Ring-Pipes Bisected by Their Diameter
How the diameter divides the water in an annular pipe into equal or unequal parts
Still under 'Water instruments,' the page presents four numbered propositions on ring-shaped (annular) pipes, each paired with a circle-and-diameter diagram in the right margin lettered a-c-d-b, e-g-h-f and a-d-c-e-b. Leonardo argues that a pipe of uniform width bent into a ring is always divided into two equal parts of water by its diameter, whatever its obliquity, and that even a ring split at the top and offset by a transverse shift is still bisected by that diameter. In the fourth case, however, a top-split ring set obliquely divides its water into unequal parts, the inequality growing as the ring is tilted further. The reasoning treats the water instrument as a geometrical figure whose diameter partitions the enclosed volume.
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A uniform ring-pipe holds water bisected by its diameter
A pipe of uniform width bent into an annular figure always has its diameter as the divider of the enclosed water into two equal parts (labels a, c, d, b). The same holds however the ring is placed.
The diameter divides equally at any obliquity
The water enclosed in a uniform annular pipe is always divided into equal halves by the diameter of that pipe, and this holds at whatever obliquity it is situated (labels e, g, h, f).
A top-split ring set obliquely divides its water unequally
If a top-split annular pipe is laid obliquely, the enclosed water is divided into unequal parts by its diameter (labels a, d, c, e, b), and the inequality is the greater the further the ring is tilted from level. When the split ring is only offset by a transverse motion, however, the diameter still divides the water into two equal parts.