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E XPLANATORY

ARITHMETICK,

NUMBER ONE;

CONTAINING MENTAL, THEORETICAL, AND PRACTICAL EXERCISES,
IN THE FUNDAMENTAL RULES OF ARITHMETICK, VIZ :

NUMERATION, ADDITION, SUBSTRACTION,

MULTIPLICATION, AND DIVISION

IN WHICH

THE PRINCIPLES OF EACH RULE ARE FULLY AND PAMILIARLY EXPRESSED ;
AND THE REASONS FOR EVERY OPERATION ON THE SLATE
MINUTELY AND CLEARLY EXPLAINED; AND ADAPTED
TO THE UNDERSTANDING AND USE OF SMALL

CHILDREN, IN FAMILIES AND SCHOOLS.

BY LYMAN COBB,

AUTHOR OF THE SPELLING-BOOK, SCHOOL DICTIONARY, JUVENILL

READERS, SEQUEL, AND EXPOSITOR.

NEW YORK:
PUBLISHED BY HARPER & BROTHERS,

82 CLIFF-STREET.

1834.

D. #..!7/79

("Entered according to Act of Congress in the year 1832, by LYMAN COBB, in the Clerk's Office of the District Court of the United States for the Southern District of New York."]

PREFACE.

THE Author of the following treatise is fully sensible, that in offering a new work to the publick there is a degree of assuming confidence necessarily implied, more particularly if others have written on the same subject. He is also aware, that every community experiences the important advantages arising from a useful education of the individuals who compose it; and that, therefore, he who offers any thing which has a tendency to promote this great object, or facilitate the means of acquiring it, has some claim to attention.

The Author has, from his own observation and experience, long since been convinced that, among the many introductory books to the useful science of Arithmetick, no one, or at least none with which he is acquainted, is sufficiently adapted to the capacities of children, and to the occasions of common life. Some are too abstruse for young beginners, while others are deficient in such examples as point out the application of the several rules to transactions of real business.

In presenting a new System of Arithmetick to the publick, some account of its plan and execution will, of course, be expected.

The Author of this work has endeavoured to furnish a clear and familiar description of the rules of Arithmetick, and to introduce the learner to this pleasing and very valuable art, by gradually unfolding to him the modes of practice, and the principles on which the several rules proceed, in plain and intelligible language; and in order to render the rules still morc clear and familiar to the learner, and also to encourage him, the first question in each rule is worked at full length, so that he is led forward in a gradual manner, both by precept and example; and is, it is conceived, more fully convinced of the truth of the rules, and the propriety of each operation.

In this work the Table belonging to each rule is first given, that the scholar may learn the nature of the rule before he is questioned respecting it, or has sums given him for exercise.

PREFACE.

06-30-36 viel

XB 2 ?

Hist. of sci. Lyman 6-26-36

iii 32.490

Examples for mental exercise are then given to awaken his reasoning powers, and thus prepare him to engage in each rule theoretically. The rule is then given in questions and answers, as this form, the Author believes, is better calculated to illustrate the rule, and to impress it on the mind of the pupil. Examples are then given for theoretical exercise on a slate, and one or more of these examples is worked out, and every operation fully and minutely explained. The remaining examples, not worked out, are for the exercise of the learner, until he shall become thoroughly acquainted with the theory of each rule. Immediately after these, are examples for practical exercise, consisting of a variety of miscellaneous questions, in which will be found much useful information.

Most children, it is believed, experience some disgust in passing through the fundamental, or first five rules of Arithmetick, occasioned, no doubt, by the fewness of examples, and by the want of interest in those that are given. “An Arithmetick should not consist, as is most generally the case, merely of an assemblage of rules and examples without EXPLANATION; so that the learner, after having committed them to memory, and learned to perform Arithmetical calculations mechanically, will leave the study totally ignorant of the principles upon which the rules are founded. Þupils are always desirous of knowing the reasons why any Arithmetical operation is performed; and if the nature and principles of the subject are clearly explained, and the rule rendered intelligible by the Author, the scholar may be able to acquire a knowledge of it without much aid from the teacher. The study would then be pleasant, and he would pursue it with delight and profit.

The rules which the scholar should commit to memory are in the largest type used in the work. The examples, explanations, and exercises, are in a type of a smaller size; and the notes intended for the teacher are in the smallest type. The EXPLANATIONS should be thoroughly and carefully read by the scholar.

The learner should be questioned as often as once in each day respecting the principles upon which the rules are founded; and the teacher should not permit him to commence a new sum, or engage in a new rule, until he is fully and thoroughly acquainted with the principles of the rule in which he has been working. Young scholars are generally anxious to make rapid progress. This propensity, however laudable, should not be indulged at the expense of a partial knowledge of the subject.

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