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PROGRESSIVE

PRACTICAL ARITHMETIC,

CONTAINING

THE THEORY OF NUMBERS, IN CONNECTION WITH CONCISE ANALYTIC AND SYNTHETIC METIIODS OF SOLUTION, AND DESIGNED

AS A COMPLETE TEXT-BOOK ON THIS SCIENCE,

FOR

COMMON SCHOOLS AND ACADEMIES.

BY

DANIEL W. FISH, A.M.,

AUTHOR OF THE TABLE-BOOK, PBIMARY AND INTELLEOTUAL ARITHMETIOL, AND

RUDIMENTS.

NEW YORK :
IVISON, PHINNEY, BLAKEMAN & CO.
PHILADELPHIA : J. B, LIPPINCOTT & CO.
CHICAGO: S. C. GRIGGS & CO.

1868.

HARVAL Cuilige Librant

Y Exitinct duc T 118.68.400

JAN 8 1937
ROBINSON'S

Series of Mathematics,

The most COMPLETE, most PRACTICAL, and most SCIENTIFIC SERIES of

MATHEMATICAL TEXT-BOOKS ever zssued in this country.

(IN TWENTY-TWO VOLUMES.)

Robinson's Progressive Table Book,
Robinson's Progressive Primary Arithmetic,-
Robinson's Progressive Intellectual Arithmetic,
Robinson's Rudiments of Written Arithmetic,
Robinson's Progressive Practical Arithmetic,
Robinson's Key to Practical Arithmetic, -
Robinson's Progressive Higher Arithmetic,
Robinson's Key to Higher Arithmetic,
Robinson's Arithmetical Examples,
Robinson's New Elementary Algebra,
Robinson's Key to Elementary Algebra, -
Robinson's University Algebra,
Robinson's Key to University Algebra,
Robinson's New University Algebra,
Robinson's Key to New University Algebra, .
Robinson's New Geometry and Trigonometry,
Robinson's Surveying and Navigation,
Robinson's Analyt. Geometry and Conic Sections,
Robinson's Differen. and Int. Calculus, (in preparation,).
Robinson's Elementary Astronomy,
Robinson's University Astronomy,
Robinson's Mathematical Operations,
Robinson's Key to Geometry and Trigonometry, Conio

Sections and Analytical Geometry,

Entered, according to Act of Congress, in the year 1858, by
II ORATIO N. ROBINSON, LL.D.,

and again in the year 1863, by

DANIEL W. FISH, A.M.,
In the Clerk's Ofice of the District Court of the United States, for the Northern

District of New York.

PREFACE.

PROGRESS and improvement characterize almost every art and science; and within the last few years the science of Arithmetic has received many important additions and improvements, which have appeared from time to time successively in the different treatises published upon this subject.

In the preparation of this work it has been the author's aim to combine, and to present in one harmonious whole, all these modern improvements, as well as to introduce some new methods and practical operations not found in other works of the same grade; in short, to present the subject of Arithmetic to the pupil more as a science than an art; to teach him methods of thought, and how to reason, rather than what to do; to give unity, system, and practical utility to the science and art of computation.

The author believes that both teacher and pupil should have the privilege, as well as the benefit, of performing at least a part of the thinking and the labor necessary to the study of Arithmetic; hence the present work has not been encumbered with the multiplicity of " notes,” "suggestions,” and superfluous operations so common to most Practical Arithmetics of the present day, and which prevent the cultivation of that self-reliance, that clearness of thought, and that vigor of intellect, which always characterize the truly educated mind.

The author claims for this treatise improvement upon, if not superiority over, others of the kind in the following particulars, viz. : In the mechanical and typographical style of the work; the open and attractive page; the progressive and scientific arrangement of the subjects ; clearness and conciseness of definitions ; fullness and accuracy in the new and improved methods of operations and analyses ; brevity and perspicuity of rules ; and in the very large number of

(iii)

examples prepared and arranged with special reference to their practical utility, and their adaptution to the real business of active life. The answers to a part of the examples have been omitted, that the learner may acquire the discipline resulting from verifying the operations.

Particular attention is invited to improvements in the subjects of Common Divisors, Multiples, Fractions, Percentage, Interest, Proportion, Analysis, Alligation, and the Roots, as it is believed these articles contain some practical features not common to other authors upon these subjects.

The improvements in Percentage made necessary by the financial changes of the last few years are especially noticable. The different kinds of United States' Securities, Bonds, and Treasury Notes are described, and their comparative value in commercial transactions illustrated by practical examples. The difference between Gold and Currency, and the corresponding difference in prices, exhibited in trade, are taught and illustrated, and many other things that every commercial student and business man ought to know and understand.

There has also been added a full and practical presentation of the Metric System of Weights and Measures, containing many new and original improvements in the arrangement, notation, and applications, not before presented to the public, and which greatly simplify and adapt the system to general use.

It is not claimed that this is a perfect work, for perfection is impossible; but no effort has been spared to present clear, scientific, comprehensive, and complete system, sufficiently full for the business man and the scholar; not encumbered with unnecessary theories, and yet combining and systematizing real improvements of a practical and useful nature. How nearly this end has been attained the intelligent and experienced teacher and educator must determine.

THE AUTHOR.

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