The rod that is suspended by its ends from two cords at equal height shares its weight equally to each of those cords.

The weight that is divided from the stable cord and joined to the moved one will have the same proportion as the motion made by the cord bears to the whole rod.

Such will be the proportion the motion of one of the cords toward the middle of the rod has to the whole rod, as the weight that is divided from the stable cord and joined to the movable one has to the whole weight of the rod.

a o and a n are the arms of one balance; m c and m s are the arms of another balance.

Let a e be the length of the rod, and e d the motion of the cord d: I say that the motion the cord d has made from e to d, with respect to the whole rod a e, which is quadruple, is the same as the weight divided from the cord a with respect to the whole weight of the rod, which is quadruple. It is proved. When the cord d was at e, the rod, which was 8 libre and 8 parts, each cord felt 4 parts and 4 libre of it. Then the cord was pulled from e to d, and left outside 2 parts and 2 libre, which make a counterweight with as much space and weight in c d. There remains the 4 between a c, of which 2 fall to a and 2 to c; behold that a, which at first sustained 4, now sustains 2; which 2 is added to the cord d, and so what is taken from a and joined to d has the same proportion with the weight of the whole rod as the length d e has with the whole length of that rod.

If the rod is suspended by its ends at equal height, and a heavy body is hung at the middle of it, then the gravity of that weight is distributed equally to the supports of the rod.

The weight that moves from the middle of the rod and goes toward one of the ends lightens the end of the rod from which it removes, and burdens the other end with a weight that has the same proportion to the whole weight as the motion made by that weight has to the whole rod.

Elements of machines.

The cord of uniform power, being overcome by excessive weight, will break entirely along its whole length, and will dissolve into minute particles, when it is stretched crosswise.

The power of the weight attached to the cord penetrates entirely along its whole length, and wholly in every part of it.

Every cord that breaks is broken by two powers equal in magnitude and contrary in their motions.

The length of the cord suffers an alteration double to that of the weight joined to it.

The cord attached straight, being of uniform power, when its forces are overcome by the weight, will break at the end of its straightness.

When the cord has its ends fixed at equal height, and the rest hangs in an arc between its ends, its forces being overcome, it will break at its attachments. It is proved. Let the cord d a e be fixed at its ends d e at equal height. I say that it will break at those ends, because there the whole weight of the cord arrives equally; and, for the opponent, it cannot break at b c, because at that part only half the weight of the cord arrives and is discharged. Whence, of necessity, having to break where it is most burdened, without doubt a greater weight of cord is sustained at d e than at b c. Thus the necessity is proved.

That end of the arced cord will break more easily which is attached higher than its opposite end. It is proved. Because the cord a b c has greater weight in b c than in a c, and of necessity, having to break, it will break where it is most burdened; and without doubt it is more burdened at b than at a.

The cord of uniform thickness, stretched crosswise, being overcome, will break at its ends. It is proved. Because at the middle of its length the contention is made by two half-cords, and in the whole the contention is of the whole cord: at e is the power of the whole weight of the cord, and there is its opposite resistance, which is as much as the weight of that cord; at c is the power and resistance of half the cord. And because the whole against the whole has greater power than the part against the part, it is necessary that the cord break at the ends and not in the middle.