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AN EXTENSIVE COLLECTION OF PRACTICAL QUESTIONS
ON THE GENERAL PRINCIPLES OF ARITHMETIC.

AUTHOR OF THE

CONTAINING

Concise and Original Methods of Solution,

WHICH SIMPLIFY MANY OF THE MOST IMPORTANT RULES
WRITTEN ARITHMETIC.

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WITH

JOHN F. STODDARD, A. M.,

BY

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NEW YORK:

SHELDON & COMPANY,

No. 8 MURRAY STREET.

STODDARD'S SERIES OF ARITHMETICS.

STODDARD'S JUVENILE MENTAL ARITHMETIC......

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SHORT COURSE.

STODDARD'S PRIMARY PICTORIAL ARITHMETIC

COMBINATION SCHOOL

COMPLETE

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OLNEY'S INTRODUCTION TO ALGEBRA.

66

INTELLECTUAL

RUDIMENTS OF

NEW PRACTICAL

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COMPLETE SCHOOL

UNIVERSITY

TEST EXAMPLES IN

GEOMETRY...

TRIGONOMETRY

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OLNEY'S HIGHER MATHEMATICS.

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CALCULUS.

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GEOMETRY AND TRIGONOMETRY, School Edition.

66

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66

University Ed

.........

Entered, according to Act of Congress, in the year 1849, by
JOHN F. STODDARD,

In the Clerk's Office of the District Court of the United States for the Southern District of New York.

Re-entered, according to Act of Congress, in the year 1866, by
SHELDON & COMPANY,

I the Clerk's Office of the District Court of the United States for the Southern District of New York.

GIFT OF THE

GRADUATE SCHOOL OF EDUCATION

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16 19

PREFACE.

HAVING felt the necessity of a more extended and systematic Intellectual Arithmetic for younger, as well as more advanced pupils, I prepared and used in manuscript, in my own school, for a number of years, such a series of questions as I deemed best adapted to the purpose. After observing the superior mental training derived from their use, and the ease with which pupils thus trained comprehended the more advanced branches of mathematics, I venture to submit them to the public in the following pages, hoping that they may prove as useful to other schools as they have to my own.

The rule which I have observed in preparing this work is: Tell but one thing at a time, and that in its proper place.

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Although in many particulars the work differs from other "Mental" Arithmetics, as an examination of the “ questions will show, mention of these differences is omitted, and the following exposition of its arrangements of subjects is presented.

Chapters First, Second, Third, and Fourth, from Lesson I to Lesson XV, treat respectively of Addition, Subtraction, Multiplication, and Division of simple numbers; each of which is rendered familiar by an extensive collection of practical questions. Lesson VII consists of questions which combine Addition and Subtraction; Lesson IX, of questions combining Addition, Sabtraction, and Multiplication; Lesson XIII, of questions combining the twelve previous Lessons; and Lesson XIV, of questions in Proportion. Thus, an intimate connection between Lessons and even Chapters is kept up through the entire work, with the exception of Chapter Fifth, Lesson XIV to Lesson XXVII, which contains some of the most important Tables of Weights and Measures; each of which is illustrated with appropriate questions.

Chapter Sixth, from Lesson XXVI to Lesson XLVI, is devoted to the subject of Fractions, in which twenty lessons are many original combinations of numbers and concise analyses.

Chapter Seventh, from Lesson XLVI to Lesson LIX, consists of practical and intricate questions of various kinds, which require for their solution a thorough knowledge of the preced

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