The imperfect pivot of the balance; proportion of weights
Why a real balance can never have a true point-centre, and why unequal weights hang off-plumb
Leonardo examines why a real balance never rests in perfect equilibrium: its pivot (polo) is not the true, universal centre of the beam, so equal weights need not stay level but may hang one high and one low. He gives a demonstration that a true centre of weight is geometrically indivisible and can never be physically formed by any pointed pivot, since a point truly indivisible would be nothing and could sustain nothing. A wheel hung with two weights illustrates that the opposite weights stand in the same proportion as the spaces between the wheel's centre-line and the verticals through each weight. A closing note asks why a slightly heavier weight does not fall plumb beneath the balance's pole.
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A real pivot cannot be the balance's true centre
The apparent equilibrium at the ends of a balance arises from the imperfection of the pole, which in use is not the true universal centre of the beam. Were it truly central, equal weights on the arms could rest one high and one low as one pleased, without any fault of the balance or inequality of the load.
The true centre of weight is indivisible and unformable
It is impossible to reduce a balance's true centres of weight to actual use: such centres are indivisible, and no physical point can form the indivisible. Even if a point could form such a centre, it would be nothing, and nothing sustains nothing — so forming it is impossible.
Weights match the proportion of their distances from the axis
Whatever proportion the spaces have that lie between the perpendicular through the wheel's centre and the perpendiculars through the centres of the attached weights, such is the proportion of the opposite weights to one another.
Why a heavier weight hangs off the vertical
A demonstration of why a weight, being somewhat greater than the other, does not fall perpendicular beneath the pole of the balance.