Two vessels draining water in changing proportion
From double to sevenfold: how outflow ratios shift as the vessels empty
A hydraulic-proportion problem illustrated by a small figure of two cylindrical vessels at the upper right. Two vessels of equal width are filled with water in a two-to-one ratio and drain through spouts at their base; Leonardo argues that the ratio of their outflows changes at every degree of time. Dividing the fall into 6 degrees for the smaller vessel and 12 for the larger, he reckons that when the smaller has dropped 5 degrees and the larger also 5, the smaller holds 1 degree of water while the larger holds 7 — a sevenfold proportion.
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Two equal-width vessels draining through basal spouts
Two vessels of equal width, filled with water in double proportion and pouring through spouts made at their lowest point, will at every degree of time change the degrees of proportion in the abundance of their outflows.
Outflow ratio shifts from double to sevenfold
If the water begins in double quantity, the outflow is at first double, one to the other, then varies at once. With the descents divided into 6 degrees in the smaller vessel and 12 in the larger, when the smaller has dropped 5 degrees and the larger 5, the smaller keeps 1 degree of water and the larger 7 — a sevenfold proportion.