Four cases of widened and narrowed river banks
Simple and compound effects when banks widen or close on one or both sides
Four short notes, each tagged 'simple' or 'compound' and paired with a marginal figure, classify how a river responds to changes in its banks. If the widenings of a channel are not opposite one another the river's depth becomes uneven ('lame'); if it is narrowed on one side alone a swift semi-columnar wave forms and its eddies undermine that narrowed bank. When both banks close equally and opposite each other the columnar waves intersect and then fall to strike and ruin the banks; and if the two narrowings are at different levels the upper columnar wave can pass beneath the lower one. Leonardo notes that the commentary must fix the distances between the narrowings and their widths.
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Compound: widenings not set opposite make the depth uneven
If the widenings of the channel are not made facing one another, then the depth of that river becomes 'lame' (uneven).
Simple: a one-sided narrowing raises a semi-columnar wave
If the river's course is narrowed on one of its sides, a semi-columnar wave is generated that runs swift; the eddies formed between the narrowed bank and the columnar wave undermine and ruin that narrowed bank.
Compound: matched narrowings make the waves intersect
If the banks are equally narrowed on both sides of the current and directly opposite, the columnar waves intersect; after that intersection they descend to strike and ruin their own banks.
Compound: unequal narrowings let one wave pass beneath the other
But if the narrowings of the bank are set lower one than the other, the upper columnar wave can enter beneath the lower columnar one. The commentary must fix the distances between the narrowings and their widths.