HARVARD COLLEGE LIBRARY

GIFT OF

GEORGE ARTHUR PLIMPTON
JANUARY 25, 1924

Copyright, 1887, by J. B. LIPPINCOtt Company.

B. LIPPINCOTTIS

STEREOTYPERSANDPRINTERS

武 COMPANY:

PREFACE.

IN preparing this edition of Chauvenet's Geometry I have endeavored to compel the student to think and to reason for himself, and I have tried to emphasize the fact that he should not merely learn to understand and demonstrate a few set propositions, but that he should acquire the power of grasping and proving any simple geometrical truth that may be set before him; and this power, it must be remembered, can never be gained by memorizing demonstrations. Systematic practice in devising proofs of new propositions is indispensable.

On this account the demonstrations of the main propositions, which at first are full and complete, are gradually more and more condensed, until at last they are sometimes reduced to mere hints, by the aid of which the full proof is to be developed; and numerous additional theorems and problems are constantly given as exercises for practice in original work.

A syllabus, containing the axioms, the postulates, and the captions of the main theorems and corollaries, has been added to aid student and teacher in reviews and examinations, and to make the preparation of new proofs more easy and definite.

In the order of the propositions I have departed considerably from the larger Chauvenet's Geometry, with the double object of simplifying the demonstrations and of giving the student, as soon as possible, the few theorems which are the tools with which he must most frequently work in geometrical investigation.

Teachers are strongly advised to require as full and formal proofs of the corollaries and exercises as of the main propositions, and to lay much stress upon written demonstrations, which should be arranged as in the illustrations given at the end of Book I.

In preparing a written exercise, or in passing a written examination, the student should have the syllabus before him, and may then conveniently refer to the propositions by number. In oral recitation, however, he should quote the full captions of the theorems on which he bases his proof.

CAMBRIDGE, MASS., 1887.

W. E. BYERLY.