Squaring the Circle: Sixteen Sectors Rectified
The circle equated to a rectangle of half-diameter by circumference; sectors spread and rearranged
Here Leonardo attempts the quadrature of the circle. A circle labelled e f is divided into sixteen sectors, which are then spread out and rectified so that the circle equals a rectangle made of half its diameter by its circumference. He describes imagining the circle resolved into almost infinite triangles that, laid along the base b d and halved in height, form the parallelogram a b c d exactly equal to the circle. He even proposes measuring a quarter of the circumference with a strip of reed or sorghum bark to derive a general rule.
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The circle equated to a rectangle of half-diameter by circumference
Leonardo states that the circle is similar to a rectangular parallelogram made from a quarter of its diameter and the whole of its circumference, or, as he restates it, from half the diameter and half the perimeter. The circle here is labelled e f.
Sixteen sectors spread out and rectified
The circle is divided into sixteen sectors, drawn spread apart and cut by a line parallel to the base, with the ends labelled a c and b d. This rectifies the curved circumference into a straight strip.
Quadrature by rearranging the sectors; measuring with a reed
Imagining the circle e f resolved into almost infinite triangles laid along the line touching their bases at b d, and taking half the height, Leonardo forms the parallelogram a b c d that is precisely equal to the circle. He adds that a quarter of the circumference may be measured with the bark of a reed or of sorghum in order to make a general rule.