Mensuration of a Circular Ring
Diameter, circumference and areas of a round structure and its surrounding wall
The verso is a mensuration of a circular ring or annular structure that 'turns within 40 braccia.' Leonardo records its inner diameter as 12 8/11 braccia, adds a surrounding wall 2 braccia thick to give an outer diameter of 16 8/11 braccia, and computes the circumference (52 2/7 braccia) and three areas: the inner circle (127 3/11 sq. braccia), the outer circle (218 50/77 sq. braccia), and the wall between them (91 3/8 sq. braccia). The left half carries the labelled ring diagram; the right half is filled with the supporting column arithmetic, and two smaller ringed figures appear below.
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Areas of a circular ring and its wall
A round figure turning within 40 braccia has inner diameter 12 8/11 braccia; a wall 2 braccia thick makes the outer diameter 16 8/11 braccia. Its circumference is 52 2/7 braccia, the inner circle 127 3/11 square braccia, the outer 218 50/77, and the surrounding wall 91 3/8 square braccia.
Column computations for the ring
The right half is filled with columns of fractional arithmetic supporting the ring measures, working with the recurring quantities 16 8/11, 52 4/7 and 127 3/11 to derive circumferences and areas.