On the Heavy Body: A Cord Feels Double Its Load
Beams and cords over pulleys; natural weight plus accidental weight makes eight
Under the heading 'On the heavy body,' Leonardo argues that every cord sustaining a load feels twice the weight it suspends. Taking a beam a c whose head weighs 4, he shows that the cord a b must supply 4 more degrees of power at b to resist the descent, so the cord feels 8 in all: 4 of natural gravity and 4 of accidental. He confirms this with a second figure of two oblique beams joined by a cord n m, where the opposing beam n f supplies with its natural weight what the accidental weight supplied before. The margins carry several diagrams of cords over pulleys and beams, lettered a, b, c, m, n, f, r, S, with weight values 4 and 8.
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Every sustaining cord feels double the weight it holds
For a beam a c whose head a weighs 4, the cord a b must supply 4 degrees of power (force, or accidental weight) at b to resist the descent, so at a the beam meets a resistance of 4 while b feels another 4. Hence the cord feels double the weight it sustains at its head a. Leonardo confirms this with the second figure, where the opposing beam n f supplies with its natural weight what the accidental weight supplied before.
Natural weight plus accidental weight makes eight
By what has been shown, the cord b c loaded with the 4 of c must be confessed to feel 8 of gravity. Of this, 4 is natural gravity and 4 is accidental.
A vertical and an oblique body joined by a cord
In the first marginal figure the cord a b feels double the weight it sustains at a, which is 4. This is proved by the second figure below, where in place of the accidental weight at b it sustains at n as much natural weight as the natural weight of m.
Cords over pulleys with weights and applied force
One margin figure shows a cord fixed to a beam and passing over a pulley, marked r 8 8 - 4, with weight r and force S. Another shows a cord on two pulleys carrying weights, marked a 8 b - 4 4, with weight a and weight b.