The Angled Cord and the Balance of a Hanging Weight
Lever and counter-lever of a weight held at the bend of a cord
Under the heading 'Of weight', Leonardo analyses a weight hanging at the bend of a taut cord as a kind of angular balance, whose two segments act as a lever and counter-lever about a pole. He argues that the straighter (less oblique) the cord, the less strained it is, and works out how a lever three times its counter-lever lets a power of one balance a resistance of three. A second demonstration shows that potential lever and counter-lever coincide in one straight line only when the real angle at the weight is undone, which he says never happens in nature. The margin carries several small diagrams of cords bent by suspended weights.
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A weight at the bend of a cord as an angular lever and counter-lever
The cord bent by a weight hung at its middle is the easier to pull straight the less oblique its ends. So the cord b g f, angled by the weight c, resists straightening less than the cord d e f, because the lever a b over the pole b is triple its counter-lever b c. A semi-real pendant with a power of one can then act against three in the opposite pendant.
A lever triple its counter-lever, and one against three
Leonardo reads the obliquity as a ratio of arms: because the lever a b above the pole is triple the counter-lever b c, the semi-real pendant a f with a power of one can stand against 3 in the opposite semi-real pendant c e. In the preceding, less favourable case a power of 3 merely stands against 3 of resistance.
When potential lever and counter-lever fall into one line
When the potential lever and counter-lever are in the position of equality they form a single line, but this happens only if the pendants meeting at the weight undo their real angle. He proves that the potential arms n a, a c and m b, b c can never be reduced to one line unless the real angle at the weight is destroyed, which never occurs in nature.