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AN

ELEMENTARY

INTELLECTUAL ARITHMETIC,

CONTAINING NUMEROUS

ORIGINAL CONTRACTIONS

MULTIPLICATION.

BY

DANIEL LEACH AND ROBERT SWAN.

BOSTON:
HICKLING, SWAN & BROWN.

1855.

042*22

Enterel according to Act of Congress, in the year 1858,

BY DANIEL LEACII & ROBERT SWAN, In the Clerk's Office of the District Court of the District of Massachusetts

STEREOTYPED BY

HOBART & ROBBINS,
KEW ENGLAND TYPE AND STEREOTYPE FOUNDRY

DOSTON

PREFACE.

In the preparation of this work, two objects have been constantly in view :- one was to prepare such gradual exercises for the pupils as are adapted to secure the most perfect intellectual training ; the other was to develop and clearly unfold the principles that are usually found in written arithmetic, - so that, at the same time that •the pupil is going through a thorough mental training, he is acquiring a clear knowledge of principles to be applied more fully afterwards.

While the work is especially designed to be studied before commencing written arithmetic, it is intended to be reviewed and studied by the pupil during his whole course; and, if so used, it will lead him more easily to comprehend principles, and will greatly facilitate his application of them.

The contractions in multiplication, if made perfectly familiar both in their extent and application, will enable the pupil to abridge very materially nearly one half of the usual business processes in multiplica tion. These abridged processes can be applied with a very great saving in time and labor, in computing interest and other usual counting-room calculations.

The contractions, which are limited in their application, if they have but little practical value, will serve as excellent exercises for mental training

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