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A rectangle is a quadrilateral all of whose angles are equal to a right angle, and whose sides may or may not all be the same length.


In the words of Euclid:

Any rectangular parallelogram is said to be contained by the two straight lines containing the right angle.

(The Elements: Book $\text{II}$: Definition $1$)

Also see

Euclid, in Book $\text{II}$ Definition $1$: Containment of Rectangle, refers to this as a rectangular parallelogram.

Euclid's Definitions

In the words of Euclid:

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.

(The Elements: Book $\text{I}$: Definition $22$)