Quadrature of the circle with bi-angles and inscribed polygons
Lunes, curvilinear hexagons and octagons, and the triangle as least figure in a circle
The leaf is filled with circular constructions for squaring the circle: bi-angles (lune-like curved figures) are shown worth the greatest portions of the greatest circle, and double circles carry curvilinear hexagons and octagons whose bi-angles equal six and eight of those portions. In a triple circle the middle circle is worth a quarter of the whole, and a long column argues that the triangle is the least surface inscribable in a circle, the square the second, with many-sided figures growing as their sides increase. Further notes seek a curved-sided triangle equal to a circle and divide each bi-angular surface into four equal parts.
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Bi-angles worth the greatest portions of the circle
The greatest bi-angles equal the four greatest portions of the greatest circle, and the remainder equals its greatest square. Removing half the bi-angles removes half that square, and the two-feathered (dipennato) figure plus the middle square remains a square equal to the greatest square of the circle.
Curvilinear hexagon and octagon in double circles
In a double circle a curvilinear hexagon's six bi-angles equal the six greatest portions of the greatest circle; in another, a curvilinear octagon's eight bi-angles equal the eight greatest portions.
The triangle as least surface in a circle
The smallest surface that can be made inside a circle is the triangle, and the second is the square; the least number of portions drawable from a circle is three. The many-sided surfaces tangent to the circumference grow as their number of sides grows.
A curved-sided triangle equal to a circle
Above a semicircle Leonardo sets the problem: let a curved-sided triangle be given equal to a circle.
Portions halved and quartered; the numbers 12, 6, 3
In a triple circle the middle circle is worth a quarter of the greatest circle and the remainder three quarters, from which three quarters of the greatest portions are drawn. Three figures beside are marked with the numbers 12, 6, 3.