Still the exercise of the faculty of abstraction apart from facts has enlarged the mind, and played a great part in the education of the human race.
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.