned axis. By means of this theorem we can show that the previous reduction of any system to a wrench is unique.