Volume of Cone is Third of Cylinder on Same Base and of Same Height/Proof 2

Proof
Let the cone be of height $h$.

Let the area of the base of the cone be $A$.

From Volume of Cylinder, the volume of a cylinder of base $A$ and height $h$ is $A h$.

Let the cone be divided by planes parallel to its base each positioned some small distance $d$ apart.

Let $d$ be sufficiently small that they can be approximated to cylinders in shape.

Let there be $n$ of these small cylinders in total.

Let the volumes of each of these small cylinders be:
 * $v_1, v_2, v_3, \ldots, v_n$

starting from the base of the cone and working up.

We have that:
 * $v_k = d a_k$

where $a_n$ is the

Let the areas of the bases of each of these small cylinders be:
 * $a_1, a_2, a_3, \ldots, a_n$

starting from the base of the cone and working up.