SECT. 2.

OF TIIE A11C IIE S.

y

and in those directions; the force c c, into the two forces c p,c q, and in those directions ; the force nd, into the forces d?’,ns, and in those directions; and soon. Then, since twoforces that are equal, and in opposite directions, do mutuallybalance each other; therefore the several pairs of forces Tinand cp, cq and df, ns and nt, &c, being equal and opposite,by tlie construction, mutually destroy or balance eacii other;and the extreme forces b»i, ev, are balanced by the oppositeresistances of the fixed points a, g. There is no force there-fore to change the position of any one of the lines, and con-sequently they will all remain in equiiibrio.

Corollary. —Hence, if one of the weights and the positionsof all the lines be given, all the other weights may thencebe found, as well as ail the oblique forces in the direction ofthe'bars or lines. And the weight which is given, may eitherbe that at the lower extremity, as B b, or it may be that atthe vertex nd, or it may be any of the intermediate ones, asc c: for, whichever of these is given, it will serve, as a diago-nal, to form the parallelogram about it; then the sides of thisparallelogram will give the sides of the two next parallelo-grams, on each side of the former ; and so on through thewhole collection of the bars. Thus, if the uppermost ver-tical weight, or diagonal nd, be the given one: Then drawdr parallel to de, and ds to DC, so forming the parallelogramrnsd: then make cq = nr, and nt = ns: and, having drawnthe several indefinite vertical lines Tib, c c, ne, at the angles,form the parallelograms pq and tv, by drawing qc parallel toec, and cp to cd, and te to ef, and ev to de. —Lastly, takeeh = pc, and make the parallelogram inn, by drawing nb pa-rallel to ae, and bin parallel to bc. And so on through thewhole.