Definition:Quadrilateral/Rectangle

Definition

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:

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 $22$)

Containment

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

• Both squares and oblongs are types of rectangle.

• Rectangle is Parallelogram: A rectangle is a parallelogram all of whose angles are equal to a right angle.

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

• Definition:Equiangular Polygon, of which the rectangle is an example.

• Results about rectangles can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): parallelogram
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): rectangle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): rectangle
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): isogon