Mechanism of Semicircles Swapped by Pulling Cords
Paired semicircles that exchange sides when a cord is drawn
A row of circular and semicircular diagrams, lettered a, b, n, m, p, q, r, t, x, v, works out a device in which paired semicircles trade places when cords are pulled. Leonardo notes that when the slider m reaches n the semicircles p and q exchange opposite sites, and that pulling the cords tied to each angle turns the right semicircle into the left and the left into the right. A small block of figures written upside down sits in the upper corner.
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Semicircles p and q exchange opposite sites
When the point m arrives at n, the two semicircles p and q have swapped opposite sites: p transmutes into q and q into p.
A cord tied to each angle of the semicircle
Every angle of the semicircle carries a cord. When b pulls the cord tied to angle r, that angle r stays at v while angle t moves to x, so that the semicircle q passes over to p.
Pulling the cords turns right into left
Pulling the cords a b sends n to f m and m to f n. The right-hand semicircle thereby becomes the left, and the left becomes the right.
Lettering of an analogous figure
A companion diagram is labelled only with its reference letters, marking the successive positions n, a, b, c d, t q p r, x v and m along the device.
A block of figures in the corner
With the sheet turned upside down, a short grid of numbers occupies the upper-left corner, unconnected to the surrounding drawings.