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AN ALGEBRA

UPON THE

INDUCTIVE METHOD OF INSTRUCTION,

BY JOHN H. HARNEY, A. M.
PROFESSOR OF MATHEMATICS IN THE LOUISVILLE COLLEGE,

THIRD EDITION.

LOUISVILLE:

PUBLISHED BY MORTON & GRISWOLD.

HARVARD
UNIVERSITY
LIBRARY

Entered according to Act of Congress, in the year 1840,

BY JOHN H. HARNEY, In the Clerk's Office for the District Court of Kentucky.

Stereotyped by J. A. James,
No. 1 Baker Street,

Cincinnati.

PREFACE.

No apology need be offered for an attempt to simplify a science now so generally studied as that of Algebra.

The following treatise commences with a series of introductory lessons, the questions in which are intended to be solved, without algebraic signs or the use of slate and pencil, in order that the learner may become familiar with the use of a letter to represent the unknown quantity in the solution of a question, without having his attention diverted by any thing else which is entirely new to him. This we consider very important. As algebra is commonly taught, the student must consider not only the questions, but the meaning of the algebraic signs; and in the attempt to write down the solution of the question, in which every mark with the pencil requires some mental effort, he forgets the rationale of the process altogether. This difficulty, which is a very formidable one, especially to the younger class of students, is, we think, entirely obviated by the method, we have given. When the signs +,=;--, are introduced, a number of questions are given, with the solution of which, the student is already familiar; so that he can give his principal attention to the meaning and use of the signs. The questions are so arranged that the solution of each one will lead to the solution of the succeeding one; and every principle is illustrated by a number of examples; so that the learner may be perfectly familiar with it before he leaves it. It is believed that the progress of students in this work will be uncommonly easy and interesting ; although there is not a more thorough treatise in use in our schools and colleges.

The second part of the work consists, mainly, of practical questions arranged to correspond, as nearly as possible, with the first. It will sometimes be useful, especially with the younger classes of students, to take the examples in the second part along with the corresponding portions of the first. This

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