Given a rational straight line and a binomial, divided into its terms, such that the square on the greater term is greater than the square on the lesser by the square on a straight line commensurable in length with the greater, then, if the greater term be commensurable in length with the rational straight line set out, let the whole be called a first binomial straight line;

but if the lesser term be commensurable in length with the rational straight line set out, let the whole be called a second binomial;

and if neither of the terms be commensurable in length with the rational straight line set out, let the whole be called a third binomial.

Again, if the square on the greater term be greater than the square on the lesser by the square on a straight line incommensurable in length with the greater, then, if the greater term be commensurable in length with the rational straight line set out, let the whole be called a fourth binomial;

if the lesser, a fifth binomial;

and if neither, a sixth binomial.