Ellipse, an oval figure produced from the section of a cone by a plane which cuts both sides of it in an oblique direction. It may also be obtained by letting the shadow of a circle fall on a plane; or it may be drawn by driving two pins into a board to mark the foci, putting a loose loop of inelastic thread over them, and drawing the curve with a pencil placed inside the loop and stretched out as far as the loop will allow. Instruments to describe an ellipse are called ellipsographs or elliptographs. The foci of an ellipse are the given points around which another point is conceived to move in such a manner that the sum of their distances from it is always the same; the line thus described is an ellipse. The centre of an ellipse is the point which bisects the straight line between the foci. The distance of either focus from the centre is called the eccentricity. A straight line passing through the centre, and terminated both ways by the ellipse, is called a diameter. The diameter which passes through the foci is called the transverse axis, also the greater axis. The ellipse is the projection of a circle; the curve which is everywhere equally distant from the sum of the foci is an ellipse.

Kepler announced the law that planetary orbits are ellipses, and upon the three simple formulas which he laid down for the solution of this problem is based all that has been done since to determine the movements of the planets. The ellipse, and the ellipsoid, which is a solid figure all plane sections of which are ellipses or circles, enter largely into mechanical contrivances. The method given above of describing an ellipse is applied in machines to turn wood and other substances into elliptic forms. An instrument similar to the ellipto-graph is employed for engraving ellipses on metals, and for dividing these ellipses accurately, so as to give the perspective representation of a circle divided into equal parts.