On the Movement of Animals, Part Two

more impossible that it should conquer and pull upwards a resistance twice as great as itself, namely the resistance of the same machine together with the attached weight Z.

PROPOSITION IV.

The same being posited, if the attached weight Z has been lifted up to D, above the natural extension of the machine AB. I say that this will be brought about by a new force, which will be quadruple the attached weight. Tab. 15. Fig. 3.

Let RS be the proper and natural measure of the power by which the fiber or arc AB exerts force so as to contract itself, if it has been distracted by an external force as far as AC, and by which it strives to be dilated if by chance it has been violently constricted in the position AD; and let the arc AB be constricted by the force of the cord EF, so that it is reduced into the compressed posture AGD. It is evident that the power of the cord acts against the rigidity and resistance of the arc, namely against the power RS, which, just as if it were a weight attached at D, resists the force by which the cord EG strives to constrict the arc AGD; and because the same arc AGD is fixed to a firm nail X, therefore the power of the cord EF, which is ST, is double the resistance RS of the rigidity of the same arc (as is deduced from Pr. 31 of the first part). Afterwards, let a weight Z equal to RS be suspended at D; it is evident that the power of the cord AEG acts with a new force, which is TY, against the traction of the weight Z, and the cord is fixed to the nail X. Therefore, again (from the same Pr. 31 of the first part), the power of the cord AEG, or TY, is double the weight Z, or RS. Wherefore the two forces ST and TY, which are exerted