Why the overbalanced wheel cannot turn forever
Against perpetual motion: 12 counterweights, percussion, and the wheel's pole (a, n, f, c).
This closely written page argues against the perpetual-motion wheel driven by falling counterweights. Leonardo answers the objection that many counterweights would keep the wheel turning: doubling the number of weights doubles the load but halves the proportion of each falling weight's percussion, so the motion is halved, and the fraction of the circle traversed diminishes proportionally without end. He then shows that the blow of a falling weight discharges upon another pole than the wheel's, so the weight a merely adds weight on one side and does not drive the wheel, distinguishing the counter-lever's position at a rather than n and at f rather than c. A short column of notes runs down the right margin and is not included in the transcription.
On this page
Adding counterweights cannot sustain the motion
To the claim that many counterweights would keep the wheel in continual motion, Leonardo replies that this deceives you: with 12 weights one turn is a twentieth of the circle, but giving 24 doubles the weight and halves the proportion of the falling weight's percussion, so the motion halves to a fortieth, and so on proportionally to infinity.
The blow discharges upon another pole (a, n, f, c)
When weight a falls, its counter-lever strikes n and the whole blow remains in n, so the wheel does not move, because the blow discharges upon what yields at a pole other than the wheel's. Thus a only increases weight on one side; the counter-lever will be at a and not n, at f and not c, and so one yes and one no.
