[dahy-ag-uh-nl, -ag-nl]
connecting two nonadjacent angles or vertices of a polygon or polyhedron, as a straight line.
extending from one edge of a solid figure to an opposite edge, as a plane.
having an oblique direction.
having oblique lines, ridges, markings, etc.
a diagonal line or plane.
a diagonal row, part, pattern, etc.
Manège. (of a horse at a trot) the foreleg and the hind leg, diagonally opposite, which move forward simultaneously.
Mathematics. a set of entries in a square matrix running either from upper left to lower right (main diagonal or principal diagonal) or lower left to upper right (secondary diagonal)
Chess. one of the oblique lines of squares on a chessboard: He advanced his bishop along the open diagonal.

1535–45; < Latin diagōnālis < Greek diagṓn(ios) from angle to angle (see dia-, -gon) + Latin -ālis -al1

diagonally, adverb
nondiagonal, adjective, noun
nondiagonally, adverb
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
diagonal (daɪˈæɡənəl)
1.  maths connecting any two vertices that in a polygon are not adjacent and in a polyhedron are not in the same face
2.  slanting; oblique
3.  marked with slanting lines or patterns
4.  maths a diagonal line or plane
5.  chess any oblique row of squares of the same colour
6.  cloth marked or woven with slanting lines or patterns
7.  something put, set, or drawn obliquely
8.  another name for solidus
9.  one front leg and the hind leg on the opposite side of a horse, which are on the ground together when the horse is trotting
[C16: from Latin diagōnālis, from Greek diagōnios, from dia- + gōnia angle]

Collins English Dictionary - Complete & Unabridged 10th Edition
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Word Origin & History

1540s, from M.Fr. diagonal, from L. diagonalis, from diagonus "slanting line," from Gk. diagonios "from angle to angle," from dia- "across" + gonia "angle," related to gony "knee" (see knee). Related: Diagonally.
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Science Dictionary
diagonal   (dī-āg'ə-nəl)  Pronunciation Key 
Adjective   Connecting two nonadjacent corners in a polygon or two nonadjacent corners in a polyhedron that do not lie in the same face.

Noun   A diagonal line segment.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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Example sentences
He decided on the diagonally pleated design shown here.
So they turned aside, perhaps a hundred paces from the dockyard into a path
  which led diagonally across a field, to a pine wood.
There was a slight breeze from the southeast, which blew diagonally across my
  path towards the antelopes.
Yet when you insert a third polarizer between the two, oriented diagonally,
  then some photons make it through.
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