Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A plane curve, especially:
 n. A conic section whose plane is not parallel to the axis, base, or generatrix of the intersected cone.
 n. The locus of points for which the sum of the distances from each point to two fixed points is equal.
 n. Ellipsis.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A closed curve, the locus of a point such that the sum of the distances from that point to two other fixed points (called the foci of the ellipse) is constant; equivalently, the conic section that is the intersection of a cone with a plane that does not intersect the base of the cone.
 v. To remove from a phrase a word which is grammatically needed, but which is clearly understood without having to be stated.
from the GNU version of the Collaborative International Dictionary of English
 n. An oval or oblong figure, bounded by a regular curve, which corresponds to an oblique projection of a circle, or an oblique section of a cone through its opposite sides. The greatest diameter of the ellipse is the major axis, and the least diameter is the minor axis. See Conic section, under conic, and cf. focus.
 n. Omission. See Ellipsis.
 n. The elliptical orbit of a planet.
from The Century Dictionary and Cyclopedia
 n. In geometry, a plane curve such that the sums of the distances of each point in its periphery from two fixed points, the foci, are equal.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

If the foci are identical with each other, the ellipse is a circle; if the two foci are distinct from each other, the ellipse looks like a squashed or elongated circle.

These foci are equidistant from the centre of the ellipse, which is formed as follows: Two pins are driven in on the major axis to represent the foci A and B, Figure 75, and around these pins a loop of fine twine is passed; a pencil point, C, is then placed in the loop and pulled outwards, to take up the slack of the twine.

Thus, if we correct the observed motion of the planets for these two influences, and if Newtons theory be strictly correct, we ought to obtain for the orbit of the planet an ellipse, which is fixed with reference to the fixed stars.

In the middle of the ellipse, which is 895x741 feet, stands the obelisk,

If, on the contrary, it is displaced, it will in the year describe a minute ellipse, which is only the reflection, the perspective in miniature, of the revolution of our planet round the Sun.

Two pins are stuck through a sheet of paper on a board, the point of a pencil is inserted in a loop of string which passes over the pins, and as the pencil is moved round in such a way as to keep the string stretched, that beautiful curve known as the ellipse is delineated, while the positions of the pins indicate the two foci of the curve.

In the first place, we observe that the ellipse is a plane curve; that is to say, each planet must, in the course of its long journey, confine its movements to one plane.

The ellipse is a curve which can be readily constructed.

Newton was REALLY SMART it is NOT obvious that the ellipse is the solution to the differential equations

By measuring the position angle of the companion star relative to the primary and the angler distance between the two stars over time, the ellipse, called the apparent ellipse, which is the orbit of the secondary in respect to the primary, can be plotted out.
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