Squaring the circle by twelve inscribed circles
Turning a given number of squares into another of equal value, and proving the great circle equals twelve small circles.
Leonardo sets out to convert a given number of squares (here 6) into any required number (15) of equal total value, invoking 'the last proposition of the second book' of Euclid's Elements. A large semicircle rises over a rectangle of twelve squares, each circumscribing a circle, from which he derives a square of equal value and argues that the greatest circle equals the twelve smallest circles. Through 'starred' circles, bi-angles and 72 curved 'portions' he demonstrates a duodecuple (twelvefold) proportionality between the largest and smallest circles.
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Making any number of squares of equal total value
From 6 given squares a b he proposes to make 15 squares S t of the same value, presently laid out as 15 parallelograms, using the last proposition of Euclid's Book II, shown at o upon the square L of the parallelograms m. What holds for squares, he adds, holds for circles and every other plane figure.
The great circle equals twelve inscribed circles
A rectangle c f g h of twelve squares, each holding a circle, yields a square a b c d of equal value; the greatest circle inscribed in it equals all twelve small circles, and its quadrature equals the largest rectilinear hexagon the great circle can contain.
Duodecuple proportionality of the circles
He states a twelvefold ('duodecuple') proportionality from the smallest to the greatest circle: removing the greatest portion n does as much as removing the twelve portions m, and the 12 portions of the smallest circle equal one of the six portions of the greatest.