ellipse definitions and example sentences on Wordnik

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Definitions (13)

American Heritage Dictionary (4)

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

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Century Dictionary (7)

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.]
Cubical ellipse. See cubical.
Focal ellipse. See focal.

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The orbit is definitely elliptical, with an eccentricity of 0.51, so that the long axis of the ellipse is approximately 15 per cent longer than the short axis. — A Case Of Conscience
We must also remember that the ellipse is an oblique projection of a circle, or an oblique section of a cone. — The Theory and Practice of Perspective
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 Story of the Heavens
Now, using the Selection Tool (V), drag the ellipse to the bottom of the rectangle until you see 2 green smart guides indicating the ellipse is alligned in the bottom center. — Pixel2Life.com: Latest 20 Tutorials
At the far point of the ellipse was a small dot. — The Dig

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Allen's Synonyms and Antonyms

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ellipsis · hyperbola · semicircle · parallelogram · rectangle · parabola

Etymologies (2)

American Heritage Dictionary (1)

French, from Latin ellīpsis, from Greek elleipsis, a falling short, ellipse, from elleipein, to fall short (from the relationship between the line joining the vertices of a conic and the line through the focus and parallel to the directrix of a conic) : en-, in; see en-² + leipein, to leave; see leik^w- in Indo-European roots.

Century Dictionary (1)

= D. Swedish ellips = G. Danish ellipse = French ellipse = Spanish elipse = Portuguese ellipse = Italian ellisse, elisse, ellipse, from Latin ellipsis, a want, defect, an ellipse, from Greek ε=λλειψις, a leaving out, ellipsis in grammar, a falling short, the conic section ellipse (see def.), from ἐλλείπειν, leave in, leave behind, omit, intransitive fall short, from ἐν, in, + λείπειν, leave. Cf. ellipsis.

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