PREFACE.

THE study of Geometry trains the eye and the hand in drawing its many figures. It calls into action the reasoning faculty in mastering the demonstrations, and especially in inventing demonstrations and solutions for the theorems and problems which are left for the exercise and development of the pupil's own skill. This work demands earnest effort and the power of continuous attention. It is, hence, an excellent stimulus to those very useful traits.

In order that pupils should receive a high degree of benefit from the study, they should be incited to self-effort. The pleasure arising from victory in an attempt at original demonstration will be a powerful stimulus.

In this book, there is much work for the student besides the memorizing of definitions and axioms, and finding the road through an argument to the conclusion, with a guide constantly leading him. Sometimes the path is blazed, and the student must find his way from one mark to the next. Sometimes he must prove himself a woodsman by determining his own direction and selecting his own mode of travel. In practical life, problems refuse to confront us in a series, graded according to difficulty; and promiscuous examples may be so carefully graded as to defeat their most important end. They should, however, be fairly based on preceding principles.

When original work is called for, if there is a general failure on the part of the class, the best plan would be to pass it for the time. Very probably they will have better success with some that follow it. Let it stand as a challenge to renewed efforts.