The first line of each sum being taken from the Tutor's Expeditious Assistant, and suitably ruled for the other parts of the sum, with faint, horizontal, and perpendicular lines, forming a square, for the insertion of every figure throughout the book, by which means the pupil will have full scope for exercise in entering his own sums, by copying them from the Tutor's Expeditious Assistant; and the master will be totally relieved either from the trouble of setting them on a slate, working them to ascertain their correctness, or from the labour in any shape of preparing a ciphering-book for their entry, while he beholds the pleasing prospect of his pupils being more than usually benefitted, and their ciphering-books being neatly filled up with figures of their own making. Each rule is also elegantly headed, with ornamental writing of various hands.

Added to these peculiar advantages, the preceptor. consequently is enabled to take the charge of a hundred youths, with more comfort to himself, and time to improve them, than he would have otherwise with twenty.

To each of the tables there is given a full explanation of their origin; and the denominations and terms used in Arithmetic, are throughout curiously traced.

J. W

ΤΟ

THE LONDON EDITION.

VERY large impressions of this work having been speedily disposed of in almost every part of the United States of America, and the Author having met with the highest commendations on the subject in every town in that country, where the work has appeared, it has been his anxious wish to prepare an edition suited also to the United Kingdom of Great Britain, which is now achieved, and cheerfully presented to the Public, with full confidence that the people of so enlightened a realm will no less appreciate its merits.

This Stereotyped Edition is still very considerably improved, and every possible care taken to avoid the smallest error: every sum has been performed several times, and the whole work rendered in every respect desirable to the community at large.

Should, however, notwithstanding every exertion, the transposition of a letter, or false figure escape, it is confidently hoped, that such error will prove venia by a generous Public.

January, 1826.

J. WHITE.

The following are but a few Copies of a great variety of Commendations with which the Author was favoured in the United States of America, from Men of the first standing in Society, and of the highest mathematical acquirements.

RECOMMENDATIONS TO

WHITE'S ARITHMETICAL PUBLICATIONS.

Í have examined the Rev. Mr. White's Treatises upon Arithmetic, with attention, and consider them as highly meritorious, reflecting honour upon their author, and of incalculable advan tage to society. Whoever abbreviates human labour in ascend→ ing the hill of science, and facilitates the acquisition of useful knowledge, merits public patronage, the good wishes of his fellow men, and is entitled to a conspicuous niche in the temple of fame.

By an acquaintance merely, with the illustrations on the four first rules, in the "Practical System of Mental Arithmetic," a child, by a single day's application and instruction, will learn to calculate, with mathematical precision, the value of goods at any stipulated price, without pen, ink, pencil, or paper. The utility, therefore, of these publications, to the mechanic, the farmer, the merchafit, and teacher, is inexpressible, and, in my opinion, their merits only require to be known to be appreciated, and to ensure their introduction into all seminaries where the interests of society and the good of the rising generation are consulted.

Woodbury, 2d Sept. 1818.

WM. RAFFERTY, A. M. Pastor of the Presbyterian Church, and Principal of the Academy, Woodbury, New Jersey.

Philadelphia, Sept. 3, 1818. Sir, I have looked over your "Practical System of Mental Arithmetic," with the "Key and Appendix," together with the "Self-Instructor, or System of Practical Arithmetic," as applied to the first four rules of Arithmetic, and have great pleasure in assuring you, that I consider them to be invaluable publications. The correctness which is given to calculations-the facility with which it is performed-and the usual expenditure of time which is avoided by your mode of computation, must render them highly useful to all who have occasion to make use of Arithme tical progression.

Rev. John White.

JAMES ABERCROMBIE, D. D. Principal of the Philadelphia Academy.

Signs.

Of the Characters used in this Compendium.

Names.

+ Plus, or more, The sign of addition, as 9 + 3 are 12. Minus, or less, The sign of subtraction, as 9—3 are 6. The sign of multiplication,as 9 × 3 are 27.

{Multiplied} Multiplied into or by Divide by

= Equal to

:: Is to

The sign of division, as 9 ÷ 3 are 3.
The sign of equality, as 9 × 3 = 27.
The signs of proportionals, as

So is

*£. s. d. and q. are initials of Latin words of the same siguification, viz. Libræ, Solidi, Denarii, and Quadrantes.