The balance: arms, weights, and the point of equality
Dividing the shorter arm by the longer to find the counterweight; heavier loads sit nearer the centre
A page of text on the statics of the balance, written without an accompanying diagram on this face. Leonardo states that the shorter arm divided by the longer gives the counterweight: if arm b c is 1 and arm b a is 4, the result is 1/4, so placing 4 at c and 1 at a sets the balance in the position of equality. Further notes hold that the heavier weight sits nearer the central line n m, that the proportions of the approaches match the proportions of the weights but are oppositely placed, and that the more the arms descend from equality the lighter they become because their motion grows more oblique.
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Shorter arm divided by longer gives the counterweight
The smaller arm divided by the larger gives the counterweight to the weight hung on the smaller arm. If arm b c is 1 and arm b a is 4, the result is 1/4, meaning a quarter of the weight on b c; so placing 4 at c and 1 at a sets the balance at equality.
Weights and arms divided in the same number
The weights hung on the arms are always equal to the divisions of the arms when weights and arms are divided into one and the same number. If the arms are divided into 5, divide the weights into 5; if into 6, likewise divide the weight into six, and so on.
The heavier weight lies nearer the central line
That which weighs more approaches nearer to the central line of the balance: a b weighs more than a e, and so a b comes closer to the central line n m than the weight a e. The proportions of these approaches match the proportions of the weights but are oppositely situated.
Descending arms grow lighter as their motion turns oblique
The more the arms of the balance descend below the position of equality, the lighter they become, because at every degree of motion that motion grows more oblique. This holds alike for the arm that rises and the arm that descends.