Gearing, screws, water-wheels; dividing a line into parts
Friction in gear-trains, weight versus spring, and the common measure of two lines
The upper half gathers mechanical studies: cranks and screws, two toothed wheels, a pair of weight- or spring-loaded balance rods, and two circular wheels driven by water. Leonardo argues that raised balls store no more power than the motor that lifted them, that a weight makes a steadier counterweight than a spring, and that every extra gear-tooth multiplies the friction that robs a machine of its force. The lower half is filled with two columns of mathematics that use successive subtraction to find the common measure of two line segments and express one as a fraction of the whole (11/19 and 1 7/11). The tags associate the mechanisms with a cloth-shearing machine (cimatrice).
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Raised balls store no free power
The balls have only as much power as the motor that lifted them into the position shown. They are therefore useless, since the same motor could just as well have driven the device directly; the 'wheel of augmentation' is worthless.
Every gear-tooth adds friction (a, b)
At a b there is friction at the poles and where the wheel-teeth meet the pinion spindles. The more wheels and toothings a device has, the more contact points there are, and the more force the motor loses, so the force left for the whole motion falls short.
A screw should pull, not push
The screw is meant to pull and not to push, because pushing twists the shaft of the screw whereas pulling straightens a screw that has been twisted.
A water-wheel that wastes half its water
One of the two circular wheels spills half the water that makes it turn, while the other retains all the water that drives it. The comparison weighs how much of the driving water each design keeps.
Common measure of two lines (a d b f e g c)
By repeatedly fitting the smaller remainder into the larger, Leonardo finds a fraction g c that measures every earlier remainder and the whole an exact number of times. He concludes that the sought fraction is 11/19 of the whole.
Weight versus spring as a counterweight
A counterweight made with a weight is better than one made with a spring, because a weight exerts a power equal throughout its travel while a spring is always unequal.