Hence Plato is led to introduce a third term which had not hitherto entered into the scheme of his philosophy.

He had observed the use of mathematics in education; they were the best preparation for higher studies.

The subjective relation between them further suggested an objective one; although the passage from one to the other is really imaginary (Metaph.).

For metaphysical and moral philosophy has no connexion with mathematics; number and figure are the abstractions of time and space, not the expressions of purely intellectual conceptions.

When divested of metaphor, a straight line or a square has no more to do with right and justice than a crooked line with vice.