EQUIDIFFERENT
, are such things as have equal differences, or arithmetically proportional. If the terms have all the same difference, viz, the 1st and 2d, the 2d and 3d, the 3d and 4th, &c, they are said to be Continually Equidifferent; as the numbers 3, 6, 9, 12, &c, where the common difference is 3. But if the several different couplets only have the same difference, as the 1st and 2d, the 3d and 4th, the 5th and 6th, &c, they are said to be Discretely Equidifferent; as the terms 3 and 6, 7 and 10, 9 and 12, &c. See ARITHMETICAL Progression and Proportion.
EQUILATERAL Figure, is one that has all its sides equal to each other. Such as the square, and all the regular figures or polygons, or a triangle that has all its sides equal. See Equiangular.
Equilateral Hyperbola, is that which has the two axes equal to each other, and every pair of conjugate diameters also equal to each other. The asymptotes also are at right angles to each other, and make each half a right angle with either axis. Also, such an hyperbola is equal to its opposite hyperbola, and likewise to its conjugate hyperbola; so that all the four conjugate hyperbolas are mutually equal to each other.
Moreover, as the 3d proportional to the two axes is the parameter, therefore in such a sigure, the parameter and two axes are all three equal to one another. Hence, as the general equation to hyperbolas is , where t is the transverse axis, c the conjugate, p the parameter, x the absciss, and y the ordinate; then making t, c, and p all equal, the equation, for the Equilateral Hyperbola, becomes ; differing from the equation of the circle only in the sign of the term x2, which in the circle is —.
