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ON THE

PHILOSOPHY OF ARITHMETIC

AND THE

ADAPTATION OF THAT SCIENCE

TO THE BUSINESS PURPOSES OF LIFE:

WITH NUMEROUS PROBLEMS, CURIOUS AND USEFUL, SOLVED BY VARIOUS
MODES; WITH EXPLANATIONS DESIGNED TO MAKE THE STUDY AND AP-
PLICATION OF ARITHMETIC PLEASANT AND PROFITABLE TO SUCH AS HAVE
NOT THE AID OF A TEACHER; AS WELL AS TO EXERCISE

ADVANCED CLASSES IN SCHOOLS.

BY URIAH PARKE.

FOURTH EDITION, REVISED AND IMPROVED BY THE AUTHOR.

“What

"What man has done, man may do." "I WILL TRY.”

PHILADELPHIA:
PUBLISHED BY MOSS & BROTHER.

No. 12 SOUTH FOURTH STREET.

Entered according to Act of Congress, in the year 1849,

BY URIAH PARKE,

In the Clerk's Office of the District Court of Ohio.

T. K. & P. G. COLLINS, Printers.

PREFACE.

IN presenting the following work to the public in a revised form, but few remarks are necessary by way of Introduction. Though not engaged in teaching, circumstances had forcibly impressed on the attention of the author, the necessity of some book adapted to the use of teachers and others desirous of studying the science of arithmetic, from principle, and tracing its uses in life. He examined accordingly every European and American publication that he supposed might meet the difficulty; but found none that seemed exactly to the purpose. Leslie's Philosophy of Arithmetic treats copiously on the use of counters, and the ancient modes of study, besides tracing some of the more curious properties of numbers; but there is nothing practical and life-like in it. Its scarcity, even in England, shows that it does not there meet the wants and the taste of the multitude. Barlow's Elementary Investigation of the Theory of Numbers, involves the necessity of an intimate acquaintance with Algebra; and though it is rigidly scientific in its development of the properties of numbers, and may suit the college, it is not sought for by the people either in Great Britain. or America. Finding the ground unoccupied, and believing that a book adapted to the wants of life in our country, was necessary, the present publication was put forth, and the result fully justified the author's anticipations. The first edition was sold, and the demand continuing to increase, the work has been carefully revised, and is now offered to the public with full confidence that it will be found a useful companion to the teacher, the student, and the enterprizing reader who loves investigation.

(3)

The author has not sought to elucidate all the properties of numbers, nor to pursue a rigidly systematic course; but studying the wants of those for whom he has written, he has aimed to make a book that will be useful to them; and that will foster a spirit of investigation and study, without affecting to despise the inferior attainments with which thousands must rest satisfied. He does not seek to supersede or to build up, any particular system, but to occupy general ground, heretofore unoccupied, and to be useful. Teachers are sometimes found, that seem greatly at a loss in seeking to explain the principles of what they teach; for to know, and to be able to tell clearly what we know, are two things, not always found together; and if a teacher were learned as a NEWTON or a LARDNER, it would not benefit his pupils, unless he could communicate his knowledge. It is hoped that this book will be found to suggest some desirable modes of explanation. LOCKE says truly, “It is one thing to think right, and another thing to know the right way to lay our thoughts before others with advantage and clearness, be they right or wrong."

To the thousands of young men in our country, who are without the aid of living teachers, and yet desire to study this subject thoroughly, we trust the book before them will prove an assistant, no less valuable than to the teacher or the pupil in the school room.

If found acceptable to his countrymen, the author will have his reward.

ZANESVILLE, OHIO, September, 1848.

URIAH PARKE,

It affords me pleasure to say that in the process of revision, I have been materially indebted to the assistance of Dr. SAMUEL C. MENDENHALL, a gentleman intimately acquainted with the science of Mathematics; and who has asked no living teacher for instruction in that branch of knowledge. To IMRI RICHARDS, Esq., also my thanks are due for valuable

assistance.

TABLE OF CONTENTS,

Every science has its object. Quantity and magnitude.
Natural and Artificial unit. Difficulties attending first effort
to number. Independent names not practicable. Adoption
of a base or radix. Why ten was adopted. Twelve
would have been better. Other radices. Hebrew, Greek
and Roman Notation. Decimal Fractions first treated of in
1582. Value of figures according to place. Carrying ex-
plained. How present system was adopted from grooves and
counters. Aught-Naught. Numeration-Difficulty of com-
prehending very large numbers. Punishment of the Wan-
dering Jew. Grouping at Madagascar. Numeration Table.

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