Here it is sought what weight of the 4 the cord a n and the cord f n feel.

Find a number that has a third and a fourth, which will be 12, in which you will divide the line a c and likewise the line d f; then look at what remains of them outside the central b g, that is the parts a b on one side and e f on the other, which serve as real arms of the balance. And you will say: a b is half of 12, which is 6, and e f is 3/4 of 12, that is 9. Now here you have made the real arms of the balance, that is a b and e f, and the potential ones are e m and e o.

The heavy body that is sustained at the angle of the cord will show itself of so much greater weight to that cord, the thicker the said angle is.

That body will show itself heavier which is more remote from the central line of the fixing of its support.

See here the weights p, q, L, n attached to the angles a, m, s, o, which, being conditioned as proposed above, that is, being equally distant from the central line of their fixing, are nevertheless not equal in power as they are in natural gravity; and this arises because the angles of the cord where they are attached are not equal in thickness.

The lever of the arm d b and of the arm b f is made by the line d e and by the line f e; and if such arms were of a material that would not bend, the weight of the 8 attached would divide into 2 equal parts, and 4 would be felt by e d and 4 by e f. But because it is a cord, it observes the rule of the 4th of the 9th.

Here, by the 5th of the 7th, the weight given to the cord a b diminishes by half its gravity, as the line n b in the space a i proves. It follows that the weight 6 returns 3 at b; and because the lever a f is 3/5 of its counter-lever, there follows a converse proportion, that is, that the weight b, attached to the counter-lever n a, returns 3, and the weight of the lever becomes 5 at f. Therefore the 6 of the principal weight d is felt by the cord c b as 5.

The gravity of the 6 of the d, which by the site b has become 3, the cord b c feels as 2 and 1/4, because its obliquity takes the space m b, which is 3/4 of L b.

Now, the lever c g being 3/7 of its counter-lever c s, the weight s will be 3/7 of the weight felt at g. Now, the weight b of 3 having become 2 and 1/4 at the cord c b, we will say that this 2 and 1/4 grows at the cord a b, and makes in it a power to resist a weight of which this 2 and 1/4 is 3/7, which will be 5 and 1/4. Thus the weight 6, attached at b, returns to its two supports as 10 and 1/4. And if these supports a b and a c were of equal height at their ends, the 6 of d would return as 36, because the axis e b enters 6 times into its hypotenuse a b.

These two figures here below differ from the one above in the sides of the cords, that is in the hypotenuses, because the one above has equal hypotenuses; this one that follows has the upper hypotenuse short and the other long; the last has the lower hypotenuse shorter than the upper: and all are defined as above.