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A

NEW SYSTEM

OF

A RI T H M E TIC,

ON THE

CANCELLING PLAN:

EMBRACING THE

RULES OF THREE, SINGLE AND DOUBLE, DIRECT AND INVERSE;
BARTER; LOSS AND GAIN; REDUCTION, MULTIPLICATION

AND DIVISON OF FRACTIONS ; EXCHANGE OF

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PUBLISHED BY MARSH, CAPEN & LYON.

NEW-YORK:
DANIEL APPLETON & CO.

1837.

Entered according to an Act of Congress, in the year 1837,

By CHARLES G. BURNHAM, In the Clerk's Office of the District Court of New Hampshire.

ASA M'FARLAND, PRINTER.

tele 6-18-39 34424

PREFACE.

5-20-38. HRT

The author of this Arithmetic has been engaged for some years past in the business of instruction, during a part of the time as a teacher of young ladies, and at other times as an instructor of pupils of both sexes. He has uniformly found, that there has been less interest excited in the study of Arithmetic than in most other branches of education.

In Rhetoric, Philosophy, Chemistry, Geography and History, there are many individuals in our schools who eagerly pursue their inquiries, while in Arithmetic this is rarely the case. Something may be set down to the circumstance, that the study of Arithmetic is more solitary in its character, and that the excitement is wanting that attends studies which are pursued more in classes. Arithmetic imparts fewer new ideas, and does not extend the range of thought and inquiry as much as many other intellectual pursuits. Its importance, as a mental discipline, and its practical advantages through life, are not sufficient to give interest to the scholar, and to beguile the tedium of a way that has few immediate attractions. Under such circumstances, the instructor will deem it highly important so to vary the mode of instruction as to render the study attractive, and to give that prominence to this department of education which its great importance demands.

The author of this work has labored earnestly, while in a course of instruction, to effect this object; and is satisfied, that the mode of instruction adopted in the work now offered to the public, possesses advantages in this respect over the systems of Arithmetic usually taught.

The process of abridging operations, by cancelling of numbers, has been in a few rules slightly alluded to in the systems of arithmetic now in use ; but their authors do not seem to be aware of the extent to which it might be carried, in all proportional questions. Finding that this

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