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

NEW SYSTEM

ARITHMETICK;

IN WHICH
THE RULES ARE FAMILIARLY DEMONSTRATED,

AND THE
PRINCIPLES OF THE SCIENCE

CLEARLY AND FULLY EXPLAINED,

HY SHOWING THE RELATION WHICH THE SIMPLE RULES BEAR TO EACH OTHER,

AND REDUCING THE MORE DIFFICULT PARTS BACK TO THOSE RULES,

BY WILLIAM RUGER, A. B.

NEW YORK

SOLD BX, THE PRINCIPAL BOOKSEĻLERL.

Quatertown, X. X.

KNOWLTON & RICE.

1836
For recommendations, see last page.

UNIVER
LIBRARY

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

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

$

INTRODUCTION.

A8 perfection is seldom, if ever, attained in matters of science, there is still

, a chance for improvement. And, as reason; under the hand of refinement, acquires new powers, so almost every scieuce 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. Those who have written on the subject, have left the principles of the 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 ihing 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 rales: 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 anncs 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 method 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 instructors, 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, his 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 intro- ! daced 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 accurate knowledge of these rules

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