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THE PRINCIPLES OF THE SCIENCE ARE FULLY
EXPLAINED, AND APPLIED TO THE SOLU-

TION OF A GREAT VARIETY OF

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PRINCIPAL OF THE BOWDITCH (ENGLISH HIGH) SCHOOL, SALEM, MASS.

BOSTON:
TAPPAN, WHITTEMORE & MASON.

1849.

Edware". +8.44.13.

18063

G
Eine weiteres

Cambridge

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

RUFUS PUTNAM,
In the Clerk's Office of the District Court of the District of Massachusetts.

STEREOTYPED BY
HOBART & ROBBINS;
NEW ENGLAND TYPE AND STEREOTYPE FOUNDERY,

BOSTON.

PREFACE.

“What are the peculiarities of the work?” “In what respects does it differ from books on this subject already in use?” are among the first questions propounded to the publisher who attempts to introduce a new school-book to a community already surfeited with textbooks in the various departments of science.

To these and similar questions, it may be replied, that while the present work is, in many respects, like its predecessors, it differs from most of them in some important particulars, among which are the following

1. In the great variety and amount of Arithmetical matter in a comparatively small compass.

2. In its practical character. 3. In treating of Integral and Fractional Decimals in connection.

4. In the number and variety of mental and oral exercises interspersed through the book, in connection with exercises for the slate.

5. In embracing the details of the science under general principles, and avoiding, as much as practicable, a multiplicity of specific rules.

A few remarks will illustrate the object and extent of these peculiarities.

1. The number of exercises for the pupil, and the amount and variety of arithmetical matter, is much greater than from the size of the book would seem possible. For example, the pupil is directed to “ Multiply 56789 by 2; by 4; by 5; by 6; by ; by 8; by 9;" and to * Divide 30654016 by 13; by 14 ; by 15; by 16; by 17; by 18; by 19 ;" — and, in Fractions, to divide mentally 5ý by 2 ; by 3; 4; 5; 6; 7; 8; 9;- and to “Compute the interest on $1418.46 from Jan. 15, 1841, to Nov. 25, 1846 ; from Dec. 14, 1845, to May 6, 1848; from July 4, 1776, to March 23, 1781; from Aug. 25, 1837, to Nov. 16, 1848,” &c. Thus, without embarrassing the pupil, exercises are embraced in a single line, which might easily be made to occupy, and which, in most books, are made to occupy, several times as much space. By this means, a great number of mental and oral, as well as written exercises, of practical importance is introduced, without making the size and expense of the book greater than of those books from which such matter is excluded.

2. While the author has aimed to make the work strictly elementary, to lead the pupil to analyze and demonstrate, as far as possible, every important principle, and to present every topic in the manner which his experience has suggested as best adapted to the capacities of the learners, as well as best fitted to develop their mental powers, he has kept in view the maxim that “ Children should be taught those things while young which they are to practise when they become men.

The modes of computing time between different dates, (Art. 69,) Discount, Accounts Current and Interest Accounts, and many other topics, though different from what the learner is taught in some text

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