Pulleys, Balances and the Three Shapes of a Shadow
Block-and-tackle, balances and the strength of iron, set beside the columnar, endless and finite forms of a shadow
This densely written page interleaves mechanics with the physics of shadow. Leonardo analyses the equilibrium of a four-pulley block and tackle, a long body hung obliquely from a balance, and equal weights pressing into soft mud, and asserts that iron resists breaking ten times more than bending. Between these he sets out three basic forms a cast shadow can take: a columnar shadow when body and light are equal, an endless reversed pyramid when the body is larger, and a finite pyramid like that of a lunar eclipse when the body is smaller. Diagrams of pulleys, a balance, weights, hooks and a ring accompany the arguments, along with an opening note on why the eye retains bright images better than dark ones.
On this page
Why the eye holds the images of bright things
The eye retains within itself the images of luminous things more than of shadowy ones. Because the eye is in itself utter darkness, and like is not distinguished among like, night and dark things cannot be registered by it. Light, being wholly contrary, disturbs the eye's habitual darkness and so leaves its own image impressed there.
Equilibrium of a four-pulley block and tackle (a b c, f e d)
A weight on the blocks of four pulleys is balanced by a fourth of that weight applied to the rope of the first motion. If the pulleys e and d carry 100 pounds on four ropes, each rope bears 25 pounds. Hanging 25 pounds on the hauling rope keeps every rope in balance with its neighbour, from a e through e b and b d to d c.
A long body hung obliquely still hangs level (c a b)
A long body of uniform thickness and weight, hung at its ends from the equal arms of a balance, stays level even when the two cords are of different lengths. The reason is that a vertical line dropped below the balance's centre also passes through the centre of the supported weight.
The three shapes of a cast shadow
There are three forms of shadow. If the body equals the light, the shadow is a column without end; if the body is larger than the light, it is a reversed, endless pyramid; if the body is smaller than the light, it is a finite pyramid, as shown in the eclipse of the moon.
A weight held by two hooks versus one double-hook (e b d, f c g)
Leonardo asks whether a weight is better carried by two hooks (e b d) or a single double-hook (f c g), and answers that ten hooks would straighten before one double-hook breaks, since iron wire is easier to twist than to snap. An overloaded hook's unsupported point d yields toward the ground, while the double-hook's base c, held at f g n m, cannot straighten and must instead break in two places, n m. The ring o r breaks between o and p, where its span bears most weight.