Quadrature studies: lunules, biangles and a cross
Numbered figures (first to fifth) equating curved areas with squares
A continuation of the quadrature studies, presenting numbered figures (first through fifth) in which arrangements of four lunules and 'biangles' around a circle — drawn so they resemble four-petalled rosettes — are shown to equal a square. In the first figure, removing the value of the four lunules and the four greatest portions of the circle leaves a square worth half the greatest square of the circle. Leonardo states rules for adding and subtracting squarable and unsquarable areas, and closes with a 'conception': if you remove the half from a whole, the whole returns to its half.
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First figure: square equal to circle minus four lunules
It is worth the greatest square of the greatest circle, from which, taking away the value of the four lunules and the four greatest portions of the greatest circle, there remains a square worth half the value of that greatest square of the greatest circle.
Fifth figure: four biangles equal four greatest portions
Fifth. Squarable. Here the four biangles together with their adjoining parts are worth the four greatest portions of the greatest circle.
A cross squarable in itself
The cross in the middle is squarable in itself, and the remainder is worth the fifth figure above.
Rules for subtracting squarable and unsquarable areas
Take a squarable part from an unsquarable whole and the remainder is unsquarable. Take an unsquarable part from an unsquarable whole and the remainder is squarable.
Conception: removing the half returns the whole to its half
Conception: if you remove the half from a whole, that whole returns to its half.