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Eaton and Bradbury's Mathematical Series.

AN

ELEMENTARY

GEOMETRY.

BY

WILLIAM F. BRADBURY, A. M.,

HOPKINS MASTER IN THE CAMBRIDGE HIGH SCHOOL; Author of a TREATISE ON TRIGONOMETRY
AND SURVEYING, AND OF AN ELEMENTARY ALGEBRA.

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KE 11182

HARVARD UNIVERSITY LIBRARY 047*172

Entered according to Act of Congress, in the year 1872.

BY WILLIAM F. BRADBURY,

in the Office of the Librarian of Congress, at Washington.

UNIVERSITY PRESS: WELCH, BIGELOW, & Co.,

CAMBRIDGE.

PREFACE.

A LARGE number of the Theorems usually presented in textbooks of Geometry are unimportant in themselves and in no way connected with the subsequent Propositions. By spending too much time on things of little importance, the pupil is frequently unable to advance to those of the highest practical value. In this work, although no important Theorem has been omitted, not one has been introduced that is not necessary to the demonstration of the last Theorem of the five Books, namely, that in relation to the volume of a sphere. Thus the whole constitutes a single Theorem, without an unnecessary link in the chain of reasoning.

These five Books, including Ratio and Proportion, are presented in eighty-one Propositions, covering only seventy pages. This brevity has been attained by omitting all unconnected propositions, and adopting those definitions and demonstrations that lead by the shortest path to the desired end. At the close of each Book are Practical Questions, serving partly as a review, partly as practical applications of the principles of the Book, and partly as suggestions to the teacher. As those who have not had experience in discovering methods of demonstration have but little real acquaintance with Geometry, there have been added to each Book, for those who have the time and the ability, Theorems for original demonstration. These Exercises, with different methods of proving propositions already demon

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