TRANSCENDENTAL

In Algebra, a term applied to any quantity which cannot be represented by an algebraic equation of a finite number of terms with determinate indices. Such quantities include all exponential and logarithmic expre ions and trigonometrical lines in terms of the arc. Thus a*, z*, log. z, tan. x, Sec., are transcendental exp res ions and; any equation into which such expre ions enter i» called a transcendental equation, and any curve defined by such an equation is called a transcendental curve. But by transcendental equations are sometimes meant such differential equations as can only bo integrated by means of curves, logarithms, or series. Trans' i:\i.kntal. A word used by German philosophers to expre that which transcends or goes beyond the limits of actual experience. This general meaning is somewhat restricted by Kant, who draws a distinction between the transcendental and the transcendent. The transcendent;.!he defines to be that which, though it could never be [s. 1273]