On the Movement of Animals, Part Two

PROPOSITION I.

a Tab. 15. Fig. 1.

If a cord AGCB, fixed at A to a nail X, is pulled directly downwards by a weight Z, and by forces of equal strength C, D, E, F, its intermediate points are pushed upwards in the same direction BCA towards A. I say that the entire length CB will remain direct and tense without corrugation, but only its uppermost portion CGA will be rendered slack and curved; and all the forces C, D, E, F, taken together, will be equal to the weight Z.

Because all the forces C, D, E, F, which are equal among themselves, pull the weight Z in the same direction BCA, and none of them opposes another, since all strive with equal effort and velocity toward the same parts towards A, therefore the portion CDB will remain direct and tense, since corrugation would require the movement of the parts of the cord to be directed partly upwards and partly downwards. Furthermore, because before the traction the cord was extended directly, when point C existed at position D, therefore after the translation of point C upwards, the length of the cord AGC is equal to the interval AD, and therefore the length AGC will be greater than the interval AC; for which reason the cord AGC will be curved. And because it is neither pulled nor held tensely by the nail X, as it was before, therefore the portion AGC will be rendered slack. Finally, because the weight Z is no longer held by the firmness of the nail X, but only by the lifting forces C, D, E, F, which are equal among themselves and push with equal velocities toward the same parts, therefore their forces taken together are equal to the entire weight Z, etc.