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Euclid's Elements, Book XI, Definitions 21 through 23
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Definition 21

When a rectangular parallelogram with one side of those about the right angle remains fixed is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a cylinder.

Definition 22

The axis of the cylinder is the straight line which remains fixed and about which the parallelogram is turned.

Definition 23

And the bases are the circles described by the two sides opposite to one another which are carried round.

Guide

Rectangle ABEC is rotated around the side AC to produce a cylinder. Its axis is AC and it has two circles for bases.

The concept of cylinder has been generalized since Euclid’s time as have so many ancient mathematical concepts. Euclid’s cylinders are right, circular cylinders since their axes are at right angles to their bases and their bases are circles.

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