Greatest and smallest weights are set opposite the middle
A balance (a b and c n) that gives the three positions without arithmetic
A large triangular-balance diagram, its beam labelled a, b and c, n and hung with the weights 2, 4, 1, heads the page, with a smaller sketch below. Leonardo states that of the three unequal weights the greatest and the smallest are always placed opposite the middle one, and that when their combined sum equals double the middle weight the two hang on one and the same perpendicular. He remarks that the balances a b and c n can give the true positions of the three weights without any arithmetic ('via d'abbaco'), as the drawing shows.
On this page
The greatest and smallest weights placed opposite the middle
Of the three different weights of the triangular balance, the greatest and the smallest are always placed opposite the middle one. The heading scheme is labelled a 5 b - c n and carries the weights 2, 4, 1.
When the outer sum equals twice the middle: one perpendicular
If the greatest and smallest weight together make a sum double the middle weight, they stand on one and the same perpendicular, in subdouble proportion of nearness to the centre relative to the middle weight. The balances a b and c n can settle the three positions without working by way of the abacus.
A geometric answer 'without the abacus'
Leonardo contrasts the instrumental balance with numerical calculation: the arrangement a b / c n yields a true verdict on the sites of the three weights 'sanza fare per via d'abbaco' — without doing it by arithmetic — as you see in the figure.