The cord that extends in one continuous straight line between its support and the weight it holds will bear all the weight attached at its lowest part; and the other cords that join it at various angles along its length bear nothing but themselves.

This is proved. Let the cord n m descend from its support g q to the heavy body f that it holds, and from p let the cord p o descend to the junction of the cord n m. I say that the cord p o bears no weight, for if it did the straight line would be bent, or a single line would be doubled, which is impossible; because no cord that does not bend is impeded, and whatever impedes it supports weight and creates an angle in the impeded cord, and a bent cord is not straight but is two lines meeting at a point to form the angle. Therefore it no longer has continuous straightness, and the cord that is the cause of breaking that straightness loads itself with part of the weight borne.

The weight hung from a single cord which branches and joins by two branches to its upper support generates two angles on its outer sides, and the proportion in which the weight is divided between the two aforesaid cords is like the proportion of the said angles. Thus let n m be the aforesaid cord branched into the two branches n a and n q, and the two angles generated on its sides are m n q on one side and m n a on the other; and by however much the first angle is greater than the second, so much more weight does the branch n q bear than the branch n a; and if the angles are equal, the branches load themselves equally with the weight into which the heavy body f is divided.

Which are the supports that bear the weight without force, and which are those that bear it with weight and with force, and which bear the weights with greater or lesser force. Certainly the supports that bear weights by an upright position bear the weights set upon them without feeling any part of their force; and those bear them with weight and with force which stand beneath their weights in an oblique position; and those supports will feel from the weights they bear, beyond the gravity of that weight, as much greater or lesser force as the position of the supports is of greater or lesser obliquity.

We shall say then that the two supports a, n, bearers of the weight a, being in the first degree of uprightness, are wholly free of force; which force will be born in the separation of the supports at their feet with as much greater or lesser power as that separation is made with greater or lesser space, etc.

Here, in this third demonstration, are investigated the rectangular powers of the weights and the arms of the balances and their real and potential appendages.

a b is the potential arm that represents the real support a f; b c is the real appendage supporting the weight c, and this shows us the rectangular junction made at b by the end of the arm a b with the appendage b c; and the opposite potential arm will be a d, which is in rectangular junction with the real appendage d e; and the potential arm of the s p, the second support, will be p b, and p n will be the opposite arm of the same balance, and the appendage of the first arm will be b c and the appendage of the second arm will be n e; and thus the positions of the two balances with their appendages are complete, and the same is understood to hold in the two opposite balances with their appendages, etc.

The part below the level line a e serves for the definition of the weight attached to the four cords, that is a, d, p, d, and just as much on the opposite side; and the weight c counts as much being in the lower angle as being in the upper, that is in f.