Balance with arms in double proportion, tested by experiment
Reducing each arm's weight to its midpoint to find equilibrium
Headed 'Tested by experiment', the page works out the equilibrium of a balance whose arms stand in the ratio 2 to 4, with a weight applied at one end. Leonardo treats the midpoints a and b of the two arms as the centres of their weights, and reasons that arm b lifts one unit from the 4 while leaving 3, so a weight of 3 hung at the far end restores balance. A diagram at the top shows the beam labelled a c b n with a hanging load.
On this page
Balancing arms of ratio 2 to 4 with an applied weight
With the arms in double proportion (2 against 4), the shorter arm's counterweight leaves 3 on the long side and nothing on the short side. Hanging a 3 at the extremity brings the beam to equilibrium, since equal weights then stand at equal distances from the pole. The beam is labelled a c b n.
Arm midpoints as centres of weight
Because the midpoints a and b of the arms are the centres of their weights, b (subdouble in weight and distance) lifts a subdouble of itself, one, from the 4; and one, being double in distance from 2, lifts 2. Thus 3 remains at a and nothing at b, and a weight of 3 added at equal distance from a c and c n balances the 3 at a.