Definitions II
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.