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[Ruger's Arithmetick, with Questions and Answers.]

NEW SYSTEM

OF

ARITHMETICK;

IN WHICH

THE RULES ARE FAMILIARLY DEMONSTRATED,

AND THE

PRINCIPLES OF THE SCIENCE

CLEARLY AND FULLY

EXPLAINED,

BY SHEWING THE RELATION WHICH THE SIMPLE RULES BEAR TO EACH OTHER, AND REDUCING THE MORE

DIFFICULT PARTS BACK TO THOSE RULES.

Second edition.

BY WILLIAM RUGER, A. B.

cu atertown, 12. V.

PUBLISHED BY

KNOWLTON & RICE, BOOKSELLERS

1832.
[For Recommendations, see last page:]

HARVARD COL. KY

GIFT OF THE
GRADUATE SCHOOL OF EDUCATION

Ara 15 1927

Entered, on the 26th day of September, in the year 1829, according

to Act of Congress, by William Ruger, in the Clerk's Office of the District Court of the Northern District of New-York.

ject, have left the principles of the hose who have written on the sub

INTRODUCTION. AS pertoction is seldom, if ever, attamed in matters of science, there is still a chance for improvement. And, as reason under the hand of refinement, acquires new powers, so alınost every science for a century past has acquired new beauties, except that of Arithmetick, which has remained almost stationary. Even in our standard works, we find the Rules completely arbitrary, without a single reason given, why they should produce their results. Thus, a science which may properly be considered as the greatest work of human wisdom, has been left shrouded in mystery.

rules unexplained, as if they were beyond the reach of human investigation, or beneath the dignity of scientifick research. The object of the author, in this treatise, is to disperse the gloom, and represent the science in its true light, freed from all its obscurity. In this work, the principles of each rule will be found illustrated by plain demonstrations; a thing that is novel in the science of Arithmetick, yet, in the opinion of the author, it is the true and only mode by which the principles of the science can be communicated or studied to advantage. It is hardly possible for the student to retain arbitrary rules: WORDS are soon forgotten, while time is scarcely sufficient to efface PRINCIPLES from the memory.

After the Examples given under each rule, it was thought best to annex a list of questions and answers for the benefit of teachers and students, illustrating more fully the principles of the rules and the operations of the work. These are calculated to brighten the faculties of the student, and leave a lasting impression on the mind. This methol of instructing by questions and answers, is considered by many to be so important, that some of the best institutions in the Union are now conducted solely on this plan.

The author has dwelt on the Simple Rules beyond what is usual, in order to make the student thoroughly understand the principles of numbers; the relation which these rules bear to each other, and their practical application in business. He believes it will generally be allowed by instructers that most authors are so deficient in these rules, that the student passes to the more intricate parts while he is yet ignorant of the first rudiments of the science; the consequence is, bis ambition is dampened; he can see no beauty in a science in which obscurity is back of him, and impenetrable darkness before him.

Federal money being next in simplicity to whole numbers, is introduced immediately after each of the Simple Rules. This arrangement will be of great service to him who has but little time or opportunity to devote to the science, since an acurate knowledge of these rules and that Currency, will enable him to transact correctly most of the business of life. The teacher will discover that in this work, the labour of the student is greatly abridged in acquiring a knowledge of the Reduction of Currencies; for, on inspection, it will be found that many authors have given nearly or quite THIRTY RULES to perform what is here embraced in two. Most authors have given several different rules for casting INTEREST, which produce different results: neither giving the proper authority of our courts, nor deciding which rule should be followed by the student in practical business. The consequence has been, that even business men follow as many different modes of casting interest, as there are different rules in our books, the results of which are widely different; but in this work the author has observed a strict adherence to legal interest; quoting the decisions of our courts. As Commission or Factorage, Brokerage, Ensurance, and likewise Buying and Selling Stocks are depending upon the same principles with Simple Interest, they are placed under the same running title, with demonstrations as they severally occur, showing that the principles involved are the same.

The Rule of Three has, in this treatise, been so illustrated by reducing its principles back to Multiplication and Division, as to render it almost as simple as those rules. Since the Double Rule of Thrce, Practice, Single and Double Fellowship, Tare and Tret, Barter, Loss and Gain, Alligation, Discount and Annuities, belong strictly to the Single Rule of Three, they are therefore placed under the running title of that rule, and shown to depend upon the same principles, so that the student when he understands the one, may properly be said to understand the whole; because he will at once perceive that he is acquainted with all the principles on which they depend.

In short, all the rules throughout the work will be found demonstrated, not merely by examples worked out, diguified with the name of demonstrations, but by plain reasoning on numbers.

THE AUTHOR. WATERTOWN, N. Y. JULY 4, 1931.

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