Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Mathematics Joining two nonadjacent vertices of a polygon.
 adj. Mathematics Joining two vertices of a polyhedron not in the same face.
 adj. Having a slanted or oblique direction.
 adj. Having oblique lines or markings.
 adj. Relating to or being the front left and back right feet or the front right and back left feet of a quadruped.
 n. Mathematics A diagonal line or plane.
 n. Something, such as a row, course, or part, that is arranged obliquely.
 n. A fabric woven with diagonal lines.
 n. A virgule.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Joining two nonadjacent vertices (of a polygon or polyhedron).
 adj. Having a slanted or oblique direction, lines or markings.
 adj. Pertaining to the front left and back right (or the front right and back left) legs of a quadruped.
 n. something arranged diagonally or obliquely
 n. a line or cut across a fabric that is not at right angles to a side of the fabric
 n. a punctuation mark used to separate related items of information
 n. a diagonal line or plane
 n. a line joining nonadjacent vertices of a polygon.
from the GNU version of the Collaborative International Dictionary of English
 adj. Joining two not adjacent angles of a quadrilateral or multilateral figure; running across from corner to corner; crossing at an angle with one of the sides.
 n. A right line drawn from one angle to another not adjacent, of a figure of four or more sides, and dividing it into two parts.
 n. A member, in a framed structure, running obliquely across a panel.
 n. A diagonal cloth; a kind of cloth having diagonal stripes, ridges, or welts made in the weaving.
from The Century Dictionary and Cyclopedia
 In geometry, extending, as a line, from one angle to another not adjacent, within any figure.
 Being in an oblique direction; lying obliquely.
 Marked by oblique lines: as, diagonal cloth.
 .
 A soft material used as a ground for embroidery, generally made very wide, and dyed in plain colors without pattern.
 A material for men's wear, especially for coats and waistcoats.
 n. A straight line drawn from one angle to or through another, not adjacent, in any plane or solid figure.
 n. Any oblique line.
 n. Specifically
 n. In chess, checkers, etc., a line of squares running diagonally across the board. See chess.
 n. Same as diagonal cloth, especially in the United States: a term introduced about 1875.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. (mathematics) a set of entries in a square matrix running diagonally either from the upper left to lower right entry or running from the upper right to lower left entry
 n. an oblique line of squares of the same color on a checkerboard
 n. a punctuation mark (/) used to separate related items of information
 adj. having an oblique or slanted direction
 n. (geometry) a straight line connecting any two vertices of a polygon that are not adjacent
 adj. connecting two nonadjacent corners of a plane figure or any two corners of a solid that are not in the same face
 n. a line or cut across a fabric that is not at right angles to a side of the fabric
Etymologies
Examples

No. 419: that the _red diagonal_ members represent the _saltire gules_ of St. Patrick, No. 421, and that the _narrow diagonal white_ lines are added in order to place this _saltire gules on a field argent_: that the

A square blanket, twelve feet in diagonal, is provided, (some were wont to cut off the corners, and make it circular;) in the centre a slit is effected, eighteen inches long; through this the mothernaked trooper introduces his head and neck, and so rides shielded from all weather, and in battle from many strokes (for he rolls it about his left arm); and not only dressed, but harnessed and draperied.
Life in Mexico, During a Residence of Two Years in That Country

First of all u must understant that the roads of Bucharest are already full of cars that make around 1.30 hours for a simple trip from a part of Bucharest in diagonal … At least!

The space itself is a gorgeous gallery, adjacent to a student center (where the panels and demos were held), and diagonal from a Bistro that very kindly opened its doors to host the portfolio reviews and be a general meeting destination throughout the weekend.

There is a strange volume to scenes viewed from on high: real places flatten into forms, space recedes in diagonal lines, and ground and horizon oscillate a magnetic field, one that both attracts and repels the eye.
Ballardian » Edward Burtynsky: Oil – A Ballardian Interpretation

I decided to use a variety of variegated threads  the quilting is going to be my basic flame meander which I tend to work in diagonal rows (approximately) anyway.

I purchased Aunt Millie's (Home style seeded Italian) because they were out of my regular brand (why the heck not its HFCS free) When I got home I wanted to make myself a sandwich, but to my surprise I found some mystery black stuff on my bread in diagonal slashes.
Searing Sword Of Schmutz Taints Aunt Millie's Bread Loaf  The Consumerist

From what I can figure, they typically work as follows: A strip of magnetic material to be used as a readhead is premagnetized along a direction diagonal from the direction the current will flow, as roughly illustrated below:

Dunlop specifies that the leeks or scallions should be cut on the bias  in diagonal slices; what Sichuanese cuisine vividly refers to as "horse ear" slices.

Below that, on the diagonal, is the African American and Vietnamese immigrantheavy Tenderloin (above Market St.) and the South of Market warehouse district (below Market).
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