Definition:Right Circular Cone/Similar Cones

Definition

Let $h_1$ and $h_2$ be the lengths of the axes of two right circular cones.

Let $d_1$ and $d_2$ be the lengths of the diameters of the bases of the two right circular cones.

Then the two right circular cones are similar if and only if:

$\dfrac {h_1} {h_2} = \dfrac {d_1} {d_2}$

In the words of Euclid:

Similar cones and cylinders are those in which the axes and the diameters of the bases are proportional.

(The Elements: Book $\text{XI}$: Definition $24$)