Parabola: definitions and examples of parabola

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noun A plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the cone or by the locus of points equidistant from a fixed line and a fixed point not on the line.

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Same as parabole. Whensoeuer by your similitude ye will seeme to teach any moralitie or good lesson by speeches misticall and darke, or farre fette, vnder a sence metaphoricall applying one natural thing to another, or one case to another, inferring by them a like consequence in other cases, the Greekes call it Parabola. Puttenham,Arte of Eng. Poesie, p. 205.
A curve commonly defined as the intersection of a cone with a Plane parallel with its side. The name is derived from the following property. Let the figure represent the cone. Let ABG be the triangle through the axis of the cone. Let DE be a line perpendicular to this triangle, cutting BG in H. Let the cone be cut by a plane through DE parallel to AG, so that the intersection with the cone will be the curve called the parabola. Let Z be the point where this curve cuts AB. Then the line ZH is called by Apollonius the diameter of the parabola, or the principal diameter, or the diameter from generation; it is now called the axis. From Z draw ZT at right angles to ZH and in the plane of ZH and AB, of such a length as to make ZT: ZA: BG: A B. AG. This line ZT is called the latus rectum; it is now also called the parameter. Now take any point whatever, as K, on the curve. From it draw KL parallel to DE meeting the diameter in L. ZL is called the abscissa. If now, on ZL as a base, we erect a rectangle equal in area to the square on KL, the other side of this rectangle may be precisely superposed upon the latus rectum, ZT. This property constitutes the best practical definition of the parabola. If a similar construction were made in the case of the ellipse, the side of the rectangle would fall short of the latus rectum; in the case of the hyperbola, would surpass it. The modern scientific definition of the parabola is that it is that plane curve of the second order which is tangent to the line at infinity. The parabola is also frequently defined as the curve which is everywhere equally distant from a fixed point called its focus, and from a fixed line called its directrix. The normal to a parabola at every point on the curve bisects the angle between the line parallel to the axis and the line to the focus. See also cuts under conic.
By extension, any algebraical curve, or branch of a curve, having the line at infinity as a real tangent. Such a curve runs off to infinity without approximating to an asymptote. If the branch has an asymptote at one end but not at the other, it is not commonly termed a parabola.

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This parabola is the curve of maximum moments for a travelling load uniform per ft. run. — Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3 "Brescia" to "Bulgaria"
A similar difficulty takes place in figuring specula for telescopes; the parabola is the surface which separates the hyperbolic from the elliptic figure, and is the most difficult to form. — On the Economy of Machinery and Manufactures
"The properties of the spiral, and the quadrature of the parabola were added to ancient geometry by Archimedes, the last being a great step in the progress of the science, since it was the first curvilineal space legitimately squared." — The Old Roman World, : the Grandeur and Failure of Its Civilization.
The focus of the parabola is here for the first time indicated, a circumstance which has escaped the notice of scientific historians.] 45. — The Private Diary of Dr. John Dee And the Catalog of His Library of Manuscripts
The axis of a parabola is along the line — LearnHub Activities

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parabola

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