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FORMING A COMPLETE TREATISE ON ARITHMETICAL SCIENCE,

AND ITS COMMERCIAL AND BUSINESS APPLICATIONS.

EDITED BY

DANIEL W. FISH, A.M.,
EDITOR OF ROBINSON'S PROGRESSIVE SERIES OF ARITHMETICS,

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.
Rudiments 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 vol. Geometry, Plane and Solid. In separate vol. Trigonometry, Plane 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 Trig., Analyt. Geometry

and Conic Sect., Surveying and Navigation.

Copyright, 1860, 1863, & 1875, DANIEL W. Fish.

Electrotyped by Suite MEDOCIETE 2 Beekman St., N. Y.

tane 11, 1928

KURAL
Exefrouge Fordham lunar

PREFACE.

THIS work is intended to complete a well graded and progressive series of Arithmetics, and to furnish to advanced students a more full and comprehensive text-book on the Science of Numbers than has before been published; a work that shall embrace those subjects necessary to give the pupil a thoroughiy practical and scientific, arithmetical education, either for the farm, the workshop, or a profession, or for the more difficult operations of the countingroom and of mercantile and commercial life.

There are two general methods of presenting the elements of arithmetical science, the Synthetic and the Analytic. Comparison enters into every operation, from the simplest combination of numbers to the most complicated problems in the Higher Mathematics. Analysis first generalizes a subject and then develops the particulars of which it consists; Synthesis first presents particulars, from which, by easy and progressive steps, the pupil is led to a general and comprehensive view of the subject. Analysis separates truths and properties into their elements or first principles ; Synthesis constructs general principles from particular cases. Analysis appeals more to the reason, and cultivates the desire to search for first principles, and to understand the reason for every process rather than to know the rule. Hence, the leading method in an elementary course of instruction should be the Synthetic, while in an advanced course it should be the Analytic.

The following characteristics of a first class text-book will be obvious to all who examine this work: the typogra

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