ELLIPSE (Lat. ellipsis, from Gr. elleikis, omission), a plane curve of such a form that, if from any point in it two straight lines be drawn to two given fixed points, the. sum of these straight lines will always be the same. The ellipse is a species of conic section (q.v.), and is obtained by a plane which cuts all the ele ments of one nappe of a right circular cone. Projectively considered, an ellipse is a conic which cuts the line of infinity in two distinct imaginary points. If these are the two circular points, the ellipse becomes a circle. These two fixed points are called the foci. In the ellipse AB CD E and F are the foci. If a straight line (E Q F) be drawn joining the foci, and be then bisected, the point of bisection is called the centre. The distance from the centre to either focus (E Q or Q F) is called the linear eccentricity. The straight line (G Q H), drawn through the centre and terminated both ways by the curve, is called the diameter. Its vertices are G and H. The diameter A C, which passes through the foci, is called the major axis; the points in which it meets the curve (A and C), •the principal vertices. The diameter (B D), at right angles to the major axis, is called the minor axis. Practically, a
tolerably accurate ellipse may be drawn on paper by sticking two pins in it to represent the foci, putting over these a bit of thread knotted together at the ends, inserting a pencil in the loop, and pulling the string tight as the figure is described, The importance of the ellipse arises from the fact that the planets move in elliptical orbits, the sun being in one of the foci—a fact which Kepler was the first to discover.
The equation to an ellipse, referred to its centre as origin, and to its major and minor axes as rectangular axes, is — -}--- where a and a are the semi-major al and semi-minor axes respectively. From this equation it may be shown, by the integral cal culus, that the area of an ellipse is equal to r ab; or is got by multiplying the product of the semi-major and semi-minor axes by 3.1416. It may also be shown that the length of the cir cumference of an ellipse is got by multiplying the major axis by the quantity \ /1.3\ /1.3.5) 2e6 \2/ 1 \2.4/ 3 ‘2.4.6 5 ba The eccentricity e, is = — and the ellipticity is the ratio a—b to a. See GEOM ETRY and Conic SECTIONS.