Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. Mathematics A circular arc of 90°; one fourth of the circumference of a circle.
 n. Mathematics The plane area bounded by such an arc and two perpendicular radii.
 n. Mathematics Any of the four areas into which a plane is divided by the reference axes in a Cartesian coordinate system, designated first, second, third, and fourth, counting counterclockwise from the area in which both coordinates are positive.
 n. A machine part or other mechanical device that is shaped like a quarter circle.
 n. An early instrument for measuring altitude of celestial bodies, consisting of a 90° graduated arc with a movable radius for measuring angles.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. One of the four sections made by dividing an area with two perpendicular lines.
 n. The four regions of the Cartesian plane bounded by the xaxis and yaxis.
 n. One fourth of a circle or disc; a sector with an angle of 90°.
 n. A measuring device with a graduated arc of 90° used in locating an altitude.
from the GNU version of the Collaborative International Dictionary of English
 n. The fourth part; the quarter.
 n. The quarter of a circle, or of the circumference of a circle, an arc of 90°, or one subtending a right angle at the center.
 n. One of the four parts into which a plane is divided by the coördinate axes. The upper righthand part is the first quadrant; the upper lefthand part the second; the lower lefthand part the third; and the lower righthand part the fourth quadrant.
 n. An instrument for measuring altitudes, variously constructed and mounted for different specific uses in astronomy, surveying, gunnery, etc., consisting commonly of a graduated arc of 90°, with an index or vernier, and either plain or telescopic sights, and usually having a plumb line or spirit level for fixing the vertical or horizontal direction.
from The Century Dictionary and Cyclopedia
 n. The fourth part; the quarter.
 n. The quarter of a circle; the arc of a circle containing 90°; also, the figure included between this arc and two radii drawn from the center to each extremity; the division of angular magnitude from zero to a right angle, or 90°.
 n. An astronomical instrument for measuring altitudes, of ancient origin, and consisting of a graduated arc of 90°, with a movable radius carrying sights, or the quadrant, carrying sights, might turn about a fixed radius.
 n. An instrument of navigation, for measuring the altitude of the sun, distinctively called the reflecting quadrant.
 n. An instrument used in giving a cannon or mortar the angle of elevation necessary to the desired range.
 n. In electricity, a name suggested for the practical unit of selfinduction. Its value is 10 centimeters.
 Foursided; square.
 Square.
 n. In embryology, one of the four blastomeres or cleavagecells in the fourcell stage of the ovum.
 n. A square or one of its sides.
 n. An oscillating arm attached to a spinningmule to give a proper rotation to the spindles during the winding of the yarn on the cop.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a measuring instrument for measuring altitude of heavenly bodies
 n. a quarter of the circumference of a circle
 n. the area enclosed by two perpendicular radii of a circle
 n. any of the four areas into which a plane is divided by two orthogonal coordinate axes
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

As we all know, the Delta quadrant is the setting of Voyager, a series best not spoken of.

You will notice that the upperquadrant is the only light that does not flash red.

Basing an intellectual circle around the quadrant is like rejecting the science, technology and ideas of democracy and equality of opportunity that arose through that age, stating a clear preference for the Old Ways.

This represents four different sectors of the mouth and as each quadrant is cleaned, the screen shows how good or bad a job is being done and when to move on.
The Toothbrush That Teaches You How To Brush Your Teeth  Impact Lab

Because of the hurricane's counterclockwise rotation, the forwardright quadrant is considered "bad."

Choose the Anchor quadrant from the 10 options to set the base location.

And in the warped world of religion the fact that a quadrant neither looks like nor is a circle has never stopped believers from going on believing that their quadrant is a circle nor trying to make us sceptics believe that their quadrant is a circle despite us seeing something else.

And, two, oftentimes, not only the right front quadrant, which is what we're in right now, but the rear quadrant as well.

We've got these tornado watches that are posted  or one until 11: 00 this morning for the potential of seeing tornadoes swirling around the northern quadrant, which is typically the most destructive quadrant.

We fully expected the eye to pass just to the west of us, which would have put us in the right front advancing quadrant, which is where the storm surge occurs most.
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