On the Movement of Animals, Part Two

AB, being slack and elongated, is diminished, and is made equal to the length AD; not indeed by a single direct motion towards one of the terminals A or B, but by a true contraction, by C approaching towards E, and E towards C. And so in the others, etc.

PROPOSITION III.

A fiber, or a contractible arc fixed to a nail, cannot lift a weight tied to its other extremity to a higher position, nor constrict or shorten itself more, than it had been extended without an attached weight.
Tab. 15. Fig. 3.

Let there be a fiber, or a contractible arc AB, fixed to a nail X at A, and let the length of its natural extension be AB. I say that if some weight Z is suspended at B, it cannot be lifted higher by the contractive force of the machine, so that the terminal B might approach closer to A, as at D. Because the machine AB by its own nature requires the extension of the line AB; therefore it cannot be elongated or shortened except by an external force, which, if it pulls back the terminal B towards C, the original interval AB will indeed be elongated as far as AC: but if it pushes the terminal B towards A, then the natural interval AB will be shortened, so as to become AD. Now, because the weight Z is an external force exceeding the strength of the machine AB, since it is able to increase its length and exerts force by pushing and receding from A—that is, from B towards C, namely by dilating the arc to the length AC—therefore, if it is impossible for the contractive force of the arc to overcome the equal force by which the machine, not pulled by the weight Z, resists contraction, it will be much