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LESSONS

ON

ARITHMETIC ;

PRINCIPLE, AND IN PRACTICE:

FOR THR

INSTRUCTION OF YOUTH OF BOTH SEXES;

AND MORE ESPECIALLY

FOR THAT OF YOUNG MERCHANTS, TRADESMEN,

SEAMEN, MECHANICS AND FARMERS,

BY THOMAS SMITH A

2

LONDON:

PUBLISHED BY LONGMAN, REES AND CO.
AND BY SHERWOOD, GILBERT AND CO. FOR THE AUTHOR,

AND SOLD BY ALL BOOKSELLERS,

1830.

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PREFACE.

To furnish a clear and a familiar description of those Rules of Arithmetic which are generally useful, and to introduce the student 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, and, to do these in correct, as well as in intelligible English, is my chief purpose in this undertaking.

How far I have succeeded in this purpose, my readers will judge.. To enable those who are already versed in the subject, and who, therefore, cannot be induced to read more than parts of the work; to enable those persons to form a ready judgment, I would, respectfully, point out to their attention : first, the manner in which, in the Introduction, I have opened the subject; second, to the writing and the reading of Figures, as taught in Notation and Numeration; then let me beg of them to turn to the manner in which, in Addition, paragraphs 40 to 43, I have explained the principle of “ carrying” the tens; and then to the principle of “ borrowing," and of repaying, by “carrying," as practiced in Subtraction, paragraphs 49 to 58.

After these, the manner in which I have described the peculiar use, and the distinguishing character of Multiplication, in the three first paragraphs on that Rule; and then, the mode in which, in paragraphs 79 to 82, the principle on which Multiplication by the larger numbers, is carried on. These will, I hope, be found worthy of attention.

Before I entered on Compound Arithmetic, I found the next step must be, on the nature of Fractions. Will the reader, who may be desirous of forming an opinion of the Work, do me the honour to read the whole of the short chapter on this branch of the subject? and, if it would not be too much, I would further request his attention to the mode in which I have developed the principle of working on the various quantities with which it is the business of com- ' pound Arithmetic to treat.

These, or a part of these, passages, will, I flatter myself, do more than justify me, in thus urging on the attention of the Public, another Book, in addition to, or rather, with a view to supersede, the many already before it, on the subject of elementary Arithmetic.

In this work, I have, I trust, not only furnished a Book, which, according to its title, will instruct the untaught Artizan, and the lesser Tradesman, but which will, also, in no small degree, serve to relieve the Teacher from a laborious and irksome part of his duties, by enabling his pupils to acquire this branch of education, with little or no assistance from him; and which will, thereby, set both parties free, at an earlier period than usual, to pursue other, and higher branches of knowledge.

The useful, the generally useful branches of Arithmetic, are all that I here profess to teach. But, then, I hope that I do téach them, and the very principles on thich they rest ; and, that prepared by these, the learner, who may have occasion, or inclination, for higher attainments, in this art, will find his progress not a little facilitated by the easy and suficient introduction which he will obtain from this Book.

I have not thought it advisable to enlarge the Book by a great number of examples ; nor by a long array of sums, and questions. The work is intended chiefly for those who have passed the age of childhood, and who bring to the study a little power of thought. For these, I think the questions, &c. which will be found in the body of the work, will prove quite sufficient. But, as it is my wish to render it as generally useful as possible, I intend to follow up the publication with a Supplement, to consist of numerous additional and select sums, for the practice of younger pupils.

Besides a Key, as it is commonly called, or answers, to the several questions proposed in this volume, I shall insert, at the end thereof, some few tables, and other matters, not strictly connected with the subject, but so frequently useful to all parties who read and write, as to render it desirable that they should be, at all times, close at hand.

It would be affectation to conceal an opinion which I entertain, as to the merits of all the Books on this subject, in our language at least, that I have been able to lay my hands on; it would be affectation to conceal this opinion, that there is not one amongst them in which is to be found any thing like

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