Incommensurable
a state of deprivation or non-existence (as regards two kindred quantities) of a common unit, or, more strictly, a magnitude which cannot be measured by another, taken as unity. Two quantities of the same kind are incommensurable with respect to each other, when they have not a common unit-that is, when there is no quantity of the same kind so small that it is contained in both an exact number of times. Thus the diagonal and side of a square are incommensurable, for it has been shown that if we denote the side of the square by 1, the diagonal will be denoted by the square root of 2; but the square root of 2 is incommensurable with 1, because the square root of an imperfect square cannot be expressed in exact terms of 1.