The lever double its counter-lever
Weights on a balance: the ratio of loads on the supports equals the ratio of their distances
Leonardo proves a proposition about a lever c d whose counter-lever c a is half its length. Placing weight 4 at the midpoint b of the lever loads the support c as much as at b, since the distances c b and 4 b are equal, and he invokes his ninth proposition: the ratio of the weights felt by two supports equals the ratio of the distances of the supports' centres from the centre of the suspended weight. He concludes that supports c and d bear the weight b equally, and that moving b beyond the lever's end by the same amount leaves the mover d feeling the same load. The marginal diagram shows the balance beam a c b d with two hanging weights each marked 4.
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Lever c d with counter-lever c a half its length
When the lever c d is double its counter-lever c a, the mover feels the same whether the weight sits at the middle b of the lever or at the end of the counter-lever, because distances c b and 4 b are equal. Transferring weight b past the lever's end by the same amount leaves mover d feeling the same load.
Ratio of loads on the supports equals ratio of distances
By the ninth proposition, the proportion of the weights felt by the supports equals the proportion of the distances of the supports' centres from the centre of the suspended weight. From this Leonardo concludes that supports c and d load themselves equally with weight b.