Archimedes proved Euclid
In modern terminology, the area of a plane figure is proportional to the square of any of its linear dimensions, 



A
∝

L

2




{\displaystyle A\propto L^{2}}

, and the volume of a solid to the cube, 



V
∝

L

3




{\displaystyle V\propto L^{3}}

. Euclid proved these results in various special cases such as the area of a circle and the volume of a parallelepipedal solid. Euclid determined some, but not all, of the relevant constants of proportionality. E.g., it was his successor Archimedes who proved that a sphere has 2/3 the volume of the circumscribing cylinder.
