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Mathematics in the age of Plato comprehended a very small part of

that which is now included in them; but they bore a much larger

proportion to the sum of human knowledge. They were the only

organon of thought which the human mind at that time possessed,

and the only measure by which the chaos of particulars could be

reduced to rule and order. The faculty which they trained was

naturally at war with the poetical or imaginative; and hence to

Plato, who is everywhere seeking for abstractions and trying to

get rid of the illusions of sense, nearly the whole of education

is contained in them. They seemed to have an inexhaustible

application, partly because their true limits were not yet

understood. These Plato himself is beginning to investigate;

though not aware that number and figure are mere abstractions of

sense, he recognizes that the forms used by geometry are borrowed

from the sensible world.