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This little book, prepared by an experienced mathematical teacher for the use of his own pupils, is based upon the prin. ciple that the best and only true education is self-education. It introduces the beginner to geometry by putting him at work on problems which will not only thoroughly familiarize his mind with geometrical ideas, but will exercise, at the same time, bis inventive and constructive faculties—a kind of mental practice of much importance, but generally neglected in our schools. These problems, which are simple at first and skillfully graded, the pupil is to solve, himself, without assist

The author prepared no key to the work, considering that any such help in getting through it would defeat its purpose.

As this little book seems well suited to accompany the 'Science Primers,” that are now appearing from time to time, it has been gotten up in the same form, and is included among the American reprints of that elementary series.



The author of this volume of exercises was the father of Herbert Spencer, the eminent philosophical thinker, and whose valuable work on Education has been translated into nearly all the languages of Europe. He cordially commends the method of the “Inventional Geometry" from both obser. vation and experience, as will be seen by the foilowing letter:

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