Definition:Quadrilateral/Rectangle
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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
- 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