Where an arch breaks, and the true running of rollers
Statics of a brick arch, rolling friction, and the uniform revolution of a shaft
The upper drawing is a round-headed arch set in a wall on two brick piers, which Leonardo analyses for its statics: the weights a b and c d press on the springing, and because the bonding of the fourteen bricks holds for only seven, the arch must fracture along the perpendicular at r i, just past the first side of the pilaster. Below, mechanical studies argue that a roller (curro) turns the harder when the load crosses its axis at more varied angles, and that a beam-roller (subbio) can revolve uniformly only when the central line of its poles coincides with the central line of the roller itself. Several rollers and shafts are lettered but drawn rather than described in the supplied text.
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Where a brick arch breaks under load
In a body of one piece the pressing of part on part keeps the same proportion as whole on whole. The weights a b and c d press on e g and h K, and the weight b c falls by its perpendicular onto f g and h i; because there the bonding of the 14 bricks works for only 7, that is the first weak place after the first side of the pilaster, so the arch must break along the perpendicular line, as shown at r i.
Rolling made harder by oblique lines across the axis
The motion of the roller is rendered the more difficult, the more the line of the moving body upon it crosses the straightness of the roller's axis at more varied angles. A load whose path runs square to the axis rolls most easily; one that runs obliquely resists.
A shaft turns uniformly only about its own centre-line
It is impossible for the beam-roller (subbio) to make a uniform revolution if the central line of its poles does not lie on the same central line as the roller itself. Leonardo defers the demonstration, promising it will be proved 'in its place'.