Book II

, were also Pythagorean; the construction of a square equal to a given rectangle (Eucl. II. 14) is one of them, and corresponds to the solution of the pure quadratic equation _x²=ab_.

The Pythagoreans knew the properties of parallels and proved the theorem that the sum of the three angles of any triangle is equal to two right angles.

As we have seen, the Pythagorean theory of proportion, being numerical, was inadequate in that it did not apply to incommensurable magnitudes; but, with this qualification, we may say that the Pythagorean geometry covered the bulk of the subject-matter of Books I, II, IV and VI of Euclid's _Elements_. The case is less clear with regard to