e-c-b-a-d; r-c a-b-ed; cba-ed. The line of motion is understood to be a b, the line of the force d a. The line of motion a b, called the lever, is understood to be the shortest path found from the centre of the wheels to their circumference, in the shortest space found between the centre and the straight line of the force, touching the wheel, that is at a b.

The points of first contact made by the lines of the cords upon the circles of the wheels that move the weights will always be at right angles, formed by these lines and those that run from those points to the centres of the said wheels. The cord lines that join with the circles of the wheels are a d and c e; the points of the right angles are a and c; the lines that run from that point to the centre of the wheel are a b and b c.

c-m b a. See how many times the space a b goes into b m, and imagine that the cord c b is the pole of that rod a m, and apply the rule of the fourth book, where it treats of the simple rod against the composite rod, and you will find this same case. For if you consider well that the rod a m is held suspended only by the cord c b, it is as though the part of the rod a b were the counterweight of the rod b m. Therefore, if a b goes 10 times into b m, convert that number of b m into a root, which being 10 makes: 10 times 10, 100; and if that space b m is 10 pounds, the cord c b will have to bear exactly 110 pounds.

o n b n a-g r c. I ask what difference there is in holding the beam c g suspended at the place r by the cord a r o, by the cord r o, or by any other that might be set between the one and the other, that is, along the line a o ending at r.

c - 20 20 - m 10 b a. If the cord c b were thousands of braccia long, you need not attend to its length, for it counts as much to be long as short. Attend only to the angles it makes at the junction of the beam, because through the inequality of those the cord has of... [text breaks off].