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AN

INTRODUCTION

ΤΟ

GEOMETRY

AND THE

SCIENCE OF FORM.

PREPARED FROM THE MOST

APPROVED PRUSSIAN TEXT-BOOKS.

STEREOTYPE EDITION, CAREFULLY REVISED.

BOSTON:

JAMES MUNROE AND COMPANY.
NEW YORK: A. V. BLAKE.
PHILADELPHIA: J. W. MOORE.

1846.

Entered according to Act of Congress, in the year 1845, by

JAMES MUNROE AND COMPANY,

In the Clerk's Office of the District Court of the District of Massachusetts.

I HAVE carefully examined the manuscript of "An Introduction to Geometry" and think it admirably adapted to supply an important want in education. It is not a mere geometrical logic, but a natural and simple introduction to the Science of Form. By a beautiful and original series of inductive processes, it avoids tedious demonstrations, develops the taste for observation, which is so strong in the quick mind of youth, and leads the pupil to a real and practical knowledge of the truths of Geometry with a rapidity which would not have been anticipated. From these considerations, and from observing the strange neglect into which this science has fallen in our schools, I have strongly urged the publication of this excellent treatise, and think that its study should be insisted upon, as a valuable preliminary to a good education either at college or in business.

BENJAMIN PEIRCE,

Perkins Professor of Astronomy anɑ
Mathematics in Harvard University.

Cambridge, April 21, 1843.

Stereotyped by

GEORGE A. CURTIS;

NEW ENGLAND TYPE AND STEREOTYPE FOUNDRY.

Harvard Univ.
10:26-36

PREFACE.

Do my readers remember the fable of the contest between Nature and Education ?" Nature chose a vigorous young pine, the incipient mainmast of a man-of-war. But while she was feeding her pine with a plenty of wholesome juices, Education passed a strong rope round its top, and pulling it downwards with all her force, fastened it to the trunk of a neighboring oak. The pine labored to ascend, but not being able to surmount the obstacle, it pushed out to one side, and presently became bent like a bow. Still, such was its vigor, that its top, after descending as low as its branches, made a new shoot upwards; but its beauty and usefulness were quite destroyed."

Let the pine in this short tragedy represent those childish faculties which long to become acquainted with the actual world, and the cunning senses which wait on these faculties, and we have a true tale of the geometrical non-culture of the young.

The curiosity which speaks in children's busy eyes and hands should be to us the voice of Nature, bidding us make our beginnings early. The infant, who cannot speak, gazes earnestly and thoughtfully at the most common object, returning to it, and glancing from one part to another, as if to learn their connection. When he can walk, he goes round it, handling it, and studying it with all his senses. When he speaks, his questions are of size, form, and distance. If our answers are careless or unsatisfactory, his quick eyes and mind, not blunted by habit, detect our errors.

He loves com

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