ellipse

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. A plane curve, especially:
2. n. A conic section whose plane is not parallel to the axis, base, or generatrix of the intersected cone.
3. n. The locus of points for which the sum of the distances from each point to two fixed points is equal.
4. n. Ellipsis.

Century Dictionary and Cyclopedia

1. 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. It is a conic section (see conic) formed by the intersection of a cone by a plane which cuts obliquely the axis and the opposite sides of the cone. The ellipse is a conic which does not extend to infinity, and whose intersections with the line at infinity are imaginary. Every ellipse has a center, which is a point such that it bisects every chord passing through it. Such chords are called diameters of the ellipse. A pair of conjugate diameters bisect, each of them, all chords parallel to the other. The longest diameter is called the transverse axis, also the latus transversum; it passes through the foci. The shortest diameter is called the conjugate axis. The extremities of the transverse axis are called the vertices. (See conic, eccentricity, angle.) An ellipse may also be regarded as a flattened circle—that is, as a circle all the chords of which parallel to a given chord have been shortened in a fixed ratio by cutting off equal lengths from the two extremities. The two lines from the foci to any point of an ellipse make equal angles with the tangent at that point. To construct an ellipse, assume any line whatever, AB, to be what is called the latus rectum. At its extremity erect the perpendicular AD of any length, called the latus transversum (transverse axis). Connect BD, and complete the rectangle DABK. From any point L, on the line AD, erect the perpendicular LZ, cutting BK in Z and BD in H. Draw a line HG, completing the rectangle ALHG. There are now two points, E and E′ , on the line LZ, such that the square on LE or LE′ is equal to the rectangle ALHG. The locus of all such points, found by taking L at different places on the line AD, forms an ellipse. [The name ellipse in its Greek form was given to the curve, which had been previously called the section of the acute-angled cone, by Apollonius of Perga, called by the Greeks “the great geometer.” The participle ἐλλείπων, “falling short,” had long been technically applied to a rectangle one of whose sides coincides with a part of a given line (see Euclid, VI. 27). So παραβάλλειν and ύπερβάλλειν, (Euclid, VI. 28, 29) were said of a rectangle whose side extends just as far and overlaps respectively the extremity of a given line. Apollonius first defined the conic sections by plane constructions, using the latus rectum and latus transversum (transverse axis), as above. The ellipse was so called by him because, since the point L lies between A and D, the rectangle ALHG “falls short” of the latus rectum AB. In the case of the hyperbola L lies either to the left of A or to the right of D, and the rectangle ALHG “overlaps” the latus rectum. In the case of the parabola there is no latus transversum, but the line BK extends to infinty, and the rectangle equal to the square of the ordinate has the latus rectum for one side.]

Wiktionary

1. n. geometry 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.
2. v. grammar To remove from a phrase a word which is grammatically needed, but which is clearly understood without having to be stated.

GNU Webster's 1913

1. n. (Geom.) 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.
2. n. (Gram.) Omission. See Ellipsis.
3. n. The elliptical orbit of a planet.

WordNet 3.0

1. n. a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it