The roots of numbers marked along a line
Four nested semicircles: d n as root 1, o m root 2, r t root 3, b c root 4
Four internally tangent semicircles rise over a common base line, cut by a line a b drawn from the middle of the greater portion to the angle of the lesser. Leonardo uses this to divide the lune c h d b a into parts equal to the portion a d c, and to 'verify the roots of numbers' along the line a b. The line crosses the midpoints of every semicircle sharing the angle at a, giving d n as the root of 1, o m the root of 2, r t the root of 3 and b c the root of 4.
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Verifying the roots of numbers on line a b
A heading announces a way to verify (re-prove) the roots of numbers on the line a b. The construction below reads successive square roots off as segments. The line is said to terminate the roots of all numbers, whole and fractional.
Dividing the lune and reading roots from the semicircles
Leonardo divides the lune c h d b a into parts equal to the portion a d c, knowing that a b h is double a d c. The line a b, from the middle of the greater portion b to the angle of the lesser portion a, cuts the midpoints of all semicircles sharing the angle at a. Along it he reads d n as the root of one, o m the root of 2, r t the root of 3 and b c the root of 4.