MEMBER OF THE INSTITUTE AND OF THE LEGION OF HONour, and of THE ROYAL
SOCIETIES OF LONDON AND EDINBURGH, &C.

BY DAVID BREWSTER, LL. D.

FELLOW OF THE ROYAL SOCIETY OF LONDON, AND SECRETARY TO THE ROYAL SOCIETY OF
EDINBURGH, &c. &c.

REVISED AND ABRIDGED

BY CHARLES DAVIES,

PROFESSOR OF MATHEMATICS

IN THE

MILITARY ACADEMY,

AND

AUTHOR OF THE COMMON SCHOOL ARITHMETIC, DESCRIPTIVE GEOMETRY,
ELEMENTS OF SURVEYING, AND A TREATISE ON
SHADOWS AND PERSPECTIVE.

FOURTH EDITION.

NEW YORK:

PUBLISHED BY HARPER AND BROTHERS,
NO. 82 CLIFF-STREET.

Stereotyped by A. Chandler.

KE 17334

ENTERED according to the Act of Congress, in the year one thousand eight hundred and thirty-four, by CHARLES DAVIES, in the Clerk's Office of the District Court of the United States, for the Southern District of New-York.

RVARD
UNIVERSITY

LIBRARY

PREFACE

TO THE FOURTH AMERICAN EDITION.

THE Editor, in offering to the public Dr. Brewster's translation of Legendre's Geometry under its present form, is fully impressed with the responsibility he assumes in making alterations in a work of such deserved celebrity.

In the original work, as well as in the translations of Dr. Brewster and Professor Farrar, the propositions are not enunciated in general terms, but with reference to, and by the aid of, the particular diagrams used for the demonstrations. It is believed that this departure from the method of Euclid has been generally regretted. The propositions of Geometry are general truths, and as such, should be stated in general terms, and without reference to particular figures. The method of enunciating them by the aid of particular diagrams seems to have been adopted to avoid the difficulty which beginners experience in comprehending abstract propositions. But in avoiding this difficulty, and thus lessening, at first, the intellectual labour, the faculty of abstraction, which it is one of the primary objects of the study of Geometry to strengthen, remains, to a certain extent, unimproved.