Commensurability

1. A common measure between like quantities. It is contained in each of the quantities under consideration an integral number of times. The lengths of a diagonal and a side of a square, for example, are like quantities but are incommensurable, lacking the integral common measure. An equally well known example of incommensurability are the areas of a circle and of a square constructed on the radius of the circle.

2. Commensurability is seen as a rational number expressing the ratio between quantities. Incommensurability is expressed by an irrational number.