Rolling a cone and a cylinder out onto a plane
The flat trace a solid leaves as it makes one full revolution on a surface
Leonardo studies the flat figures produced when a solid is rolled through one complete revolution on a plane. A cone whose base diameter is double its axis, rolling on its slant side, sweeps a triangle equal to the circle of its base, with axis equal to the cone's axis and base equal to the base's circumference. A cylinder whose diameter is quadruple its height leaves a quadrilateral trace equal to the circle of its base. The diagrams, labelled a b c, show the cone, the swept triangle, and the rolled cylinder.
On this page
Cone rolled on its slant sweeps a triangle equal to its base circle
The cone whose base diameter is double its axis, revolving on its straight slant side across a flat place, describes a triangle equal to the circle of its base. That triangle has axis equal to the cone's axis and base equal to the periphery of the cone's base.
Cylinder of quadruple diameter leaves a quadrilateral trace
A cylinder whose diameter is quadruple its height, revolving once on a flat place, leaves a quadrilateral trace equal to the circle of its base. Leonardo then reprises the cone whose base diameter is double its slant, whose surface equals the base circle.