hyperbola

[Low. Lat. hyperbola, from Gr. hyperbole a throwing beyond; exce ; the conic section, hyperbola, so named because the angle which its plane forms with the base of the cone is greater than in the case of the parabola.] Math .: One of the three conic sections. It is a plane curve of such a form that if from any point two straight lines be drawn to two given fixed points, the exce of the straight line drawn to one of the points above the other will always be equal. The two points are called the foci. If a cone be cut by a plane in such a direction that the plane cuts the base at a greater angle than the side of the cone makes, a hyperbola will be generated. If two cones, A and B, placed apex to apex, be both cut by a plane ab, cd, the hyperbolas, xby, pcq, will be generated with their convexities turned to each other. If a straight line be drawn from the foci and then bisected, the point of bisection is called its center. The IMG:content-1409.jpg:[graphic] IMG:content-1410.jpg:[merged small][merged small][ocr errors][merged small] IMG:content-1411.jpg:[blocks in formation] hyperbole [Eng. 1. Geom.: Of or pertaining to the hyperbola; of the nature of an hyperbola. "Of an hyperbolical or a parabolical figure."-Ray: On the Creation. 2. Rhet .: Of the nature of or containing hyperbole; exaggerating or diminishing beyond the truth; exaggerated. "Insipid and hyperbolical adulation." -Macaulay : Hist. Eng ., ch. vii. hyperbolic-arc, s. Geom.: An arc of the hyperbola. hyperbolic-conoid, s. cathartic.] 2244