INCOMMENSURABLE

, Lines, or Numbers, or Quantities in general, are such as have no common measure, or no line, number, or quantity of the same kind, that will measure or divide them both without a remainder. Thus, the numbers 15 and 16 are Incommensurable, because, though 15 can be measured by 3 and 5, and 16 by 2, 4, and 8, there is yet no single number that will divide or measure them both.

Euclid demonstrates (prop. 117, lib. 10) that the side of a square and its diagonal are Incommensurable to each other. And Pappus, prop. 17, lib. 4, speaks of Incommensurable angles.

Incommensurable in Power, is said of quantities whose 2d powers, or squares, are Incommensurable. As √2 and √3, whose squares are 2 and 3, which are Incommensurable. It is commonly supposed that the diameter and circumference of a circle are Incommensurable to each other; at least their commensurability has never been proved. And Dr. Barrow surmises even that they are insinitely Incommensurable, or that all possible powers of them are Incommensurable.

INCOMPOSITE Numbers, are the same with those called by Euclid prime numbers, being such as are not composed by the multiplication together of other numbers. As 3, 5, 7, 11, &c.|