Weights on Angled Cords, and Why Winding Rivers Silt Up
A level beam gives equal obliquity; a weight splits its load in proportion to the angles it makes
Under the heading 'Gravity and water,' Leonardo sets weight-on-cord studies beside a note on rivers. He argues that if a beam hangs level from two cords of different length, their obliquities are equal, and that a weight hung at the angle of a cord divides its load between the cords in proportion to the angles they make with the weight's central line (labels a, b, c, d, f, g). Between these comes a passage on rivers: the more a river winds and lengthens, the slower it runs and the sooner it drops its sediment. The right margin carries several beam-and-cord figures and a small weight on a cord.
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A level beam makes its two cords equally oblique
If two cords of different length, converging or diverging, descend to support the ends of a beam, and the beam lies level, then the obliquities of the two cords are equal to one another.
A winding river runs slow and silts up soonest
The river that lengthens most through long transverse windings fills soonest with material, because the water that is slowed most discharges soonest what it carries. Hence the more tortuous the river, the slower and more clogged it becomes.
A weight divides its load in proportion to the cord angles
A heavy body g hung at the angle b a c of the cord divides the weight between the cords as the angles included between the cords and the weight's central line. Cutting the angle by line f b and dropping the perpendicular d a, the ratio d f to d b gives the ratio of the loads on cords b a and f a.