SECT. 2,

OF THE ARCHES.

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This necessarilyhappens, from theequality of theweights, and thesi-milarity of the po-sitions and actionsof the whole inboth cases. Thus,from the equalityof the correspond-ing weights, atthe

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like angles, the © j ®

ratios of the ®

weights, ab, bd, dh, he, &c, in the lower figure, are the verysame as those, ab, bn, dh , He, &c, in the upper figure; andfrom the equality of the constant horizontal forces ch , ch,and the similarity of the positions, the corresponding verticallines, denoting the weights, are equal, namely, ab ~ ab, bn— bd, dh = dh , &c. The same may be said of the obliquelines also, ca, cb, &c, which being parallel to the beams a b,be, &c, will denote the tensions of these, in the direction oftheir length, the same as the oblique thrusts or pushes in theupper figures. Thus, all the corresponding weights andactions, and positions, in the two situations, being exactlyequal and similar, changing only drawing and tension forpushing and thrusting, the balance and equilibrium of theupper figure is still preserved the same in the hanging fes-toon or lower one.

Scholium .—The same figure, it is evident, will also arise,if the same weights, i, k, l,m,n, be suspended at like dis-tances, a b, be, &c, on a thread, or cord, or chain, &c, havingin itself little or no weight. For the equality of the weights,and their directions and distances, will put the whole line,when they come to equilibrium, into the same festoon shapeof figure. So that, whatever properties are inferred in the

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