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Plato appreciated the value of this faculty, and saw that it

might be quickened by the study of number and relation. All

things in which there is opposition or proportion are suggestive

of reflection. The mere impression of sense evokes no power of

thought or of mind, but when sensible objects ask to be compared

and distinguished, then philosophy begins. The science of

arithmetic first suggests such distinctions. The follow in order

the other sciences of plain and solid geometry, and of solids in

motion, one branch of which is astronomy or the harmony of the

spheres,-to this is appended the sister science of the harmony of

sounds. Plato seems also to hint at the possibility of other

applications of arithmetical or mathematical proportions, such as

we employ in chemistry and natural philosophy, such as the

Pythagoreans and even Aristotle make use of in Ethics and

Politics, e.g.