Finding the volume enclosed by a sphere
Great circle 38 1/2 times diameter 7, then two thirds, gives 179 2/3
A pen circle split by a vertical diameter, marked 22 at the top, 7 at the center and 38 1/2 at the bottom. The note asks for the 'air' (volume) enclosed within a spherical body. Leonardo multiplies the area of the great circle, 38 1/2, by the diameter 7 to get 269 1/2, then takes two thirds of that number to reach 179 2/3 as the capacity of the sphere.
On this page
Volume of a sphere from its great circle and diameter
The bisected circle again represents the ball: the diameter marked 7, the great circle 22, and its area 38 1/2. Here the target is the interior volume, the 'air' the sphere shuts inside itself. The two-thirds step encodes the ratio of a sphere to the cylinder that would contain it.
Worked rule: (great-circle area x diameter) x 2/3
Leonardo multiplies the area enclosed in the greatest circle, 38 1/2, by the diameter, saying '7 times 38 1/2 makes 269 1/2'. He then takes two thirds of that number to obtain 179 2/3, which he names the capacity of the spherical body. The figures 22, 7 and 38 1/2 carry over from the surface rule on the facing pages.