The Friction of Weights on Sloping Surfaces
How friction diminishes as the obliquity of the surface falls away, shown on quadrant diagrams
Under the heading 'The disposition of bodies subject to friction,' Leonardo studies how a weight resting on a sloping surface offers resistance that changes with the angle of the slope. Using quadrant diagrams divided into sectors, he reasons that as a body moves from steeper to gentler obliquities its frictional resistance is halved and halved again until, on the flat, both gravity and friction vanish. A worked example puts a four-pound weight's resistance at one pound, and follows it as the obliquity is progressively reduced.
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Friction is consumed as the slope flattens
The rubbing body a on the surface f g gives a weight equal to a quarter of its natural gravity; b has half of that, c a quarter of it, d an eighth, which in the motion from d to e is converted into nothing at the last obliquity, where friction reaches the straight line and every gravity together with the friction is destroyed.
A four-pound weight resolved into resistances
Note that reducing the gravity by reducing the obliquity where it rubs also reduces the power of the friction. Thus if a rubbed weight is four pounds, its friction resists with the power of one pound; at the middle obliquity c, halved, two pounds remain, of which the quarter is half a pound.
Quadrant divided into sectors
The construction is a quarter of a circle divided into four sectors together with a segment of a circular ring (annulus), used to lay out the successive obliquities along which the weight is imagined to slide.