PROGRESSIVE

PRACTICAL ARITHMETIC,

CONTAINING

THE THEORY OF NUMBERS, IN CONNECTION WITII CONCISE ANALYTIO
AND SYNTHETIC METHODS OF SOLUTION, AND DESIGNED

AS A COMPLETE TEXT-BOOK ON THIS SCIENCE,

FOR

COMMON SCHOOLS AND ACADEMIES

BY

DANIEL W. FISH, A.M.,

AND

AUTHOR OF TED TABLE-BOOK, PRIMABY AND INTELLEOTUAL ARITHMBTIO

BUDDENTS.

NEW YORK:
IVISON, BLAKEMAN, TAYLOR, & COMPANY,

EducT118.71.402

ROBINSON'S

Series of Mathematics,

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

MATHEMATICAL TEXT-BOOKS ever ossued in this country.

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,
Kiddle's New Elementary Astronomy,
Robinson's University Astronomy,
Robinson's Mathematical Operations,
Robinson's Key to Geometry and Trigonometry, Conic

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 Office of the District Court of the United States, for the Northern

District of New York,

HARVARD COLLEGE LIBRARY

GIFT OF THE
NEWTON FEFE !!SZARY

AUG 9 10 11

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)