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GRADUAL LESSONS

IN

ORAL AND WRITTEN

A R I T H M E TIC.

PART 1.

THOUGHT COMBINED WITH PRACTICE.

TAKE THE FIRST STEP RIGHT.

BY DAVID B. TOWER, A. M.,
AUTHOR OF “INTELLECTUAL ALGEBRA, OR ORAL EXEB-

CISES IN ALGEBRA, FOR COMMON SCHOOLS,” &c.

BOSTON:
TAPPAN, WHITTEMORE & MASON.

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IN

ORAL AND WRITTEN

A R I T H M E T I C.

PART 1.

THOUGHT COMBINED WITH PRACTICE.

TAKE THE FIRST STEP RIGHT.

BY DAVID B. TOWER, A. M.,
AUTHOR OF “INTELLECTUAL ALGEBRA, OR ORAL EXEB-

CISES IN ALGEBRA, FOR COMMON SCHOOLS," &c.

BOSTON: TAPPAN, WHITTEMORE & MASON.

POPULAR SCHOOL BOOKS, ,

PUBLISHED BY

TAPPAN, WHITTEMORE & MASON,

114 WASHINGTON STREET,

BOSTON.

Putnam's Arithmetic. THE AMERICAN COMMON SCHOOL ARITHMETIC ; in which the Principles of the Science are fully explained and applied to the Solution of a great Variety of Practical Examples. Designed for the Use of Common Schools and Academies. By Rufus PUTNAM, Principal of the Bowditch High School, Salem, Mass.

Comer's Bookkeeping. A Simple Method of keeping Books by Double Entry, without the Trouble or Formula of the Journal. By G. N. COMER, Accountant.

New Reading Books. Used in more than five hundred towns. The Series consists of, 1. RUSSELL'S PRIMER. 2. RUSSELL'S READING AND SPELLING Book. 3. INTRODUCTION TO RUSSELL'S PRIMARY READER. 4. RUSSELL'S PRIMARY READER. 5. RUSSELL'S SEQUEL TO PRIMARY READER. 6. RUSSELL AND GOLDSBURY'S INTRODUCTION TO THE AMERICAN SCHOOL READER AND SPEAKER. 7. RUSSELL AND GOLDSBURY'E AMERICAN SCHOOL READER AND SPEAKER.

Entered according to Act of Congress, in the year 1849,

BY DAVID B. TOWER,

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

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PREFACE.

From a trial, in the younger department of the author's school, of various methods of teaching numbers, experience has given a decided preference to the plan developed in this little book. The details are full, because it has been found, in actual practice, best that they should be so. Each step, which the pupil is called to take, should not only be a distinct step, but should be taken understandingly; otherwise habits of mind will result, seriously impeding true progress in other branches of study.

In the higher studies, first a proposition is announced, and then the reasoning is given which demonstrates its truth ; a fact is stated, and then the proof adduced which establishes it. The philosophy of this is not questioned, but its application has been restricted; it has seldom been duly weighed in preparing text-books for a child.

In this book, first a STATEMENT is made of a simple truth ; then the truth is illustrated by EXAMPLES, showing its application to objects; from these examples the INFERENCE is deduced of its universal application. Next, practical Questions, involving a simple process of reasoning, are asked, to exercise the understanding; then questions in numbers alone, to test the memory.

This mode of introducing a child to the study of numbers, and to a clear comprehension of their changes, has

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