Volume of Cone is Third of Cylinder on Same Base and of Same Height/Proof 2
In the words of Euclid:
Let $d$ be sufficiently small that they can be approximated to cylinders in shape.
Let there be $n$ of these small cylinders in total.
- $v_1, v_2, v_3, \ldots, v_n$
We have that:
- $v_k = d a_k$
where $a_n$ is the
- $a_1, a_2, a_3, \ldots, a_n$
The technique of finding the Volume of Solid of Revolution by dividing up the solid of revolution into many thin disks and approximating them to cylinders was devised by Johannes Kepler sometime around or after $1612$, reportedly on the occasion of his wedding in $1613$.
His inspiration was in the problem of finding the volume of wine barrels accurately.
He published his technique in his $1615$ work Nova Stereometria Doliorum Vinariorum (New Stereometry of Wine Barrels).