Why a River Erodes Its Bed and Banks
Natural motion seeks a straight course; changes of slope and width make the current break its channel
A full page of text (no drawing) argues that every natural, continuous motion tries to keep its course along the line of its beginning, and that rivers therefore fight and consume whatever opposes the straightness of their flow. Leonardo reasons that a perfectly straight channel of equal width, depth, and slope would let the water steadily gain speed. Because real rivers vary in slope and width, the current speeds up and deepens where the bed narrows and slows where it widens. Seeking a straight, ever-faster course, the water finds wider and deeper stretches, slows, and so breaks the bottom and the banks.
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Variety of slope and width makes a river scour its channel
In a straight channel of equal width, depth, and slope the water would gain a degree of velocity at every degree of motion. Because real rivers vary, the current deepens where it narrows and slows where it widens; seeking a straight and ever-faster course, on reaching wider and deeper stretches it slows and breaks the bottom and the banks.