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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.

The figurative association was mistaken for a real one; and thus

the three latter divisions of the Platonic proportion were

constructed.