This little book is constructed for the purpose of instructing large classes, and with reference to being used also by teachers who have themselves no knowledge of Geometry.

The first statement will account for the many, and perhaps seemingly needless, repetitions; and the second, for the suggestive style of some of the questions in the lessons which develop the matter contained in the review-lessons.

Attention is respectfully directed to the following points:—

First the particular, then the general. See page 25.

Why is m n g an acute angle?

What is an acute angle?

Here the attention is directed first to this particular angle; then this is taken as an example of its kind, and the idea generalized by describing the class. See also page 29.

Why are the lines e f and g h said to be parallel?

When are lines said to be parallel?

Many of the questions are intended to test the vividness of the pupil’s conception. See page 29.

Also page 78. If the circumference were divided into 360 equal parts, would each arc be large or small?

Many of the questions are intended to test the attention of the pupil.

The thing is not to be recognized by the definition; but the definition is to be a description of the thing, a description of the conception brought to the mind of the pupil by means of the name.