Where the science of weights is deceived by practice
Balances and fulcrums, percussion of moving weights, and a note on fire
On this blue sheet Leonardo argues that the science of weights is deceived by practice, because the ancients treated the poles (fulcrums) of balances as immaterial mathematical points while real balances need corporeal ones. Diagrams of balances and fulcrums accompany propositions on equal weights resting on equal slopes and on the three possible positions of a balance's pole, of which only the middle is perfect. Further notes treat the percussion of equal weights moving at unequal speeds, illustrated by a ball-player's hand, a remark on water spreading from a narrow into a wide place, a short list of materials, and a claim that fire drives out air and water and leaves earth as ash.
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The science of weights deceived by practice
The science of weights is deceived by its practice and cannot be reconciled with it, because the poles of balances, treated by the ancient philosophers as mathematical lines and points that are incorporeal, must in practice be made corporeal to bear the weight of the balances and their loads. Leonardo says the ancients erred by mixing corporeal and mathematical poles, and sets out those errors below.
Equal weights on equal slopes resist equally
Equal weights placed on equal slopes equally resist the descent of one another. A companion note adds that weights differing by little in natural weight move the opposing arm of the balance but little from the position of equality.
The three positions of a balance's pole
The pole of the balance may lie in three positions within the thickness of the beam: below the central line, on the central line, or above it. Only the middle one is perfect; the upper is the worst and the lower is the less bad. The lettered fulcrum diagrams are marked c b a; o b r q p m o; c n m r b o p q d a.
Percussion of equal weights at unequal speed (a m b n c)
When equal weights strike with unequal motion, the faster does not rebound; c rebounds twice as much from the percussion b while m does not rebound. Ball-players teach this: the striking hand, faster and heavier than the ball, makes the ball rebound with the greater power the nearer the lines of percussion lie to the central lines of their motions.
Water from a narrow into a wide place (a c d b)
Beside a small lock diagram: water descending from a narrow into a wide place spreads equally and breaks the opposite banks; and if one bank resists it, the other breaks twice as much.
A materials list and a note on fire
A numbered list of workshop materials: 23 the bench, 8 the frame, 4 the glue, 9 the copper, 24 the iron. Below it a natural-philosophy remark: where fire enters, it drives out air and water and leaves the earth in the form of ash.