Definition of Ellipse
Definitions
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.
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.