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PROGRESSIVE

PRACTICAL ARITHMETIC;

CONTAINING

THE THEORY OF NUMBERS, IN CONNECTION WITH CONCISE
ANALYTIC 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.,
AUTHOR OF THE TABLE-BOOK, PRIMARY AND INTELLECTUAL ARITHMETICS,

RUDIMENTS, AND THE “SHORTER COURSE."

IVISON, BLAKEMAN, TAYLOR & CO.,
NEW YORK AND CHICAGO.

ROBINSON'S

Mathematical Series.

Graded to the wants of Primary, Intermediate, Grammar,

Normal, and High Schools, Academies, and Colleges,

Progressive Table Book.
Progressive Primary Arithmetic.
Progressive Intellectual Arithmetic.
Rudiinents of Written Arithmetic.
JUNIOR-CLASS ARITHMETIC, Oral and Written. NEW.
Progressive Practical Arithmetic.
Key to Practical Arithmetic.
Progressive Higher Arithmetic,
Key to Higher Arithmetic.
New Elementary Algebra.
Key to New Elementary Algebra.
New University Algebra.
Key to New University Algebra.
New Geometry and Trigonometry. In one yol
Geometry, Plane and Solid. In separate vol.
Trigonometry, Plavo and Spherical. In separate vol.
New Analytical Geometry and Conic Sections.
New Surveying and Navigation.
New Differential and Integral Calculus.
University Astronomy--Descriptive and Physical.
Key to Geometry and Trigonometry, Analytical Geometry and Conic Seco

tiops, Surro, ing and Navigation.

Entered, according to Act of Congress, in the year 1858, 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.

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PREFACE,

PROGR

ROGRESS 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 ; brerity and perspicuity of rules; and in the very large number of examples prepared and arranged with special reference to their practical utility, and their adaptation to the real business of active life. The

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