Definition 1.

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 is commensurable in length with the rational straight line set out, let the whole be called a first binomial straight line;

Definition 2.

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

Definition 3.

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

Definition 4.

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

Definition 5.

If the lesser, a fifth binomial;

Definition 6.

And, if neither, a sixth binomial.

Book X Introduction - Proposition X.47 - Proposition X.48.

© 1996
D.E.Joyce
Clark University