The Swiftest Channel Section Is a Half Circle
Least contact with the bed gives the fastest water; the semicircle wins
This mirror-written red-chalk page, with a small semicircular (D-shaped) diagram drawn at the right, asks what cross-sectional figure lets a given quantity of water move fastest over a given slope of bed. Leonardo answers that it is the figure with the least contact with its bed, namely a half circle. A second note adds that water is swiftest where the portion turned back by striking the bed and sides is least in relation to the rest, which he identifies with the greater river.
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The half circle: the section of least contact
Asking which figure a fixed quantity of water should take, over the same obliquity of bed, to move as fast as possible, Leonardo answers the one with least contact with its bed, that is, a half circle. A semicircular diagram accompanies the note.
Least back-turning water is the swiftest
The water is faster in which the portion turned back by the percussion of the bed and the sides is of lesser quantity relative to the remainder. Leonardo identifies this swiftest case with the greater river.