Scaling problem, balances and a boat with a paddle-wheel
A word problem on capacity, weights on balances, and the relative motion of boats
A mixed working sheet joining a squaring word problem, several balance diagrams and studies of boats. The word problem scales sacks of wheat: ten sacks of 4 staia each, unstitched and made into one, are reckoned to hold 400, since the linear dimensions square. Balance schemes with hung weights explore where a load exerts its force, while two boat sketches state that the lesser power yields to the greater, showing how a man pushes a boat from shore or from within it; a further sketch of a paddle-wheel boat advises that the driving wheel should dip only a quarter of a braccio into the water.
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Scaling the capacity of sacks by squaring
Ten sacks each holding 4 staia of wheat, unstitched and sewn into one, are reckoned to hold 400: if the first sack has a circumference of one braccio (1 x 1 = 1, times 4 = 4) and the great one 10 braccia (10 x 10 = 100, times 4 = 400). A hundred such sacks made into one would hold 40,000 staia.
A weight hung on the balance exerts its force
In a balance lettered c b a, if the weight 4 is hung at a c it exerts its simple force at b; so that placing 4 at a loads the balance equally. Companion schemes carry the figures 5/3, 3/5 and 2 4 2 with 4.
Relative motion of man and boat
The lesser power yields to the greater: if a man pulls or pushes the boat from dry land the boat yields to its mover, but if he stands on the boat and thrusts with the oar against the land the boat moves. In the demonstrative diagram b a f p, if b holds fast p goes to f, and if both are free to move, b goes toward a as much as p toward f.
A boat driven by a paddle-wheel
A boat is fitted with a driving wheel, and Leonardo notes that the less the wheel touches the water the better; it suffices that its lowest point dip in by one quarter of a braccio.