Balances and weights: the centres of gravity govern the beam
A candle floating in water, balance diagrams, and proportional division of weights
The centre of the sheet is dominated by balance-beam diagrams lettered with weights and distances, surrounded by columns of calculation. Leonardo argues that the balance is indifferent to its own form and attends only to the centres of the weights, and he wonders aloud whether the extremes of a weight guide its centre or the centre guides the extremes. Rules of proportion — 2 is to 6 as one-third — govern the spacing of the arms, worked out through fractions such as subquintupla and subtripla. At upper left a small figure shows a candle floating in water, held upright by a little counterweight; a large ink blot obscures part of the lower sheet.
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The balance attends only to the centres of the weights
Leonardo insists that the balance has no regard for its own form or for the quality of the weights' centres, but attends solely to those centres; its extremes are neither known to it nor necessary, and must be sought by another way.
Do the extremes guide the centre, or the centre the extremes?
He resolves to set the two extreme weights in every proportion he knows and watch how the heavier middle weight shifts as its gravity changes, then confesses his doubt: whether the extremes of the weight guide its centre, or the centre guides its extremes.
Dividing the beam by proportion
To place the weights, divide 2 d into 6 parts against the opposite 6 of c f; since f is one-fifth of c, give one-sixth of d to f and five-sixths to c. If 3 is one-third of 9, divide a b into three and set one part from the centre of 9 b to the weight c.
A candle floating in water with a counterweight
A small figure at upper left shows a candle standing in water, kept upright by a little counterweight (sesino) attached at its base.