This is very strikingly the case with Geometry.

The class study the definitions, and the teacher supposes they fully understand them; in fact, they do _understand_ them, but the name and the thing are so feebly connected in their minds that a direct effort and a short pause are necessary to recall the idea when they hear or see the word.

When they come on, therefore, to the demonstrations, which in themselves would be difficult enough, they have double duty to perform.

The words used do not readily suggest the idea, and the connection of the ideas requires careful study.

Under this double burden many a young geometrician sinks discouraged.
A class should go on slowly, and dwell on details so long as to fix firmly and make perfectly familiar whatever they undertake to learn.