Definition:Cylinder/Similar Cylinders

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Let $h_1$ and $h_2$ be the heights of two cylinders.

Let $d_1$ and $d_2$ be the diameters of the bases of the two cylinders.

Then the two cylinders 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 $24$)