On the Movement of Animals, Part Two

the power Z is equal to that which, at F, pulls the rope DF towards F, and by these the power S is balanced. Therefore, c Same.c the power S has the same proportion to the two aforementioned equal opposite resistances—that of Z, and that which acts at F—as the altitude DO taken twice has to the two equal lengths DG, FD. And by similar reasoning, the power R has the same proportion to the two equal resistances, namely that of the nail X and that which pulls the rope CF towards F, as the altitude IC taken twice has to FC taken twice, or as DO taken twice has to DF taken twice. Therefore, the two powers S and R taken together have the same proportion to the four resistances equal among themselves—namely those of Z itself, the nail X, that which pulls the rope DF towards C, and that which pulls the rope CF towards D—as the quadruple of the altitude DO has to the quadruple of the inclined rope DF; and because the four powers equal among themselves, ZX, and the two contrary ones pulling the rope at F are quadruple of the single power Z: therefore, the two powers S and R taken together have the same proportion to the resistance Z as the quadruple of the sine DO has to the total sine DF, etc.

Hence it is clear that only one fourth part of the powers S and R, namely half of the power S, truly sustains the weight Z; the remaining half of S is opposed to, and balanced by, half of R; and the remaining half of R acts with equal moment against the resistance of the nail X, and thus the tensed rope is retained.

Now, with the angle GDF being 14 degrees and 2 minutes, the quadruple of the sine DO will be equal to the whole total sine DG. Therefore, at that point, the two powers RS will be equal to the weight Z. And if the aforementioned angle were more obtuse, then the powers RS would be less than Z; but if it were more acute, R and S taken together would be greater than Z.