The lenticular solid is one third of its cylinder
A double cone within a cylinder, with a volume proof
The folio shows a double cone set within a cylinder, together with a cross-section of the same, and states a volume theorem: every lenticular body is one third of its cylinder. Treating the lenticular body as two cones joined base to base with their apexes opposite, and taking each cone as one third of its cylinder, Leonardo argues that the two cylinders together lose a third of their whole, so that the lenticular solid equals one third of the total.
On this page
Double cone within a cylinder
The figure sets a double cone (bicone) inside a cylinder and shows a cross-section of the same. It is the drawing that accompanies the volume argument set out below.
Proof that the lenticular body is one third of its cylinder
Leonardo reasons that since every cone is one third of its cylinder, and the lenticular body is two cones with bases touching and apexes opposite, each half is a third of its own cylinder. Joined together, the cylinders lose a third of their whole in forming the lenticular solid, which is therefore one third of the total.
