191 ) 11 7 4 3 1

a d f o e b c

Resolution of geometric fractions.
I wish to know what part b c is of a b, and the rule says that I set it upon that a b in the space d b, and a d remains over; which enters into d b once and e b remains over; and this e b enters into d e once and d f remains over; which enters into f e once and o e remains over; which o e enters exactly 3 times into f e; and this o e enters 11 times into b c and 19 times into a b. Therefore the line b c comes to be 11/19 of the whole line a b.

The line a b enters once into the line a c and the unknown fraction b c remains over; b c enters once into a b and d a remains over; d a enters once into d b and e b remains over; e b enters once into e d and d f remains over; d f enters once into e f and e o remains over; e o enters exactly 3 times into o f. Therefore we have found the measurer of the whole and of the parts, which always enters without fractions into each part, that is, it enters 29 times into the whole, and 18 into the first fraction and 11 into the second and 7 into the third and 4 into the fourth and 3 into the fifth. Therefore we shall say that the first divider of the line is 18/29 of the whole line.
We shall make the example by number. The 18 enters once into 29 and 11 remains; 11 into 18 enters once and 7 remains; 7 into 11 enters once and 4 remains; 4 into 7 enters once and 3 remains; 3 into 4 enters once and 1 remains; and this 1 is the measurer of each part and measurer of the whole line without leaving behind any fractions.

On the utility of machines (engines).

The water always strikes upon one tooth, and half of the other that stands above it.

This wheel is made light under the water, and its blades enter and leave that water edge-on, and in the air they enter face-on. And this lowering of the wheel is done to gain greater weight and greater fall of water.