Balances, weights and motion, with sums and expense notes
Seven-pulley balance, a self-turning wheel, a waterfall weighed, plus expense notes and sums
Two mounted fragments carry a dense study of balances and weights: a beam raised by seven pulleys on a vertical pole, equal weights tested for level, an oblique suspended beam, and a falling stream of water weighed on a balance, together with a reflection on a wheel that keeps turning after its mover lets go. A lower fragment adds expense notes written crosswise and worked calculations of place value and multiplication by twelve. Some figures are in a later, non-Leonardo hand.
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Balance raised by seven pulleys on a vertical pole
A balance hangs from a vertical pole serving as fulcrum, fitted with seven pulleys for seven cords fixed to one end; the points run o a b c d e f g h k against a load of 100. Leonardo asks how much weight must sit at h to raise the load with the lever o, and how that weight must change as the pull shifts from a to b, from b to e, and so on step by step.
Will the balance stay level?
Two equal weights of 10 hang at a and b. Leonardo asks whether, when b is drawn toward the centre of the beam in the way shown, the balance will remain level or tip.
A wheel that keeps turning after its mover lets go
Noting that a wheel set raging in its motion turns many times after the hand leaves it, Leonardo reasons that keeping up the same speed seems to take ever less force the longer it runs; yet he concludes the mover is always at equal effort, and by nature will in fact tire.
Weighing a falling stream of water on a balance
Letters m, n, b, p, S, f mark a balance on which falling water is weighed. Leonardo argues that a weight driven forcibly through the air must be the heavier in effect the further it descends and the further it moves from the balance's pole, and contrasts this with the weak, slow, short throw of the briccole (trebuchet-engines).
Notes of expense written across the sheet
Running crosswise are money jottings: 20 giulî to Lorenzo, 12 giulî for hose, and a March entry of 19 ducats and giulî.
Place value and successive multiplication by twelve
A worked calculation labels a as units, b as tens and c as hundreds, and runs a chain of multiplications by twelve: 1,728,000, then 3,456,000, up to 20,736,000.