* A

PRACTICAL TREATISE

ON

ARITHMETIC,

WHEREIN

EVERY PRINCIPLE TAUGHT IS EXPLAINED IN A SIMPLE AND
OBVIOUS MANNER;

CONTAINING

NUMEROUS QUESTIONS,

AND

COMBINING THE USEFUL PROPERTIES OF FORMER WORKS,
WITH THE MODERN IMPROVEMENTS.

BEING

A COMPLETE SYSTEM.

TO WHICH IS ADDED

TWO METHODS OF BOOK-KEEPING,

WITH EXAMPLES FOR EXERCISE.

BY GEORGE LEONARD, JR.

FOURTH EDITION, STEREOTYPED,

BOSTON;

OTIS, BROADERS, AND COMPANY.

NEW YORK, ROBINSON, PRATT, & CO, AND COLLINS, KEESE, & CO.;
PHILADELPHIA, THOMAS, COWPERTHWAIT, & CO.; BALTIMORE,
CUSHING & BROTHER; CINCINNATI, E. LUCAS & CO.; LOUISVILLE,
MORTON & GRISWOLD.

1841.

Educ T 118.41.518

GEORGE ANTRUE PLINF109
JANUARY 25, 1824

Entered according to Act of Congress, in the year 1840, by
GEORGE LEONARD, Jr.,

in the Clerk's office of the District Court for the District of Massachusetts.

CAMBRIDGE;

STEREOTYPED BY

FOLSOM, WELLS, AND THURSTON.

PREFACE.

THE manner of teaching arithmetic was formerly very different from that employed at the present time. Certain arbitrary precepts or rules were stated, according to which the scholar performed the examples, remaining in entire ignorance of the propriety of his operations. Such rules are soon forgotten; no person regards them, but solves the questions that occur in business, by means of principles suggested by common sense. There seems to be an obvious improvement, then, in late works, where the scholar, in learning the science, is taught to investigate and apply those principles on which he must depend in practice.

This treatise combines the conciseness of the old system with the advantages of the new. It commences in a very simple manner, so as to be readily understood by a person of moderate capacity, having no previous knowledge of the subject. As it advances, the examples and questions are so arranged, that the scholar is led by imperceptible degrees to discover new principles. The reasons for every rule and operation are made obvious, and when explanations are necessary, great care has been taken to render them very lucid and concise.

The subjects are arranged and discussed in a more natural order than that usually adopted; for instance, even in the late improved arithmetics, Fractions are partially described in Division; Federal Money follows immediately after Division, so that many of the principles of Decimal Fractions are employed before they can be well explained