Geometric construction of square and cube roots
A semicircle over a b c d yields the square root f d and cube root m d, after Euclid
A geometric construction, drawn as a semicircle over a base line with several labelled points and a rectangle at the right, serves to extract square and cube roots. Captions state that f d is the square root of the parallelepiped a b c d and m d its cube root as a cylinder. The longer note, described as a crossed-out diagram, gives the full rule: square the face a b c d by the last proposition of Euclid's second book, draw the circle c f q, and read off the square root f d and, by a compass transfer from d to n, the cube root m d.
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Square root f d and cube root m d of a b c d
Captions identify the results of the construction: f d is the square root of the parallelepiped a b c d, and m d is its cube root taken as a cylinder. A note adds that the circle o m p is not needed, since it only serves the space from d n to e m.
Rule for square and cube roots by a semicircle
Leonardo gives a rule to find the cube root of any rectangular solid or cylinder. Squaring the face a b c d by the last proposition of Euclid's second book fixes the midpoint e of the line c q; the circle c f q cut by the line d r at f gives the square root f d, and transferring the compass span from the angle d to the midpoint n locates the point m, so that m d is the cube root a b c d.