Squaring the Circle by Cone, Cylinder and Sphere
Solids unrolled by motion to rectify the circumference and construct the equal triangle
This folio applies rolling solids to the squaring of the circle. A cone whose base-diameter is quadruple its axis has a surface half its base; the whole revolution of a cylinder describes a rectangle equal to the cylinder's circular base. Under 'Squaring of the circle', the revolution of a cone's base traces a straight line equal to its circumference, on which the axis is set perpendicular to form a triangle equal to a circle. A final note treats the sphere's revolution describing the periphery of its greatest circle; marginal figures show a cone, an unrolled cylinder, and four concentric circles with orthogonal diameters.
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Cone and cylinder surfaces from motion
The cone whose base-diameter is quadruple its axis has a surface half its base; lending it as much surface again yields the cylinder, likewise with diameter quadruple its axis. The entire revolution of that cylinder describes a rectangular quadrilateral equal to the cylinder's circular base, and the cylinder's curved surface is worth as much as its base.
Squaring the circle by the cone's revolution
The whole revolution of the base of a cone whose base is double its axis describes a straight line equal to its circumference. On this line the cone's axis is set perpendicular, and at its summit lies the vertex of a triangle worth the surface of a circle equal to the cone's base. A closing note adds that the sphere's revolution by straight motion describes the periphery of its greatest circle.