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1REATISE

ON

4th Seavey.

ALGEBRA,

FOR THE USE OF

SCHOOLS AND COLLEGES.

BY

WILLIAM SMYTH, A. M.

PROFESSOR OF MATHEMATICS IN BOW1 OIN COLLEGE.

BOSTON:

SANBORN, CARTER & BAZIN.

PORTLAND:

BLAKE & CARTER.

1855.

UNIVERSITY
! LIBRARY
·46*130)

Entered according to Act of Congress, in the year 1852,

BY WILLIAM SMYTH, A. M.

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

Stereotyped by
HOBART & ROBBINS,

KAW ENGLAND TYPE AND STEREOTYPE FOUNDERY,

BOSTON.

PREFACE

THE present Treatise is composed substantially of the Elements of Alge¬ bra of the author, with such additional matter as fully to adapt it to the advanced course of mathematics now generally pursued in the American Colleges. In its preparation the object has been to give a clear view of the nature and powers of Algebra. The analytic method is uniformly pursued, and the topics are so presented as, in general, to lead the student to feel the want of a new principle before proceeding to its investigation. Thus, the work commences with the exposition of Algebra, as a concise language adapted to facilitate the processes of reasoning required in mathematical investigations. The operations of Algebra, therefore, with which most treatises begin, are not introduced until, in the use of the algebraic language in the solution of questions, the manner in which these operations arise, and the reason for them, are seen. The same general plan is pursued throughout. Much attention is paid to the Discussion of Problems and Equations, a topic of the highest importance to the clear understanding of the true nature of Algebra. A section is given on the Indeterminate Analysis, a subject not usually introduced into our text books, but of great value in itself and in its relation to Analytic Geometry. A full view is given of the General Theory of Equations, and of the method of solving Numerical Equations of any degree. The several subjects are presented in the manner found by experience best adapted to the convenience of recitations and the progress of the pupil. All needed help, it is believed, is furnished, without that diffuseness of explanation which leaves to the learner no room for the exercise of his own powers. The difficulties to be encountered are such only as pertain of necessity to the subject, and which serve to furnish a healthy stimulus to exertion and the mental discipline necessary to the successful prosecution of more advanced studies.

The work in its present form is still better adapted, it is hoped, to the use of Academies and High Schools, in which it has heretofore been extensively used. For a younger class of pupils, the Elementary Algebra of the author will be found sufficiently simple, and an easy introduction to the present work. WM SMYTH

Bowdoin College, 1853

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