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AN INDEPENDENT TREATISE UPON THE
BASIS OF MENTAL ARITHMETIC,

BY

BENJAMIN GREENLEAF, A. M.,

AUTHOR OF A MATHEMATICAL SERIES.

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BOSTON:

PUBLISHED BY ROBERT S. DAVIS & CO.

PHILADELPHIA: KEYSTONE SCHOOL AND CHURCH FURNITURE CO.

NEW YORK: BAKER, PRATT, & COMPANY, 19 BOND STREET.
CHICAGO: JANSEN, MCCLURG, & COMPANY.

DUBUQUE: GROSVENOR & HARGER.

Educ 7 118.77.436


GREENLEAF'S

MATHEMATICAL SERIES.

HARVARD
UNIVERSITY
LIBRARY

A COMPLETE COURSE, ANALYTICAL, PRACTICAL, PROGRESSIVE,

AND SCIENTIFIC.

New Primary Arithmetic,
New Elementary Arithmetic,
New Practical Arithmetic,

New Elementary Algebra,
New Higher Algebra,
Elements of Geometry,
Geometry and Trigonometry.

MANUAL OF INTELLECTUAL ARITHMETIC.

SHORTER COURSE IN GEOMETRY.

ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY.

COPYRIGHT, 1877,

BY HENRY B. MAGLATHLIN.

RIVERSIDE, CAMBRIDGE:

ELECTROTYPED AND PRINTED BY

H. O. HOUGHTON AND COMPANY.

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INTRODUCTION.

RAL exercises in numbers of an inductive nature, in the estimation of sound educators, have a peculiar power in strengthening and maturing the mind.

The appreciation of mental arithmetic as a means of education has given rise to urgent demands for improved methods of teaching the science.

To meet in a degree new educational wants, this manual, based upon the works of Benjamin Greenleaf, has been prepared. Its lessons recognize the normal growth of the reasoning powers. The aim throughout has been to make the subject treated attractive and interesting; and by easy steps to advance the learner by sure progress.

Some pages of slate or blackboard work have been appended. These may be used in supplementing the oral exercises of the text, and the same form of solution be shown to apply alike to mental and written problems.

In the preparation of the present edition of this book, credit is due to J. V. Jackman for testing the copy in the schoolroom and for many valuable suggestions.

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